approche multi-modèle pour les systèmes à evènements...

179

Upload: others

Post on 03-Jul-2020

8 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

������������� ��������� �����������������

��������

!#"$"&%('*),+&-/. 0&1325476�. '*8&9:1;-<"='>0?%@13-�ACB D?A�259�E -�AGFHJI�K�L -�E - L 2MAONP4;A5)Q%(-R2MATSVUW"$"$134�)RUX2543' L F 1;U Y>-�A�2543' L 8&-�A

E '*8$-�AG8&-[Z\' L )]254;' L$L -�E - L 2

^ ���;����`_��������;acb��`_d,egfh��_jik_jl�_m�mbc_jin���ob�pq����mrts;iu����s���v� ^�^ puinwxl���������Wd�y����

^ ��l�����z�_�����in�{ }|�~����X ��X ��X���q�� ���~

� s;��pu�X���xs;_����jbcpu� � � pu��s3_j�����iuw�l��c� � pu��s3_j���_j�;s7����iuw�l��c�o��l�_�����bc_jinwxl��r ^ �;s�i�bcpuin_�� ����l�_�����bc_jinwxl��Xfh����l��_j��in��pnpu�

^ b��

� � { ����/�J���������

rt��lt_j����l��Wpu�����  m��s��;�¡z¢���������������3acb��`_mpub*£������*iu�in���?��e¤�3¥�b��*���X�

¦¨§M©�ª

«���b��t¬­d®��l�iu�¯�°²±v±vf­°²± ³,���´µ�����l�� ±mb ^�^ ����_j�;l��«���b��¶³,in�������°²dMdM·R¸ ³,���´µ�����l�� ±mb ^�^ ����_j�;l��¹V��l�_jb ^ �ob*�º·X»�±v°²d5¯t�,¼�½ ³,���´µ�����l��� ��ins�±R»m¼:¼�°²� ³,���´µ�����l��� ��ins��mf­°²d ³,���´µ�����l��  �iu���s;_���l��d5b�l�����`_m³,f � ¼�±��v£ ¹Vbc¾u_����X���>£�����´µ�;���;��s��;  �iu���s;_���l��

¿MÀ`Á5ÂxÃ�À�ÄÅÂtÆuÃ�Ç�ÈÊÉÌË>Í¢ÄÅÂtÎÏÀ�Ä3ÆuÐÑꢂ Ò7ÓqȨÍqÔ7ÄÅÃÕÆuÇcÖ�ÖuÇ ÈqÇ׿,ÉØÒ7Ù×ÚÑËGȨÇ�¿5ÛtÂtÓ

Page 2: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 3: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

����������� ��������������� � �

� ������� !�#" $ �&%�'�(#)��"

*,+ -/.1032�4657-98�0�+;:�<=+�<�.�>@?�A B�C

D -9>E-F2�AG?IHJ>K.9- B�L

MONQP�©SR=TM§VU,PXWYR7N Z/[Z \]R7NQP�©S^7_Y`�aVb�©dcÕ§�aK`x©Xe�WYcfWJR7NT�`/chg�i�j k=Z

�mlk� � ^�^ ���xs7���W��yx�ob��*iuw�l��nl]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol ����mlk�mlk� rx_j�l�s;_�l����Ws��;�`_j�jbcpuiu��� lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol ���

�mlk�mln�,ln� fh�`_j���x��l�s3_jin��� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol ����mlk�mln�,l � d®� ^ ���xs������ lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol �,q�mlk�mln�,lrq d®�Wl ^ ���axin���l�� l]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol �c��mlk�mln�,lg� £�����s;� ^ _m����s����`_��ts�pub�z�iupnin_�� lol]lplol]lolol]lol]lolol]lplol]lol ����mlk�mln�,l � � _jl����W��e¤l��Ïyx_tu��*� lolol]lol]lplol]lolol]lol]lolol]lplol]lol �,v

�mlk�ml � rx_j�l�s;_�l����;m�*�x��l�p�bciu���m�;_v���;s����`_��jb�pniu��;�wl]lplol]lolol]lol]lolol]lplol]lol �mx�mlk�ml �/ln� fh�`_j���x��l�s3_jin��� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol �mx�mlk�ml �/l � °(¥�in_�����s;�>����l ^ �;�axiu��l��yl]lol]lplol]lolol]lol]lolol]lplol]lol �,z�mlk�ml �/lrq · ^ _jin�×b�pnin_�� lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol �,{

�mlk�ml|q rx_j�l�s;_�l����W��in���jbc��s7��inwxl�� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�q���mlk�mlrq9ln� fh�`_j���x��l�s3_jin��� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�q���mlk�mlrq9l � ¹V�x����pniujb\_jiu���?���� ^ ��ts;�����;}lol]lplol]lolol]lol]lolol]lplol]lol�q���mlk�mlrq9lrq rxyx�`_j�1u;������Ws;���`_j�~s�pu�;l��� l]lol]lplol]lolol]lol]lolol]lplol]lol�q`��mlk�mlrq9lg� £�����iu_jb���s;�>��in����b���s7��inw�l���l]lol]lplol]lolol]lol]lolol]lplol]lol�qmq

�mlk�ml¤� rx_j�l�s;_�l����W��in���jbc��s7��inwxl��X��iu�_j��inz�l��;� l]lol]lplol]lolol]lol]lolol]lplol]lol�q���mlk�ml � £�����s;pul�iu����l]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�q`�

�ml � � ^�^ ���xs7���W_jbc_jinwxl���l]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�qmv�ml �9lk� ��l�_�����bc_j�;v�3_ ^ ���;��ius�bc_j�lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�qmv

�ml �9ln�,ln� ��l�_�����bc_j�;:s�p�bc��inw�l����lolol]lol]lplol]lolol]lol]lolol]lplol]lol�qmv�ml �9ln�,l � ��l�_�����bc_j�;:��iu�;�jb��s7��iuw�l��;dl]lol]lplol]lolol]lol]lolol]lplol]lol�q�x

Page 4: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� �1���������@�y�������������@�

�,l �9l � ±������b�lt¥Ï���W³M�;_j�i lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�qm{�ml �9l �9ln� � ^�^ ���xs7����vs��;�`_j�jbcpuiu���;}lol]lplol]lolol]lol]lololololol]lol]lol�qm{�ml �9l �9l � � ^�^ ���xs7����v���;s����`_��jb�pniu��;���l]lplol]lolol]lol]lololololol]lol]lol �`�

�ml|q £�����s�pnl��in��� lolol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol ���

k � `9cIPSWYR7N T�`/c�� R=T�`9c�T�`�� R7NVU,PXWYR7N�N�`�� `/NQP ���9lk� ¹Ï�t���;����X´µ����s;_�iu���������*���`_v�;_mrt��³ lolol]lol]lplol]lolol]lol]lololololol]lol]lol ���

�/ln�mlk� d®��W°]¹ ¹V� lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol ����/ln�ml � � ^�^ ���xs7���W��iu�;�jb��s7��iuw�l��X�3_�bcz�_��jb�s3_jiu��� lol]lolol]lol]lololololol]lol]lol ��v�/ln�ml|q £�����s;� ^ _m����p�b¡���s;��� �o��l��jbc_�iu���$����p�b ^ b��_�iu�X� ^ ����bc_jika��&lolololol]lol]lol ��z�/ln�ml¤� ¹V�3_j���x����pn����iu�X£��Xr�³¢��f�¹ l]lolol]lol]lplol]lolol]lol]lololololol]lol]lol ��{�/ln�ml � rxyx�`_j�1u;��>����pu��inR�����l���a��;iupupub���s;� lol]lplol]lolol]lol]lololololol]lol]lol ���

�9l � ¹Ï�t���;����X´µ����s;_�iu���������*���`_v�;_mr�°²  b�lÏd5�mf�l]lplol]lolol]lol]lololololol]lol]lol �c��/l �9lk� ¹V�x�1u�pn�X�����l���a��;iupupub���s;� lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol �c��/l �9l � � ^�^ ���xs7���W��iu�;�jb��s7��iuw�l�� lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol �mx

�9l|q ¹Ï�t���;����X´µ����s;_�iu���������*���`_Õ�¢r�£ �;_�r� �½ l]lol]lplol]lolol]lol]lololololol]lol]lol �,{�/lrq�lk� � ^�^ ���xs7���W���pn���$pu�;vr� º½ l]lolol]lol]lplol]lolol]lol]lololololol]lol]lol �,{�/lrq�l � � ^�^ ���xs7���W���pn���$pu�;:yx_tu��*���s;���`_jin�xl��lol]lolol]lol]lololololol]lol]lol�v��

�9l|q�l �9ln� £����*�¡l�_jbc_jin���?��in����s3_j� l]lol]lplol]lolol]lol]lololololol]lol]lol�v���/lrq�l|q £����*�¡l�_jbc_jin���&iu����iu���;s;_�� lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�vmq

�9l¤� £�����s�pnl��in��� lolol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�v��� W _Jb N#T�` _���� Pfb�P T�`y_�� b�©XP ���

�G0E-/.1A��6.10�� 0��/8 -�8�0�+ ��L

M NQPÕ© R�Tʧ�U,PSWJRQN � [� �ha�aÊ©SR=U ��`�� §V_ PSW"!#� R=T%$/_J` & Z

q�lk� fh�`_����x��l�s;_�iu���nlol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol xt�q�l � £Rbcv���W����lt¥Ï�*�t����:���X´µ����s3_jin�������;���;��_ lol]lplol]lolol]lol]lololololol]lol]lol x,q

q9l �9lk�  ��'�o��in_�iu���� ^ ���;puiu�*iu��b�iu��� l]lolol]lol]lplol]lolol]lol]lololololol]lol]lol x,qq9l �9l � £����*�¡l�_jbc_jin���&��l$���x�1u;pu�

G1

bclV�*�t��u�pu�G2

lol]lol]lololololol]lol]lol x,vq9l �9l|q £����*�¡l�_jbc_jin���&��l$���x�1u;pu�

G2

bclV�*�t��u�pu�G1

lol]lol]lololololol]lol]lol�z��q9l �9l¤�  ��'�o��in_�iu���$s;��� ^ p u;_��X��� Gi,et

lol]lol]lplol]lolol]lol]lololololol]lol]lol�z`�q9l �9l � °(¥t��� ^ pu����egb ^�^ pnius�bc_jin��� lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�zmq

q�l �9l �9ln� ¹V�x���������*iu�obcp l]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�z��q�l �9l �9l � ¹V�x�����������jb���� lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�z`�

Page 5: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

����������� ��������������� � q

q�l �9l �/lrq £����*�¡l�_7b\_jiu���&�����*iu�ob�p→��������b���� lolol]lol]lolol]lplol]lol�z�x

q�l �9l �/lg� £����*�¡l�_7b\_jiu���&��������b����→�����*iu�ob�p lolol]lol]lolol]lplol]lol�zmz

q�l �9l �/l � £Rb���,�op e¤�;_jbc_�������� ^ b��_v���_ qd,0

lplol]lolol]lol]lolol]lplol]lol�zm{q�l �9l �/lrv £Rb�m���op e¤�;_jbc_�������� ^ b��_v���_ qd,2

lplol]lolol]lol]lolol]lplol]lol�{��q�l|q £Rb�����;������b�p��

n���x����wlolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�{��

q�l|q�lk� fh�`_j���x��l�s3_jin���#lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�{��q�l|q�l � � ^�^ ���xs7���>��l�pn_�ik¬h�*�x�1u�pn�v�������;�jb�pniu��;� lol]lplol]lolol]lol]lolol]lplol]lol�{��q�l|q�l|q ¯o������b�puinjbc_�iu���*��lÏ���;sÕb���iu��*�X����s������¡lt_7bc_�iu��� lol]lol]lolol]lplol]lol�{mqq�l|q�l¤�  �� ����in_�iu���$s���� ^ p u;_��X��� Gi,et

l]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�{`�q�l|q�l � °(¥��;� ^ pu����egb ^�^ pniusÕb\_jiu��� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�{mv

q�l|q�l �/ln� ³,�������`_7b\_jiu��� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�{mvq�l|q�l �/l �

I = {n}lololololol]lol]lolol]lolpl]lol]lolol]lol]lololololol]l�{mz

q�l|q�l �/lrqI = {d1, d2}

lplol]lolol]lol]lololololol]lol]lolol]lol]lplol]lol�{m{q�l|q�l �/lg�

I = {d3}lol]lplol]lolol]lol]lololololol]lol]lolol]lol]lplol]lol����`�

q�l¤� £�����s�pul��iu��� lpl]lolol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol������� gqª�NQP � $/c ` T�` UmR7NQP�©S^7_Y`x§5© c Z�� &

�1lk� fh�`_j��t��l�s;_�iu���nl]lolol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�����x�1l � °(¥tiu�_j����s��W�;_vl���ins�in_��X��e¤l��Vl ^ ���axin���l�� ^ bc�:���x����lplol]lolol]lol]lolol]lplol]lol����mz

�1l �9lk� ¹Viu�����Ï�in_�lobc_�iu��� lol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol����mz�1l �9l � ¼:�������tu��*� l]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol����m{�1l �9l|q  ����*�����_j��bc_jin��� lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol������

�1l �9lrq9ln� °(¥t_�����iu���V��l ^ ���xs��;��� Gi

l]lol]lplol]lolol]lol]lolol]lplol]lol�������1l �9lrq9l �  ��;_������in�obc_jin���&��lÏp�b����`b����º�����in���

Klolol]lol]lolol]lplol]lol���� �

�1l �9lrq9lrq °(¥�in_�����s;�>��e¤l��Ï�l ^ ����axiu��;l��vl���iuw�l�� Si,et

l]lol]lolol]lplol]lol����Xq�1l �9lrq9lg� ·ºz���;�acbc_jin��� ^ b���_jiu�;pupn�Flolol]lol]lplol]lolol]lol]lolol]lplol]lol����Xq�1l �9lrq9l � � wxl�inacb�pu�;��s������;�s�������in_jin����

1lolololol]lol]lolol]lol]lplol]lol�����

�1l �9lrq9lrv � wxl�inacb�pu�;��s������;�s�������in_jin����2lolololol]lol]lolol]lol]lplol]lol���� �

�1l|q »v�V�*�t��u�pu������ ^ ��s�i �osÕb\_jiu��� ^ b������x���;lolol]lol]lplol]lolol]lol]lolol]lplol]lol����Sx�1l|q�lk� � _7bc_v������� ^ b��_v��lÏ�*�t�1u;pu�º����� ^ ��s;i �os�bc_jin���� Ej

lol]lol]lolol]lplol]lol����Xz�1l|q�l � � _7bc_v�������3_j��l��:��lV ^ �;s�i �osÕbc_�iu��� Ei

l]lol]lplol]lolol]lol]lolol]lplol]lol�� ����1l|q�l|q °(¥��;� ^ pu����egb ^�^ pniusÕb\_jiu��� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�� �t�

�1l|q�lrq9ln� ¹V�x�1u�pn��������Ï�;_�������l� lolol]lol]lplol]lolol]lol]lolol]lplol]lol�� �t��1l|q�lrq9l � £������_j��l�s;_jin���Ï���

Ed,et

lolol]lol]lplol]lolol]lol]lolol]lplol]lol�� �t��1l|q�lrq9lrq £������_j��l�s;_jin���Ï���

En,et

lolol]lol]lplol]lolol]lol]lolol]lplol]lol�� �c��1l|q�lrq9lg� £���� ^ b��jbciu����$b�a���sWp egb ^�^ ��ts7���Ws;���`_j��b�puin��;� lol]lolol]lplol]lol�� ���

�1l¤� ������i �osÕb\_jiu���Ï���Ws;���`_j�~s�p�b�z�iupuik_j�v�;_v�����x¬hz�pn�ts�b���� l]lplol]lolol]lol]lolol]lplol]lol�� �,z�1l � £�����s�pul��iu��� lpl]lolol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Xq��

Page 6: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� �1���������@�y�������������@�

� �ha�a _YWYUmb�PSWJRQN bo§ Umb ch\��hg i�j Z�����9lk� fh�`_����x��l�s;_�iu���nlol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Xqmq�9l � ³,�����;�`_7bc_�iu���Ï����p e¤�3¥t��� ^ pn� lol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Xqmq

�/l �9lk�  ��;�s��i ^ _�iu���$��lÏyx�_ u��*� lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Xqmq�/l �9l �  ��;�×b��s7���W��eg�3_jl���� lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Xq`�

�9l|q � _jb ^ � �,���*�x���X�����*iu�obcp¨�����Ï�;_�������l lol]lol]lplol]lolol]lol]lololololol]lol]lol��Xqmv�/lrq�lk� ³,���xs��;���>��b����pu�X�*�t���º�����*iu�obcp

Gn

l]lplol]lolol]lol]lololololol]lol]lol��Xqmv�/lrq�l � r ^ ��s;i �os�bc_jin����:��l���x���X������in�ob�p En

lplol]lolol]lol]lololololol]lol]lol��Xqmv�/lrq�l|q �º�;��i �osÕbc_�iu���&���Wpub�s����`_j�~s�p�bcz�iupnin_j� lol]lplol]lolol]lol]lololololol]lol]lol��Xqmz

�9l¤� � _jb ^ �>�����*�x���X�������jb����������V�3_j������l lol]lol]lplol]lolol]lol]lololololol]lol]lol��Xqm{�/lg�1lk� ³,���xs��;���>��b����pu�X�*�t���º�������jb����

Gd

l]lplol]lolol]lol]lololololol]lol]lol��Xqm{�/lg�1l � r ^ ��s;i �os�bc_jin����:��l���x���X���;���jbc��� Ed

lplol]lolol]lol]lololololol]lol]lol��Õ�`��/lg�1l|q �º�;��i �osÕbc_�iu���&���Wpub�s����`_j�~s�p�bcz�iupnin_j� lol]lplol]lolol]lol]lololololol]lol]lol��Õ���

�9l � � _jb ^ �oqR� ^ ���xs�������v�;_j�;����l�nlol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Õ����/l �9lk� ��pk_j�;���ob���s�����lÏ���x���X�����*iu��b�p¢a����mpn�X���x���X���;���jb���� lolololol]lol]lol��Õ����/l �9l � ¹V�x�1u�pn�X�;_�������l

Gd,et

l]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Õ����/l �9l|q ��pk_j�;���ob���s�����lÏ���x���X���;���jb�����a����mpn�º���x���X������in�ob�p lolololol]lol]lol��Õ����/l �9l¤� ¹V�x�1u�pn�X��l ^ ���xs��;���>�3_j�;����l Gn,et

lol]lplol]lolol]lol]lololololol]lol]lol��Õ����9l|v � _jb ^ ���:�� ^ �;s�i �osÕbc_�iu����v�3_vs����`_j�~s�pu�;l���:�3_j�;����l� l]lolol]lol]lololololol]lol]lol��Õ���

�/lrv�lk� r ^ ��s;i �os�bc_jin���$�;_j�;����l��W����*�t���X��������b���� Ed,et

l]lol]lololololol]lol]lol��Õ����/lrv�l � £����`_j�~s�pu�;l��:�;_�������l¶���Ï�*�t���X��������b����

Cd,et

lolol]lol]lololololol]lol]lol��� x�/lrv�l|q r ^ ��s;i �os�bc_jin���$�;_j�;����l�� En,et

lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Õ� x�/lrv�l¤� £����`_j�~s�pu�;l��:�;_�������l¶���Ï�*�t���X������in�ob�p

Cn,et

lolol]lol]lololololol]lol]lol��Õ��z�9lrx £�����s�pnl��in��� lolol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Õ��{

� 0@+65 ?�4 �/8�0�+ B��EC

� �&§=PXR � b�PX`/c�`�P P � �/RÑ© WJ` T�`9c�_Jb N�� b�� `/c Z��&�]ln���ml�_j���×bc_����lolol]lol]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�� �mx

�]ln�,ln� ��lt_j����bc_j�;:���;_������in��iu�_j�� l]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�� �mx� lk�mlk�mlk�  ��'�o��in_�iu���� l]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�� �mx� lk�mlk�ml � ³,���x��l�ik_�yx��s7��������W�;_vs���� ^ ���ik_jiu��� ^ b���b�pup u�pu�ololololol]lol]lol�� �,z

�]ln�,l � ��lt_j����bc_j�;:��������;_������in��iu�_j�� l]lol]lplol]lolol]lol]lololololol]lol]lol�� �,{�]l �/d5b����`b����;v�����l�puiu�;��@l]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�� �,{

�]l �/ln�  ��'�o��in_�iu�����l]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�� �,{�]l �/l � · ^ �;�jbc_�iu����:�l���pu�;:p�b����`b����; lol]lol]lplol]lolol]lol]lololololol]lol]lol��Xv��

Page 7: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

����������� ��������������� � �

� � $ �7_Y`�T�� �?© T�`/N Z����\ �d_ �7RÑ© W P � � `�T�`��V§ � b�© Z����

Page 8: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

v �1���������@�y�������������@�

Page 9: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

����������� ��� �����V���@� x

� ������� !�#" ���!)��#"

�mlk� ¯o����s3_jin�������;���;��_��;�Vz¢��l�s;pu�º´µ�;���*������l ^ ���xs��;����s����`_j�~s�pu� ^ b���pu�ºl ^ �;�axiu��l�� l ����ml � £����`_��ts�pn� ^ b����l ^ ����axiu�in���$����s;���`_j��b�puin��;��lolol]lol]lplol]lolol]lol]lolol]lplol]lol �mx�ml|q rx_���l�s3_jl���>���Wl ^ ���axin�iu���Ï��iu����b���s7��iuw�l�� lolol]lol]lplol]lolol]lol]lolol]lplol]lol�q���ml¤� �ml�_j����bc_��X���>¹V�t�������

Gl, θ � �3_����x�1u�pn�X��lÏ��ina��Õb�l$�ob�lt_m�;w�l�inacb�pn���`_ Gh

lol]lol�q`��ml � °(¥t��� ^ pu����e¤�;_jbc_j ^ bc�_j�;�ob�in�����lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�qmq�ml|v rx_���l�s3_jl���>���Ws;���`_j�~s�pu� ^ bc�:�l ^ ����atin�in���V��iu����b���s7��iuw�l��X��in_j�iuz�l���� lolol]lplol]lol�q���mlrx °(¥t��� ^ pu����e¤l��Vb�l�_����×b\_j�º��in����b���s7��inw�l�� lolol]lol]lplol]lolol]lol]lolol]lplol]lol�qmz�ml|z °(¥t��� ^ pu�������yt�`_��1u�� ^ b���±��o³��3_�_j���;����in�X����v���;��iu�����lolol]lol]lolol]lplol]lol �`��ml|{ rx_���l�s3_jl���>��iu_���inz�l����X���Ws;���`_j�~s�pu� l]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol ���

�9lk� d®��W°]¹ ¹Ï� ��l�in���º��e � _jl����>���>¹V�x���;m���>¹¶bc��s7���;m�3_m�¨eg�m���� 3_j lol]lplol]lol ��v�9l � rx_���l�s3_jl���>��iu����b���s7��iuw�l��X�;_v�~s�pu�X��lÏ���;_jin�����obciu��� lplol]lolol]lol]lolol]lplol]lol � x�9l|q ³Êb���b����W����p e¤�;_7b\_vb�s;_�l���p

Ea

��p e¤�;_jbc_���z���;s;_jik´Eo

lplol]lolol]lol]lolol]lplol]lol ��z�9l¤� fh�`_j�;���jb\_jiu���Ï���Wpub������_jiu���Ï��������x���; l]lolol]lol]lplol]lolol]lol]lolol]lplol]lol ��{�9l � °(¥t��� ^ pu�������*�t��u�pu������s���� ^ ��jb��`_���lÏs�in��s�l�in_mr�±�f lol]lolol]lol]lolol]lplol]lol �t��9l|v ±�� ^ ������`_7bc_�iu���Ï��e¤l��Ï���x��l�pn�º���W�l���a���inpupub���s��Ŭhs;������b������ l]lol]lolol]lplol]lol �,q�9lrx  ��;�×bc��s7��� ^ ��� ^ ����� ^ ��l��:p�b��yt�`_��1u�������pu��iuR����l��a���iupnp�b���s�� l]lolol]lplol]lol �c��9l|z rx_���l�s3_jl����bc��� ^ _���������p�b¡l��a���iupnp�b���s�� � p�b¡s�������b������Ŭhl ^ �;�axiuiu���&������in�ob�pn� l ����9l|{ °(¥t��� ^ pu�������*�t��u�pu�;:����s���� ^ �����bc_j�;l����;_������l ^ �;�axiu��l���l]lol]lolol]lplol]lol �,v�9lk����rx_���l�s3_jl���>���Ws;���`_j�~s�pu��bÕa��;s>s;�t������in�obc_j�;l��:iu�`_�����¬ ���x���; lolol]lol]lolol]lplol]lol �,z�9lk���T°(¥t��� ^ pu�������*�t��u�pu�;:�����l ^ ����axiu��;l���v�;_v��lÏs��x�����iu�ob\_j��l��dl]lol]lolol]lplol]lol �,{�9lk� � �m��s7��ik_j��s3_jl���>��l�pn_�ik¬hs;���`_j�~s�pu�;l�� lol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�v���9lk�Xq�rts7������b*��� ^ �iu��s;i ^ �X����p�b¡s;������b������X�¡l�pn_�ik¬ s����`_j�~s�pu�;l�� lol]lol]lolol]lplol]lol�v���9lk�Õ�Jrx_���l�s3_jl���>��l�pn_�ik¬h�����l�p�bc_���l��QbÕa���s>b�s;s����*���x�obc_�iu��� lol]lolol]lol]lolol]lplol]lol�v`��9lk� � £����*�¡l�_jbc_jin��� ^ b��:s;���`_j�~s�pu�;l��:��ius���;_�l]lolol]lol]lplol]lolol]lol]lolol]lplol]lol�v`��9lk�Xv�rx_���l�s3_jl���>��l�pn_�ik¬hs;���*�×b������m����l�����ob�pn� ^ ��l��:pu����yt�_ u;���;�� ��d�����r�� lol]lol�vmqq�lk� ±������l��s��;�s������¡l������b�lx¥$���x���;vi¨�;_�� lol]lol]lplol]lolol]lol]lolol]lplol]lol x��q�l � rx_���l�s3_jl���>��l�pn_�ik¬h�*�x�1u�pn�v��b����pu�Xs�b����������lt¥Ï�*�x����:���X´µ����s;_jin�������;���;�`_ l]lol xc�

Page 10: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

z �����������@��� ��� ���6�@�

q�l|q £Rbc�ob�p®��e¤iu��´µ������bc_jin���π1,2

���`_j��Wpn��:�*�t��u�pu�;:���� ^ ��ts;�����; G1,et

�;_G2,et

lol]lol x,vq�l¤� ³Êb��_�in_�iu���&����p e b�p ^ �ob�z¢�;_ Σ1

lol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol xmxq�l � °(¥t��� ^ pn�W�¨e b ^�^ puinsÕbc_�iu��� l]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol x,zq�l|v £Rbc�ob�p®��e¤iu��´µ������bc_jin���

π2,1

lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�z��q�lrx r�yt�_ u;���W�×bc�xlt´ b�s;_�l���in��� �¡_j���iu:��b�s7��in����:�3_v_j�xs � iu�`_������*����i�b�in��� lolol]lol]lol�z��q�l|z ¹Ï�t�1u;pu�;mbcl�_j����bc_���:���;v��b�s7��in����

M1

�M2

�3_M3

lolol]lol]lololololol]lol]lol�z`�q�l|{ ¹Ï�t�1u;pu�

Gn

��lÏ���x���º������in�ob�p7l]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�z`�q�lk����¹Ï�t�1u;pu�X�3_j������l

Gn,et

_���� ^ ���jb�in���º��lÏ�*�t���X������in�ob�p�lol]lol]lololololol]lol]lol�zmvq�lk����¹Ï�t�1u;pu�

Gd

��lÏ�*�t���X��������b���� l]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�zmvq�lk� � ¹Ï�t�1u;pu�X�3_j������l

Gd,et

��lV�*�x���º���;���jb���� l]lol]lplol]lolol]lol]lololololol]lol]lol�zm{q�lk�Xq�¹Ï�t�1u;pu�X�3_j������l

Gn,et

��lV�*�t���X�����*iu�ob�p�lol]lplol]lolol]lol]lololololol]lol]lol�{��q�lk�Õ� � s7�obc������v��e¤iu��´µ������bc_jin���������s��;��b�iu��� ��pub¡�����_jiu���Ï����v���x����Flolololol]lol]lol�{`�q�lk� � £������¡lt_7bc_�iu���?�;�`_j���Wpu�;:���x�1u;pu��:���� ^ ���xs��;���� lol]lolol]lol]lololololol]lol]lol�{mqq�lk�Xv�r�yt�_ u;���W�×bc�xlt´ b�s;_�l���in��� ��w�lobc_������×bcs7��iu���;��;_v_��ts � in�`_j������;��i�bciu��� lol]lol]lol�{mvq�lk�Sx ¹Ï�t�1u;pu�;mbcl�_j����bc_���:���;v��b�s7��in����

Mi

�i ∈ {1,2,3,4} � lolol]lol]lplol]lolol]lol�{mv

q�lk�Xz d®�;v��i��q�����;�`_j��vs������¡lt_7bc_�iu���� ^ ���inz�pu�; lol]lplol]lolol]lol]lololololol]lol]lol�{�xq�lk�X{ ³,�iu����;�Vs;�����in������bc_jin���&���;ms;������l�_7bc_�iu����

n → d1

�;_n → d2

lolololol]lol]lol������q�l ��� ³,�iu����;�Vs;�����in������bc_jin���&���;ms;������l�_7bc_�iu����

d1 → n�;_

d1 → d3

lololol]lol]lol����`�q�l �t�T³,�iu����;�Vs;�����in������bc_jin���&���;ms;������l�_7bc_�iu����

d1 → n�;_

d1 → d3

lololol]lol]lol����mqq�l ��� ¹Ï�t�1u;pu�;v�3_j�;����l�vs���� ^ pn�;_j:���� ^ ���xs��;���� lol]lplol]lolol]lol]lololololol]lol]lol�������1lk� �m��s7��ik_j�;s;_jl��������Ws����*�×bc����� ^ �� ^ ����;� l]lol]lplol]lolol]lol]lololololol]lol]lol����mz�1l � d®� ^ ���z�p u;��������yx�`_j�1u;��¡����s;���`_j�ts�pu��l�� lol]lplol]lolol]lol]lololololol]lol]lol����m{�1l|q �ml�_j���×bc_�� ^ �����;�ob��`_m����lt¥&�;_7b\_j�������� ^ b��_ lplol]lolol]lol]lololololol]lol]lol�������1l¤� ¹Ï�t�1u;pu��b�lt_j����bc_j�X�����$�;_j�;����l

Gi

l]lolol]lol]lplol]lolol]lol]lololololol]lol]lol���� ��1l � ¹Ï�t�1u;pu��b�lt_j����bc_j�X�3_j�;����l

Gj,et

lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol���� ��1l|v

Gi,et

s;��l ^ pn�Wb�a���sWpu�Xl ^ �;�axiu��l�� Si

axi�b�p�b¡´µ����s;_jin���&��� ^ �� ���s3_jiu��� Pl]lol]lol����Xq

�1lrx ¹Ï�t�1u;pu�;v�����$�;_j�;����l�m��l ^ ���xs��;���W�;_v����� ^ �;s�i ��sÕbc_�iu���� lol]lololololol]lol]lol�� ����1l|z ³,��ts;�����W�;_� ^ �;s�i ��sÕbc_�iu������3_j������l�v��lV�*�x���º���;���jb���� l]lol]lololololol]lol]lol�� �,q�1l|{ £�����_��ts�pn��l��:�3_j�;����l¶��lV�*�t���X��������b���� lol]lol]lplol]lolol]lol]lololololol]lol]lol�� �,v�1lk����¹Ï�t�1u;pu�;v�3_j�;����l�v��lÏ���x���X�����*iu��b�pq�3_v��������b���� l]lolol]lol]lololololol]lol]lol�� �,v�1lk����£�����_��ts�pn��l��:�3_j�;����l¶��lV�*�t���X�����*iu�ob�p l]lol]lplol]lolol]lol]lololololol]lol]lol�� �mx�1lk� � ¹Ï�t�1u;pu�X��pn��zob�p¨��l ^ ���xs��;��� lol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol�� �mx�1lk�Xq�¹Ï�t�1u;pu�;v����� ^ ��s;i �os�bc_jin���� lol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Xq���9lk� £Qyxs;pu����� ^ ��in����;_v������� ^ ���� lol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Xq���9l �  m����b���s7��� ^ �� ^ ������&lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lololololol]lol]lol��Xq`��9l|q ¹Ï�t�1u;pu�;v��������;����l���s;�����b����pu�X�*�t���X�����*iu�ob�p l]lolol]lol]lololololol]lol]lol��Xq�x

Page 11: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

����������� ��� �����V���@� {

�9l¤� ¹V�x�1u;pu��������V�3_j������l�v����� ^ ��s;i �os�bc_jin����������*iu��b�pu�;!l]lolol]lol]lolol]lplol]lol��Xqmz�9l � £����`_��ts�pn��l�����l$�*�t���X������in�ob�pKlplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Xqm{�9l|v ¹V�x�1u;pu���;_�������lÏ��l$a��;��iu�Ï�����i��;���`_7b�p=lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Xqm{�9lrx �ml�_j����bc_��

Gd

��lV�*�x���X�������jb���� l]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Õ�`��9l|z ¹V�x�1u;pu������;m ^ �;s�i �osÕbc_�iu����:��lV�*�x���X�������jb���� l]lplol]lolol]lol]lolol]lplol]lol��Õ�`��9l|{ r ^ ��s;i �os�bc_jin���$��pu��zob�pu�m��lÏ���x���X���;���jb���� lol]lol]lplol]lolol]lol]lolol]lplol]lol��Õ����9lk����£Rb���b�p®��e¤iu��´µ����×b\_jiu���

πn,d

lol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Õ����9lk���T±�� ^ ������`_7bc_�iu��� ^ b���_jin��pupn�º��l$�*�t�1u;pu�X�3_j������lV��lV�*�t���X��������b���� lolol]lplol]lol��Õ����9lk� � £����*�¡l�_jbc_jin���&��lÏ���x���º������in�ob�p¢a����mpn�X���x���X���;���jbc���lol]lol]lolol]lplol]lol��Õ����9lk�Xq�r ^ ��s;i �os�bc_jin���$�;_�������l��>�;�V�*�t���X��������b�����lol]lol]lplol]lolol]lol]lolol]lplol]lol��Õ� x�9lk�Õ��±�� ^ ������`_7bc_�iu��� ^ b���_jin��pupn�º��l$s�����_��ts�pn��l����3_j������lV��lV�*�t���X��������b���� l]lplol]lol��Õ��z�9lk� � £����`_��ts�pn��l����;_�������lV��lÏ�*�t���X������in�ob�p lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Õ��{��lk�/�ml�_j����bc_��X��l ^ ���xs������ G

lol]lplol]lolol]lol]lololololol]lol]lolol]lol]lplol]lol��Xv��£�lk� £��ob\¾�������� ^ ��t��l�s;_jin��� l]lolol]lplol]lol]lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Xv�x£�l � �ml�_j����bc_��

G��� ^ ���;����`_jb��`_�pn�Xs���� ^ ���_j�;���;�`_���lV�yx_ u;��� l]lolol]lol]lplol]lol��Xv�x

£�l|q �ml�_j����bc_��S���� ^ ��s;i �os�bc_jin���$��lÏ_j�xs � lolol]lol]lplol]lolol]lol]lolol]lplol]lol��Xv�x

£�l¤� �ml�_j����bc_��Xs�������� ^ �����ob��`_�b�l ^ ���x��l�ik_:��� G�;_

Slololol]lol]lolol]lol]lplol]lol��Xv�x

£�l � � _7b\_j�iu�`_j�;����ik_j{M1A21, M1M21}

lolol]lol]lololololol]lol]lolol]lol]lplol]lol��Xvmz£�l|v �ml�_j����bc_���b���ts;iu�Wb�l$p�b����`b����

SupC(K)lolol]lolpl]lol]lolol]lol]lololololol]l��Xvmz

Page 12: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 13: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� %�)�� �� %�'�� � �� � � )y�����

Page 14: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 15: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� �V���3 ����������� ������� ����� �Xq

d5bW_��������iu�v��l×s;���`_j�~s�pu� ^ b��]�l ^ ����axiu�in���?bW�;_���iu��in_jin����b�l×����z�lt_R���;Rb��������� z�� ^ b��Qpn��²_j��b\¬acb�lt¥X���]±mb���b������,�;_ � �����ob����¤±��nz`��� �µ����l�Ml�_jinpuin����������¨e b�inpupn��l������;��l�pui u�����*���`_5pu��_������*�²���_��������iu��±vb���b������Ŭ�� �����ob�� ��l _j���;����in��±�� ^ ��l�� ^ b���pn���,����pubX_���������iu����l*s�����_��ts�pn� ^ b��²�l ^ �;��¬axiuiu��� � l �Rb����Rl������;�s�����s�� ^ _j,�in� ^ pu����Wp eg�3_7bc_Ê�;_,p eg�3a��;�����*���`_��W�;pupn�Q;egin���s;��in_(�obc_�l����;pupu�;���;�`_�obc��,pu�:s�b�����������p eg�3_jl����:����Qrxyx_tu��*�� � � a������;���;��_�� miu�s;���3_j � r�°²  � �;_²�;_Qb ^�^ puiuw�l��;� �Xl��������b�������acb��iu�;_�� �����yx_ u;���;>_���puWw�l��*pu����yt�_ u;���;¡��� ^ ���x��l�s3_jiu������pu�;>�yx_ u;���;����*���;_jin�����l _j��b �os��5pn��Wyx_tu��*���pn����in_jinw�l���;�®pu�� ^ ���_j�xs���pu�������s����*�¡l���iusÕb\_jiu�����¨�3_js,l(rt��� ���iu��in�ob�puik_j��;_���� ^ ��� ^ �����¡l��Ts�b�����×´µ�����*��p ^ �����*�;__7b��`_�p e¤�;_jl����?��� ^ ����z�p u��*���� s�p�bc��inw�l���¡�;��b�l�_��c¬��bc_jinw�l��?s�����_�iu��l��$��b�iu�b ^�^ puinw�l��� ius;i �=p egb�l�_����×b\_jiuw�l�����ius��~u;_j��� _j�;pu�w�l��$p�b=yx�`_j��u���V���_��jb ��;s;_j��iu���;���yx�obc��inwxl�����tp�b�a����i �os�bc_jin���×��� ^ ��� ^ ��in�;_j�;R���ms����`_j�~s�p�bcz�iupnin_j�c�`��egbc_�_���iu���ob�z�inpuin_��:��l��e¤��z�����a�bcz�iupnin_j� lt£��� ^ b���_jius;l�p�bc��in_���]���`_ ^ �;���*iuQl��&���;a���pn� ^�^ ���*���`_viu� ^ ����_7b��`_Q���Xs��3_�_��º_j���;�c¬�iu����� ^ l�iu ^ pul�Q����axiu���c_�bc�� lt ��v�����¡z����lt¥*_��jbÕacb�lt¥*���`_�b�iu��i ^ b���_jius;i ^ � �Ws;�����3a���pn� ^�^ ���*���`_^ bc�ºp�b ^ ��iu�¡��� s;��� ^ _j�¡����_j�l�s;_�l����;�����s;���`_j��b�puin����;��gd��nz�x�� �q���x��l�pub�iu�����g±��nz�x�b�� �¨��iu�;�jb��­¬s7��inw�l�������¨����{`���¢��l*��in���jbc��s7��inwxl��v��iu_���inz�l������ �J¼v¹¶½������ �`��l ^ b��]p e¤l�_�iupuinjbc_�iu���>���:´µ������b�pniu��*����i �¨�;���;��_�º���;Xb�l�_����×b\_j�� �×�3_7bc_���q_���pn�w�l��¡pn��Xb�lt_j����bc_j�; ���;_7b\_jº��in����b���s7��inw�l���!�g¹���`���(��l��i �¨�;���;��_����s�pub����v���W±v�;���b�lt¥Ï���W³Ê�3_j�i � ±��o³ � �¤½�"p{����#� �½�{����#�¤±v� �f{mv$� l

 �� ^ l�iu*�X{m{��%�¤�º«m{����²pu�;�_��jbÕacb�lt¥ ��� p eg�;wxl�i ^ � �Ïr'&���;_����3_�rtl ^ �;�axiuiu��� ���;¡rxyx�_ u��*��>���³,���x��l�s3_jin��� � � q`r�³ � �����_Ïb ¥��;Vl��&pu�=s;����s;� ^ _Ï��� � rt��s;l���ik_j� · ^ ���jb\_jiu��������pnpu� ��w�l�iºaxin���Ïiu�`_j�;�����;��pu�;¡b� ^ �;s;_�¡��;s�l��in_j���;_ ^ ���x��l�s3_jinaxik_j�*���� r�yt�_ u;���;���l�_����×b\_jiu��W���?³,��t��l�s;_jin���� rt�º³ � lt ºb����s���sÕb������pub�_��������iu�m±�� � �¨��m���� ^ ��� ^ ��s;_�ina����_��tu�Q��ins7����Ol�°,pupn�vs;�����_jin_�l���������sl�����l�_jinpv���¶_j��b�acb�inp ^ ��inaxinpu����iu�&��� p eg�;w�l�i ^ �,l�d5�;×_j��bÕa�bclt¥ ��Õb�pniu��×����_?b�iu���i ^ ����_j����l��&�����_j��l�s;_jl����������l��a���iupnp�b���s��ºzobc����;��l������;m±��o³ ��z���;_��s����`_j�~s�pu�;��¤±v� �f{mv�� ���l��:�����_���l�s3_jl�����������s���l�ax�����*���`_v�l�in_j� ��l��������3´ b�iupnp�b���s��!�¤�m��l1{�x�� ���l���pub �_7b�z�iupuinjbc_�iu���������r�°²  � �_j�l�s;_�l����a���s;_�����in��pnpu�(�gr�b��t{m{$� �¨l��Xl���� �l ^ �;�axiuiu���=��in����b���s7��inw�l����;_X��iu_���inz�l����(� £��ob����$� ����l ����s;������l��p eg�3_jl����W���;�r�°²  _j�;� ^ �����;pu��)"���b����$� lq£����_jb�iu������>s���m_j�jbÕacb�lt¥*�¤�m��l1{�x���� £���b����$�Ê���`_ ^ �����in���m������_����;�Qw�l��ºpub ^ �iu�m�;�&s���� ^ _j�v���;R���x���;Q���m´µ����s;_�iu���������*���`_Q��l?yx�_ u��*�º���;s��;��ik_j�c�ob�l���;p �:��l ^ ����z�p u��*�,���]p e¤�3¥ ^ pn���in����s����¡z�iu�obc_���iu����;p e¤�;_jl����²���Q�_j�l�s;_�l����;(���]s����*��b������,�3a���pnl����; l£�� ^ �;���ob��`_ºs;�;__j� ^ ��iu�>�;�¶s;��� ^ _j�W��� ^ ��lt_ ^ bcm�>´ b�in��� �*iu� ^ pu�;���;��_ � ^ b��mb ^�^ pnius�bc_jin���&����_j��l�s;_jl�����>��iu�;�jb��s7��iuw�l��;��3_ �c��l ����s;���`_j��b�puin��;����Ms����`_��jb�in�����*���`_�b�l s�b�Ws���l���b��`_ �µ�,+ l�� ��;l�p�*�t���&��_�s������in������ � p e¤�;_jl����$���Vpub=�����_jiu��� ��� ^ pnl��in��l��*�*�x���� ���;s����ik_j�¶pub=��� �o��in_jin�������^ pnl��in��l���s�����_��ts�pn��l�� � �3_]b�l��i �c����l�²pu�������`_�������������b���,s��3_�_���_��1u����`��� ^ pul�iu��l��� ^ ��ts;�����; �

Page 16: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�� ��� �V���3 ����������� � ������ �����

b���iujb��`_������ ^ pnl��iu�¡l�pn_7bc�����*���`_]�×bciu]�l�s;s����ika����*���`_ lÑd5�;Q_��jbÕacb�lt¥ ^ ���;s��������`_j:���`_ ^ �;���*iu���������`_������R_���l�_�p egin��_���� ;_:�3_�p�b¡��i � s;l�pn_��X���Xp�b ^ ��iu�X���Ïs���� ^ _��X���Xs��;m�*�t����:�ob���:pu�XsÕbc���������p�b¡_j���;����in��±�� l¢£��;_�_��X_j�1u;��>b ^ ��l��:��z����s3_jin´(��egb�acb���s������obc���s��;__j��a���in�,l

£��:�*���*��iu����;_²�s;iu�����:��� ����lx¥ ^ b���_jin�� l�dMb ^ �����*i u;��� ^ b��_�iu�R��������l ^ �Rpu�;,s7�ob ^ ik_j���;:�:�;_Q��;_��;_(s������b�s����� �vp�b ^ ���;��;��_jbc_jin��������p e¤�;_jbc_M����p e bc�_fl\£������*�²����l�Êp egb�a�����Ê��in_ ^ ���s��;�����*�*���`_Õ�s���_��jbÕacb�iup5����_��1u��¡�� ^ p�b�s;��������pul��*���`_º��b���ºpn��sÕbc�����>���¡p�b _j���;����in�¡±����¢s�e¤��_ ^ ��l���w�l���iÊpu�s7�ob ^ ik_j���$�*���_>�;�`_ji u;���;���;��_>s�����jb�s;��� �&s��;__j� _j���;����in�,l�� _��jbÕa��;��Ws��*s7�ob ^ ik_j���c�®����l���*���`_j��3¬�������wxl���pu�������l�pn_jbc_jºb ^�^ ���_��� ^ b��ºpu�;º�3¥x_�����iu���� ^ ��� ^ ����;�� �l�_ji �o���`_Xpub��������*���`_ºp egin��_���� ;_^ ����_j� � p�b�_j�������iu����lÏs����`_j�~s�pu� ^ b����l ^ ����atin�in��� ^ b��:���W�����¡z����lt¥&s7�����s7����l��º����p�b�s;������lt¬�ob�l�_��>s�iu�;�`_ji ��wxl��>in��_�����obc_jin���ob�pn�,lt�m��l� ^ ������`_j����ºb�in���i���ina��;������Å¥x_j�����iu����m���Wp e b ^�^ ���xs7�����eg����iu��iu���#���_j��l�s;_jl�����]���;s����`_��jb�pniu��;��;�`���x��l�pub�iu�����\�;_�s���bciu��i�w�l���pu��,����lt¥�b ^�^ ���xs7����,´µ�����ob\¬���;��_jb�pu�;����>p�b*yx�`_j�1u;������>s����`_j�~s�pu�;l���¨�qp e b ^�^ ���xs7�����tyt��b���inw�l����obc���pub�w�l���pnpu��p e¤�;a������;���;��_��_ºs�����iu���;���>s����*���Wpu�Ws�����s�� ^ _º´µ������b����;�`_7b�p ^ �����*�;__7b��`_�p�b yx�`_j�1u;�� ����s;���`_j�~s�pu�;l����b�iu��iwxl��Wp e b ^�^ ���xs7���º�_7bc_�iuw�l��º��b���:p�bcwxl���pupn��sceg�;_�p e¤�� ^ b�s;�X��eg�3_7bc_Rwxl�i����l��Xs;�X�ts�pn�,lt�m��l� ^ ��� ��_��������`b�pn���*���`_W���*s��*s7�ob ^ ik_j��� ^ ��l��Ws���� ^ b�����X���;lt¥ ´µ������b�pniu��*��m_j�tu;>lt_jiupniu�� ^ ��l���p e¤�;_�l���� ����r�°² ��Ñ�;_���� ^ b���_jins�l�pniu��� ^ ��l��:p�b¡�*iu�º���Ï�t�;l�ax�������Xpub�_j���;����in��±�� �opn���b�l�_�����bc_j�; ���;_7b\_j��;_pu���±����Õb�lx¥&����³M�;_j�i � ±��o³ � l�d®�Xs7�ob ^ ik_j���X����_�������in��b�lt¥×���x��������º´µ����s3_jiu���������*���`_�� �¡pu�;l����� ^ �������`_7b\_jiu���?�;_ �>pu�;l���]�*iu��;Q�;����l�ax��� l�³,l�in�w�l���pn��]yx_tu��*��:bcl�_j����bc_�iu��;²��� ^ ��t��l�s;_�iu�������`_?����_j��V�����×b�in���$b ^�^ puius�bc_jik´ ^ ��ikatinpu�;��iu�c��p�b ^ ���;��;��_jbc_jin��������?b ^�^ ���xs7���; ^ ���_jb��`_�l��×s;�;_b ^�^ pniusÕb\_jin´5s;�����_jin_�l��Xp�b¡��b ��;l���� ^ bc�_jin�º����s��Xs7��b ^ in_���� lo�m��l� ^ �������`_j����m�;���l�in_j�Xpn���b ^�^ ����_j����p e¤��w�l�i ^ � q�r�³ ^ ��l��ºp eg�3_jl���������X�*�t����X���¡´µ����s;_jin�������;���;�`_X����Wrt°] O�ob���Xpu��s�b����������p�b_j���;����in��±�� lM£��*s7�ob ^ ik_j���� _������in��� ^ b���l���� ^ �����;�`_7bc_�iu��� ���� ^ ����z�p u;���;W���*s7��b������;���;��_�������x���X���X´µ����s3_jin�������;���;��_��;�¶bcl�_j����bc_�iuw�l��Xs�����_�iu��l�� l

d5b ��;s�������� ^ b��_�iu�?�;_ s;����jbcs����;� � ����_j�� ^ ��� ^ ��in_�iu��� �3_�s���� ^ ���_��×_j���iu�s7�ob ^ ik_j���; l,d®�s7�ob ^ ik_j��� q×s�����s��;�����¡p eg�3_jl�������l ^ ���xs������ ^ b��mp�b ^ ��in��W���=s���� ^ _��>������i �¨�;�����`_�º���x�1u;pu��vs�����¬���� ^ �����ob��`_ � ���;m�*�t���������´µ����s;_�iu���������*���`_v�l�s;s��;��ik´µ���lVyx_tu��*�,l¨£��;__j�>b ^�^ ��ts7���W�¡l�pk_ji̬���x�1u�pn�,�����r�°²  s;����_�in_�l��Qp eg����iu��iu�ob�pnin_��M���Q���c_j��� ^ �� ^ ���in_�iu��� lÕ�m��l�Ê���;_7bciupupn��������pn��M��i��q������`_js�����s;� ^ _�X����s;��jb�in��� �×p egl�_�iupniujb\_jiu���&���¡s��3_�_�� b ^�^ ��ts7���(�¨l��=�*��s�b���iu���W���¡l�inaxiÊ���¡p�b*��yx�ob\¬��inwxl�����l=�yt�_ u;����bciu��iÊw�l�e¤l��=�*��sÕbc��iu���W���¡s;������l�_7bc_�iu���Ï���`_����¡�*�t��u�pu�;��¢��inm�;�=�t�;l�ax���������s;� � p egb�� �����s3_jin���T��e¤l����;_7b\_ ^ b��_�ius;l�puin��� �=s7�obcwxl��V�*�t��u�pu���×bc��i ^ l�pu�,l(�m��l�������`_����������wxl��×s��3_W�;_7b\_��;_>����s;����b�iu�� ^ ��l������'�o��in� �&_j��l�_Wiu���_7b��`_Wpu� �*�t�1u;pu� b�s3_jik´�l®d®�*s7��b ^ in_����*�V�;_s������b�s��� � p�b �yx��_��1u�� ���=s����`_j�~s�pu�;l���×���Jb���� ^ _7b��`_&pub _���l�s3_jl���=�¡l�pk_jik¬ ���x�1u;pu� ^ ��� ^ ������ob����pu��s7��b ^ in_���� q�l��m��_���� ��z���;s;_jik´]��_W��egb���xs�iu�;� �$s7��b�w�l�� ���x�1u�pn�¡��l ^ ���xs��;��� l�� ���x�1u�pn����� ^ �;s�i �osÕbc_�iu��� s��������; ^ �����obc��_ �Ï����W��z����s3_jik´µ>���*s�����_��ts�pn� ^ ��� ^ ����>b�l ���x��� ��� ´µ����s3_jiu���t¬�����*���`_�s������in������,lM£����*�t�1u;pu�>���� ^ ��s;i �os�bc_jin���=���;acb��`_�l�inax�����Å¥ ^ puins�in_����*���`_ºp eg�3a���pnl�_jin��� ��l^ ���xs��;�����,inpQ���3ax�jb��,s;�����*�×pn�?�*�t�1u;pu����l ^ ���xs��;������lt_jiupniu����pn�?�*��sÕbc��iu���?���&s����*�¡l�_jbc_jin���^ ���;s��������*���;��_vs;in_j� lo�m��l�:������_����;������ ^ b��:b�inpupu�;l���Qw�l�eginp��3¥tin_j�Xl��Ïl ^ ���axin���l��vl���iuw�l�� ^ ��l��

Page 17: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� �V���3 ����������� ������� ����� � �

s7�obcwxl��V�*�t���&���&´µ����s;_�iu���������*���`_ �� ��*�&pu����w�l��&pu�&�*�x���&s������iu������� ^ ��l�_� 3_j���Ïb�s3_jika��$�l�i̬acb��`_ ^ pul�iu�;l���*��yx�ob��*iuw�l��;���i �¨�;���;��_���Ol�d®�Ïs7�ob ^ ik_j���¶� �;_×������in� � p egb ^�^ puius�bc_jin���T���Ï����_����b ^�^ ���xs7���?l��¡l�� �Å¥t��� ^ pu� ^ ��� ^ ���� ^ b��¡pn��������l ^ �?���*_j��b�acb�inp �¶£�������b������×� ^ ����bc_jin�������;pupu����; rxyx_tu��*�� � � a������;���;��_�* �ius����3_j � � £:·�r�°²  � w�l�iQ´ b�ik_���b�in��_����obc��_ ^ b���_jin�×��lT�����l ^ �� f­�m���;��iu�;��iu�����Wp�b�£:·º����b������W�3_º���Wp�b�rtl ^ ����axiu�in��� � � f­��£:·�r � ��l�����l ^ �>����±���s7���;��s7�����¹V�x���;puiu�bc_jin���×�m�ob�pkyt�X�;_v£�������l�ik_j�X���;vrxyx_ u;���;���yx�ob��*iuw�l��� � � ¹V�v£:r � ��lV£R�m±�rQlo£��;_�Å¥��;� ^ pu�Ï����l� ^ �;���*�;_�_��jb ���¶���;_7bciupupn����pn��*��i��q������`_j×b� ^ ��s3_j×���¶����_���� ^ ��� ^ ��in_�iu�����l��×l���Å¥��;� ^ pu� ^ ���ob�������iuw�l�� l

�m��l��s;����s�pnl�����W��� �o� s������;����iu�����;� ´ b�injb��`_Wl�� z�iup�bc� l������c_j����b ^�^ ����_ �Ïp e¤�;_�l����×����rxyx�_ u��*�� � � a��������*���`_j* �in�s���;_� l��v��l�¡�3a��xw�l�����¡�;�`b�pn���*���`_¡���; ^ ���� ^ �;s;_�ina��;����?l�in_�� ����c_j���º_��jbÕacb�iup l

Page 18: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 19: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� %�� % !� ���m��)h%

Page 20: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 21: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

������� �� ��� ����� �X{

��� %�)�� �� %�'�� �

£��;__j� ^ ���;��i u���� ^ bc�_jin���`s;����_�in_�l����v���v����lt¥�s7�ob ^ in_�����;����_�s�����jb�s;����� �>pub ^ �������`_7b\_jiu���×��ls;���`_j�3¥x_��>�������c_j���º_��jbÕacb�iup¨�;_ ��p�b ^ ���z�pu�;�×b\_jiuw�l����;_jl���iu�;�,l

 ºb���¡pu� ^ ���;��in���Ws7�ob ^ ik_j��×����l� ^ ���;��;��_���������;>_��jbÕacb�lt¥ wxl�iQ;egin��_����������`_�b�l ^ ����z�p u��*�����p�bÏyx�`_j�1u;��&���?s;���`_j�~s�pu�;l���>���pn��� pub$_��������iu�����×s;���`_j�ts�pu� ^ b��>l ^ ���axin�iu����l(d,e¤��z���;s;_jik´����s;�;_�_�� ^ ������`_7bc_�iu��� ��_����×in_�l����>pu�*sÕb�����×��������W_j�jbÕacb�lt¥ ^ b�����b ^�^ ���_ �Vp eg�3_7bc_>���×p e bc�_W���pub$_��������iu�×±�� l�inacb��`_�����lt¥ b\¥t��¨�(pu�;����;�×bc��s7���;¡�;_¡b���s7��ik_j�;s;_jl���������?s�������b������ ^ ��l���pub�yt�`_��1u�� � ��iu����b���s7��iuw�l����¨���x��l�pub�iu��,l l l � ��e¤l���� ^ bc�_��;_Wpn��º´µ����×b�pniu���;ml�_�iupniu��; � bcl�_j����bc_��� ��3_7bc_���ѱ��o³Vl l l � ��egb�l�_j�� ^ b��_ ld®�²����lt¥ti u��*�]s7��b ^ in_����²����l� ^ ������3_5��e bczq��������5pn� ^ ����z�p u��*�,s��;��_��jb�p`���Qs;�]�*���*��in�����;p e¤�;_�l�������;��*�t����W����´µ����s;_jin�������;���;�`_����;�rxyx�_ u��*�� � � a��;�����*���`_j  miu�s;���3_j � r�°²  � lÊ�m�c_j�����;_�l����z�inz�puin������b ^ ��inwxl�� ^ ����_j�R�;���;�`_jiu�;pupn���*���`_²�l��,pn����*�;_����x����,b ^�^ puinw�l����;²b�lt¥�yx_tu��*��]b�l�_����×b\_jik¬��R��� ^ ���x��l�s3_jiu��� � rt��³ � l�°,�&� �¨�3_:s��;:yx_tu��*��:��� ^ ���;��;��_����`_vp�b�s;p�b��� ^ b��_�ius�l�pui u;��������rt°] ^ ��l��Qp�b�w�l��;pupu�vp�bW���;s7�����s7�����l��:pn����*�x����Q����´µ����s3_jin�������;���;��_R��_Rp�b ^ pul�:bÕacb���s;��� l��m��l� ^ ���Ŭ���`_j���������b�pu�;���;��_mpu�;:_j�jbÕacb�lt¥V���Wp e¤��w�l�i ^ �]q`r�³ l��vpu��v�*�t���;m���W´µ����s;_jin�������;���;�`_Õ�o_j��b�acb�lx¥w�l�i]���`_¡�3_j�&b ^�^ puinwxl���>b�lt¥Trt�º³M�Ê��b�iuWw�l�i]�����`_������`_ �obc���pn��s�b������ ^ pul�>���������jbcpQ����p e¤�;_�l�������;ºrt°] ]l¨°,� �o�¨�qs;��s7�ob ^ in_j��>�W_������in��� ^ b��vl���� ^ ���;����`_jbc_jin��� ����_j��b�acb�lx¥Ï�������s7���;��s7���¡l��l�����b ^�^ ���xs7���v�¡l�pn_�ik¬ ���x�1u�pn�Q���m�yt�_ u;���;�s�����_�iu��l�]s��vw�l�iÑ����l� ^ �;���*�;_]����´ b�iu���l����mb��ob�pn����iu��;��_����:s;�R_hy ^ �:��egb ^�^ ��ts7���:l�_jinpuiu��� ^ ��l���pu�;�yx�_ u��*��²s;���`_jiu��l�,�3_,����_���� ^ �� ^ ���ik_jiu���¡b ^�^ puiuw�l��;�b�lx¥Vr�°²  l

Page 22: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 23: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�t�

� � ����'7%�)�� �

� � � %�)�� ��� ����) " �� � )� '="d'�� � !�#" ��

�m��l� ^ ���;��;��_�����v�ob����s;�Xs7�ob ^ ik_j���Xpn�� ^ �iu��s;i ^ bclt¥&s;����s�� ^ _j;�Ñb ^�^ ���_�:�;_��Å¥t_�����iu����v���Wpub_��������iu����l�s����`_j�~s�pu� ^ b��¡l ^ �;�axiuiu��� l,£��;__j�?_��������iu�?in�`_j���x��l�ik_j� ^ b���±vb���b��������;_ � �����obc�b ^ ����´µ���������*���`_¡�*�x��i �o�*p e¤�;_�l����?���� r�°² @��� ^ ������3_�_jb��`_¡��egb ^�^ pniuw�l��;� �¶s;��¡�yt�_ u;���;*����^ �� ^ �iu�;_���;� �l�w�l��ºp �W���;�����a��;�� ��p eg�3_jl����m�����yx_tu��*��Rs;���`_jiu��l�;�t_���pupn��]w�l��ºp�bWs����`_��ts�pub�z�iupnin_����pubv�_7b�z�inpuik_j�²�;_(p e¤� ^ _jin�×bcpuin_��,l;d®�� ^ �iu��s;i ^ ��Miu��ik_jiub�lt¥X���Rs��3_�_j�]_j���;����in�Q���`_,p�b��� ^ b���bc_jin�����;��_����Rpn�^ ��ts;�����v�;_]pn�vl ^ ���axin���l��Qw�l�iÑs�����_��ts�pn��s�����_7b�in��²�;a������;���;��_�����;������� ^ b��²pu� ^ ��ts;����� lxd²e¤�;_�l�������:pubº��yx�ob��*iuw�l��R��l��yt�_ u;������R´ bcin_ ^ bc��p�b ^ �iu�:��� s���� ^ _��:���:p�bºl�s�s;���iu���*���;]�3a��;�����*���`_j���;�������Olo£��;__j�Xb ^�^ ���xs7���m��yx�ob��*iuw�l����x��ik_j�ºb ^�^ ���xs7���ms����`_��jb�pniu��;� �µl��?��;l�p ^ ���xs������º�;_�l��?��;l�pl ^ �;�axiu��l�� � �xl�_jinpuin���pu�;�b�lt_j����bc_j�; �>�;_jbc_jQ�;_�pu��]p�bc���`b����; ^ ��l��QpubW�*�t����puinjbc_�iu������l ^ ���xs��;����3_���l¶�l ^ ����atin��;l�� l ��iu�;�¶w�l�egb ^�^ pniusÕbcz�pu��������������� �*_j��l��pn���r�°²  s��3_�_j��b ^�^ ��ts7������>���3_j����l�a��_��tu�:axin_��Xs����t´µ�����`_j�;� ��l�� ^ ���z�p u;�������X_7b�inpupu�m����v�*�t�1u;pu�; l

� �������:���;���l������:pu� ^ ����z�p u;���Q���:p�bm_jb�iupnpu�²���;,���x�1u�pn��;�c���:����l�a��;pupn��,b��s7��in_���s3_jl����,���`_,�3_j�^ �� ^ ����;�� ltd5b ^ ����*i u;���v���s3_jin���?���ms���s7��b ^ in_����v���_Rs�����jb�s;���;� ��p�b ^ �����;�`_7bc_�iu���?����s��;��_j��l�s3¬_�l����;º��;pu���=p e b ^�^ ���xs7�����tyt��b���inw�l��,l¨�m��l� ^ ���;����`_�����X_j��lt_º��egb�z¢�����=pub�_���l�s3_jl����s��;��_��jb�pniu���b ��� ���*��� ����iu�Wpu�;>s;����s�� ^ _j�����s;����b�iu��� �Ïp�b$s���� ^ ������;���in��� ���*p e¤���������z�pu�*����>�3¥x_j�;���in����^ ������`_j�;����;���l�in_j�(�®���x�1u�pn��X��l ^ ��ts;����� �;_���l l ^ �;�axiu��l��;� ^ ��� ^ ��iu�3_j����� s;���`_j�ts�p�b�z�inpuik_j�W�;_�*�t��u�pu�Ï���= ^ �;s�i ��sÕbc_�iu����l�³,l�iu?����l�&b�z¢���������?pn��?�_j�l�s;_�l����;Ï�*�x��l�p�bciu���$�3_$����s;���`_j��b�puin����c���in����b���s7��inw�l�� ^ l�iuv��iu�;�jb��s7��iuw�l��>��iu�_j��inz�l��;�����¶��� �o��iu��b��`_Xpu�;�����l�a���b�lt¥¶s�����s;� ^ _�Xiu�`_j��t��l�in_�^ bc�Qs7�obcs�l����X�¨eg�;��_����º�;pupn�� lx�v��l�Rs;����s�pnl�����Qs��3_�_j�m��;s;_jin���?l��Rp�b�s���� ^ pn�3¥tin_��m�;�?s���� ^ bc�jb��`_Rpub_jb�iupnpu�v����v���x�1u;pu��:��b���i ^ l�pn�� l

d5b�s;��� ^ pu�3¥tik_j�W�����*��l���b��`_ºl�� ^ ����z�p u��*�W�×b ��;l��v��eg�Å¥ ^ pu��ik_7bc_�iu���$����p�b�_j���;����in�>���>p�b*yx�t¬_��1u����²p�b=���;lt¥ti u��*�Ï���s3_jin��� ���Vs;�Ïs7��b ^ in_����Ï���_×s;����jbcs����;�¶bclt¥ b ^�^ ��ts7����*wxl�ivs7������s7�����`_ �������l�������pn� ^ ����z�p u;���º���Wpub�_7b�inpupn�m���;����x�1u�pn�� ^ b��:l��$s7�ob��������*���`_v����sÕb�����Xiu� ^ ���_7bc��_���pu�;b ^�^ ���xs7����M_jbc_jinw�l���Ol��������! "�#�$�����,���;(b ^�^ ���xs7���� ^ ���;s��;�����`_j�;��cs���pnpu�;�¬hs;i����Q���`_ ^ b�Êz�b���;��(l��p eg�3_jl����²���]p�b:��yx�obc��inwxl��]����M�;a��;�����*���`_�(��b�iu®l��Êp eg�3_7bc_5��l>�yt�_ u;��� l�£��]s7�ob��������*���`_ ^ ������3_b�lx¥ bcl�_j�;l���>���×s;���_��jbÕacb�lt¥ ��e¤l�_jinpuiu������egb�l�_�����>´µ������b�puin��*��X�obc���pn���w�l��;pu>p egb�l����*���`_7b\_jiu���

Page 24: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

iu� ^ ����_7b��`_��m��l×�����¡z������e¤�;_jbc_jQ��l?�yt�_ u;���º�¨eg�;��_��jbc¾u��� ^ bcRb�l�_�����bc_jinwxl����*���`_]l����º�Å¥ ^ pu��iu������Rp�b:_7bciupupn�,��l¡�*�t��u�pu� l\�m��l� ^ ���;��;��_�����,�obc��(s;�;_�_�����s;_�iu��������lt¥>_hy ^ �;���egb ^�^ ��ts7�����w�l�it����l������z�pu�;��_]z�in��� �*���`_j���;�,p�b�_������obc��s������;�b ^�^ ���xs7����²�_7bc_�iuw�l���Ol`¼Ê��l�_²��egb�zq����� ����l� ^ ������`_j����pu���b�l�_j���×bc_���Ê��iu�;�jb��s7��iuw�l��;�w�l�i���� ^ pul�Ê��e bÕa���iu��l����R_���l�s3_jl���:���Rs;���`_j�ts�pu� ^ bc�(���3_j��l�����e¤�;_7b\_Õ�l�_jinpuiu���`_M����(��ina��Õb�lt¥>��in����b���s7��inw�l���Ê�����*�t��u�pu�;Mb �o�¡��e¤��z�_�����in�Ê����(�*�x�1u�pn��5s�pub�iu�M�3_���� ^ �3_jik_j�_7b�inpupu� l¢�m��l�ºb�zq����������º����l�in_���pu�;Xb ^�^ ��ts7����X�����yt�`_��1u��*s;�����_j��l�in_j�;�b�l�_���l��º��e¤l����¡´ bc��inpupu�����´µ����×b�pniu���;R_j�tu;�l�_�iupniu��; ^ ��l���p e¤�;_�l����>����ºr�°²  �¨pu�;�������b�lt¥¶���¡³M�;_���i lq�m��l� ^ ������`_j����p � b�l��i®pu�;���i��q������`_j�s�����s�� ^ _jv��inR�������lx¥ l

�v��l�:s�����s�pnl�����R�;� �o�Ïs��Xs7�ob ^ in_���� ^ bc�Rl����Xs;��� ^ b��jb�in����×���Xp e¤�������¡z�pu�º���;�b ^�^ ��ts7������;_´µ������b�puin��*�� ^ ���;����`_��� l

��� !#"Ï"&%Ê'*),+$-[8?D L UWE 4��*0&-

B�� B��~B � -9.�4�5 -�4�.1A&5QA=+ -/.1>�?�8��/<=AZ��YZ��YZ�� Z M NQPթ R�Tʧ�U,PSWJRQN

d5bT_���l�s3_jl��� s;���`_j��b�puin���� ��� pub�s;���*�×b������ �g±��nz�xcb������_Ïp�bT_���l�s3_jl��� ���iu��in����pnpu�Ï��� p�b_j���;����in�m���ms����`_��ts�pn� ^ b��]�l ^ �;�axiuiu����l�fhs;iqpn� ^ ��ts;����������s;��inacb��`_Qpu�vs���� ^ ���_����*���`_ ^ ��yxiuw�l��º��lyx_tu��*� ��s����*��b������;�����_(�� ^ �����;�`_j� ^ b��®l��>b�l�_j���×bc_�� �:�;_7b\_j �o��in�g½m»�x,{$� � �g¹ ��zmz$� l\£��ob�w�l���;_7b\_Q���vp e bcl�_j����bc_��R��� ^ ���;����`_��ºb�pn����,l�����b�s3_jikatik_j�R��l�l��*�;_jbc_]���:´µ����s3_jiu���������*���`_]��l*yx_tu��*�,ld5��s7�ob������;���;�`_���egl����Xb�s3_jinaxik_j�v��_�� & ��p egb ^�^ bc��in_�iu��� ��e¤l��&iu���obcpq��in�s;���;_���b ^�^ �;pu���3a��;�����*���`_fl� �o� �����`bc�jb��`_jin��pu��� ^ �;s�i ��sÕbc_�iu����Wiu� ^ ����;�� ^ b���l�� s�b���iu�;�����×s7�obc�����c�Ml�� �l ^ �;�axiu��l��¡�;_b���ts;iu�?bcl ^ ���xs��;���×�3_¡���T�ts�pn� ��?s�b��`_j������� �Vin��_������iu�����l b�l�_j����iu���Ws��;�_7bciu��>�;a��;�����*���`_��ob���,pn� ^ ��ts;����� l�d®�Rs���� ^ ���_����*���`_���l��obcin_j�Q���_²s���pnl�ix��l ^ ���xs��;���:�;a���pul�b��`_,����z¢��l�s;pu�Q´µ�;���*������l�vpu�Xs;���`_j�~s�pu�X��lÏ�l ^ �;�axiu��l�� � �o��l������mlk� � l

événements

autorisés

Procédé

générés

événements

Superviseur

�������5�mln���! ��� �� �����!�#"%$&"��! �"��('��*)!�%+,".-/"��0$&12"�3�) ��� � �214351 �����! �76*+,1 � �$�8+,"�9%) ��"��0: �,9;"%) �

d®� ^ ���xs������:��_�s�����iu���;���Rs;���*���]l������;������bc_j�;l�����e¤�;a������;���;��_� lx£��;,�;a��;�����*���`_�]���`_,iu���¬_7b��`_7bc����;�® ^ ���`_7b����; � b�l�s;l�� ���;sÕb���iu��*�����¡atin���`_ ��´µ���s���� �¶p eg�xs�s;l��������s;��������3a��������*���`_j ��;_�b��yx��s7���������� � bcl�s�l��&�*��s�b���in��*����e¤�����pu�����m����axiu�;�`_:yx��s7�������in����:p eg�xs�s;l��������s;�º���;:�;a��;���3¬

Page 25: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � ��������� ����� �� ��������� ��� �,q

�*���`_jX�3_X���;lt¥ �;a������;���;�`_jW��� ^ ��l�a����`_ ^ b��bÕa���in�ºpuin��l �;�=� ;����_���� ^ � l®d5b?�l�ik_j�¡������;a��3¬���;���;�`_j��������;���� ^ b��]pu� ^ ���xs��;����s;����_�in_�l���l��×p�b�����b�������in_Q���;��l�pniu����� lxd5�m�l ^ ����axiu��;l��R��z������a��pn����3a��;�����*���`_jv�;_R����&�~s�pu�ms�����iu�_j� �¡in��_������iu�����l ��b�lt_j���iu��;��s;���_jb�iu��R��e¤���`_j��X��lt¥Ql�� �o�&���s;����´µ������,bcl ^ ���xs��;���:l����R�_j�l�s;_�l��������Rs;���`_j�~s�pu�c��p e¤���������z�pu�Q����,�3a��������*���`_j;�tb ^�^ �;pu��b�p ^ ��b�zq�3_��l ^ ��ts;����� � Σ � ���;_W�s;iu�������;� ����lt¥ ��l�­¬h���������z�pu�;W��iu ���iu�`_j��¨p e¤�������¡z�pn�¡���;W�3a��;�����*���`_js;���`_j�ts�p�b�z�pn�� �

Σc � �;_�p e¤�������¡z�pu�v����Q�;a��;�����*���`_�:iu��s;���`_j�ts�p�b�z�pn�� � Σu � � Σ = Σc ∪Σu

lx»v�?�;a��3¬���;���;�`_²��_²��in_,s;���`_j�ts�p�b�z�pn��io���� �xs�s�l������;��s�� ^ ��l�_,_���l ���l���� 3_j����in��_������in_�� ^ b���pn�R�l ^ �;�axiu��l���µ�l��]pu�;Q�yt�_ u;���;R��� ^ ���x��l�s;_�iu���¨�xsceg�;_�pu�vsÕb� ^ b��]�3¥t��� ^ pn�����;��;a������;���;�`_j:��e¤����s;pu�;��s7�����*���`_����_���s7��� ��l ��� ����w�l 3_j�c�M�����p�b���s����*���`_�W���*�� ^ bc�jbc_�iu����l l l � l®°,� ��;acb���s7���*p e¤�xs�s�l������;��s�� ��e¤l���3a��������*���`_:iu��s����`_j�~s�p�bcz�pu�:��� ^ ��l�_ ^ b� ;_j���in��_������in_�� ^ b��Qpn�ml ^ ���axin���l�� � s�b��������3a��;�����*���`_j��� �o�T��e¤�3¥t��s;l�_jin�������×_ �cs7���������?���;�l�pk_7bc_����×_j�;_Õ�(��� ^ b������,l l l � l� ºb����s;�;_�_��&b ^�^ ���xs7���&��in_��pn����iuw�l��W_j��l�Xpu����;a��;�����*���`_�>���`_���z���;�acb�z�pn��Xs;��wxl�i,�iu����i �o�>w�l�� pu�¡l ^ �;�axiu��l��X��z���;�a�� �_���l�_ �*�����;�`_�pu�&s;��� ^ ����_j���*���`_����Ïp eg�;����;�¡z�pn�&��l ^ ���xs������,l²d®�?_j�;� ^ ^ bc��s����`_j��$��egin�`_j���­¬axiu�;�`_ ^ b�Q���m��b���i u����:�Å¥ ^ puins�in_��,l�d,e¤�;_jl����m� ^ p�b�s;�m������s �>l��*��ina��Õb�l�w�lob�puik_7bc_�in´x��pn�� ^ �� ^ ��in�;_�����yx�obc��inwxl�������X_j�;� ^ :���W�� ^ �����>��� ^ ��l�a����`_ ^ b� ;_������;_�l���iu�;��Ol

 ºb����pub l�in_��Ï���Vs;�;_�_��¶��s;_�iu��� ����l�×b�pnpu��������������;��pub=��� �o��in_jin����´µ�����*��pnpu�?��l ^ ���xs��;���b�in���iow�l��vs��;pupn�:���mpubº´µ����s;_�iu��� ���v�l ^ �;�axiuiu����l�d®�;Qs;����s�� ^ _jQ���vs����`_j�~s�p�bcz�puik_j���c���v�����t¬ z�pu�xsÕb�����;� z¢��l�s;pu�?´µ������;���²b�in���i�wxl��Ïpub=����_jin���T���$p�bc���`b����&l ^ � ��*�Ïs;���`_j�~s�p�b�z�pu�?�3_�pn�� s�������in_�iu������e¤�3¥tin_j�;��s��W�����l ^ �;�axiu��l��m��������_m����b�pu�;���;��_���b ^�^ ��pn����Ol

Z��YZ�� Z�� k ��` aM©SR=U �/T%� ºb���vpub>_j�������iu�X���Xs;���`_j�ts�pu� ^ b����l ^ ����atin�in�������3_ ^ b���b��obcpu����in� �¡p e b�lt_j����bc_jinw�l���s;���`_jiu��l��c�

pn�×´µ����s3_jiu���������*���`_��;��zq��l�s�pu�&��l�a��;�_j�$�;_ sÕbc�jb�s3_j���iu� ^ b���l�����;l�pRs7������b\¬hz�pu�xs?s����`_����ob��`_l���iuw�l����*���`_vpu�X�*�x�1u�pn�Xb�l�_����×b\_j�º��l ^ ��ts;����� � w�l�i5�3a���pnl��� ^ ���`_7b����;���;�`_ � ld®�����x�1u�pn�Xb�l�_�����bc_j�º�;_ml���� ) � +,"� �����_j�

G ^ ��l��:pn� ^ ���xs��;���W�;_���������� ^ b����

G = (Q, Σ, δ, q0, Qm)�,+

:

�Q�Ñ�������¡z�pu�W����m�;_7b\_j��Ñs�b��jb�s3_j�;��iu�b��`_ ^ b��m�Å¥t��� ^ pu��p e¤���������z�pu�W�����b�s;_�inaxin_��� ^ ���iuz�pn��

��l ^ ���xs������ ��

Σ�Ñb�p ^ �ob�z¢�;_R��lV�;����;�¡z�pn�W������;a������;���;��_�����;������� ^ b���pu� ^ ���xs������ �

�q0

�o�;_jbc_viu��ik_ji�bcp¢��l ^ ��ts;��������

δ�Q×Σ −→ Q

���_Qpubm´µ����s3_jin��� ^ b���_jiu�;pupn�Q���R_��jb����in_�iu���>_j��pnpu�Rw�l�� ^ ��l��,l��*�3_7bc_���e bc����ika��;��q′ ∈ Q � �;_Ïl�� �;_7b\_V��� ��� ^ b���_ � q ∈ Q � ��� b���xs�iu�=l�� �;a������;���;�`_ �

σ ∈ Σ � ��� "��

δ(q,σ) = q′l�£��3_�_j� ´µ����s3_jin��� ^ �;���*�;_$��� �� ^ �����;�`_j��� ^ b��$�Å¥��;� ^ pu�=pu�;&s7�ob��������*���`_j

������������������� � �!����"���"#��$&%�"#'�� (���$*)�+-,#'.+/������"#��"�� 0�'�(1�2�3'.+54�+-$&� 6�%879��(:�9��$;'����<��=.��$-�*>->-(�,��?$&%�"#'���( @3$-�BADC5�����8=.�C�E

Page 26: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�c� �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

^ ����inz�pu�;���egb�s;_�inaxin_������l ^ ���xs��;���,l`°,pnpu� ^ �;l�_ ;_����R�3_j������l��:s������*��l�in_ δ : Q×Σ∗ −→ Q_j�;pupu��wxl�� ^ ��l���_j��lt_j����;w�l�����s;���¨eg�3a��������*���`_j s ∈ Σ∗ �3_ ^ ��l���_j��lt_ σ ∈ Σ�δ(q,sσ) =

δ(δ(q,s),σ)�;_

∀q ∈ Q�δ(q,ε) = q

��

Qm

�Ñ�������¡z�pn������v�;_jbc_jv�×bc��w�l��� � bczq��lt_jiu� �*l��V�;_jbc_v�×b��w�l������ ^ l�iu�p e¤�;_jbc_viu��ik_ji�bcpq��l^ ���xs��;���W�iu����i �o��p egb�s�s;��� ^ puiu��;���;��_R��egl����W_���s7������l ^ ���xs��;��� � l

 ��;lt¥*p�bc���`b����;,´µ�����*��pn,sÕb���b�s;_�����in��;��_Qpu�:s;��� ^ ����_j�;���;��_]��l ^ ��ts;����� G��pn�:p�b�����b����:���;������

L(G)�²�;_�pu�$p�bc���`b����$��b���w�l��

Lm(G)l]d®�Vpub����`b����

L(G)�;_ ^ ��� �t¥��Ŭhs;pu��*s�e¤���_ � ��iu��Ïw�l�e¤iup

s����`_jin���`_:_j��l�_j�;:pu���s7�obc¾�����:��e¤�;a������;���;��_�m�������;�����;���� ^ l�iu:p e¤�;_jbc_Rin��in_�i�b�po��l ^ ���xs������,lod®�Xp�bc�t¬�`b����

Lm(G)���_:´µ�����*� ^ bc�Rp e¤�������¡z�pu�º���;����w�l��;��s��;���e¤�;a������;���;�`_j ^ �;���*�;_�_jb��`_:��egbc_�_���in�������

l��V�3_7bc_v��b���w�l��X��� ^ l�in�p e¤�;_7b\_�iu��ik_ji�bcp lx¯o�����*��pnpu���*���`_®�

L(G) = {s ∈ Σ∗ | δ(q0,s)!}

Lm(G) = {s ∈ Σ∗ | δ(q0,s) ∈ Qm}

d®���º����p e¤�;_�l�������e¤l�� yx�_ u��*���®pn�¡�*�t�1u;pu�>��pu��z�b�pÊ��l ^ ���xs������ G��e¤���_>�������;�jb�pn���*���`_ ^ b�

s������_j�l�in_>��iu���s3_j���*���`_ ^ b���pu� s;����s�� ^ _j�;l�� lÊ ºb����p�b&��b ����in_j�������s�b�Wpu� yx_tu��*�×�3_jl���in���;_s���� ^ �������� ^ pul��iu�;l���vs���� ^ ��jbc��_� lqd®�¡s�����s�� ^ _j��l��ºs�����_j�l�in_ºb�pu�����pu�>���x�1u�pn� Gi

���¡s7�ob�w�l��s���� ^ ��jb��`_ ^ l�iuM��z�_�iu�;��_Mpn�]�*�x�1u�pn�]��l ^ ��ts;�����Q��pu��z�b�p ^ b��Ms���� ^ ���ik_jin��� ^ b���b�pup u�pu� � a���in�Mb������Å¥��� � ����s��;m�*�t��u�pu�;R����s���� ^ ��jbc��_� l

Z��YZ��YZ�� � �@` c�§�aK`�©Xe�WYc `x§M©»v�¶�l ^ �;�axiu��l���b���ts;iu� ��l�� ^ ���xs��;�������_����;iu�`_�pn��s���� ^ ���_j�;���;�`_m��l ^ ���xs��;���W��� z¢��l�s;pu�

��l�a��;�_��,l¢·º� ^ b��pu�Xb�pn����Q���Xs���� ^ ���_����*���`_:�;�&zq��l�s�pu�m´µ�����*��� lo¯o�����*��pnpu�;���;��_]l��$l ^ �;�axiu��l����_ml����Wb ^�^ puinsÕbc_�iu���?��� �o��in� ^ b����

S : L(G) −→ ΓbÕa��;s

Γ = {γ ∈ Pwr(Σ) � | Σu ⊆ γ}

³M��l��(s7��b�w�l��:��;wxl�����s;�v�¨eg�3a��������*���`_js�����������;�R�ob����pu� ^ ���xs��;��� G

�\pu��l ^ ���axin���l��(´µ��l����in_p�b¶pniu_�������¡�3a��������*���`_j*b�l�_�����in��;

γ ∈ Pwr(Σ)l(£��;_�_��?puin_���s;���`_jiu�;�`_�iu���3axin_7bcz�pu�;���;��_>p e¤���x¬

�����z�pu�>����º�3a��;�����*���`_jXin��s�����_��ts�pub�z�pn�� �Σu ⊆ γ � ^ l�iuw�l���s;��º���;����in������� ^ �;l�a��;��_ ^ b� 3_j���iu����inzq�; ^ b���pu�ºl ^ �;�axiu��l��Olod®�Xp�b����`b����ms�������� ^ �����ob��`_vb�l&s;��� ^ ����_j���*���`_:�;�&zq��l�s�pn��´µ������;���

����_j�L(S/G)

�o������'�o��ik_m���Wpub¡�×bc��i u;���X���;s�l���ika��W�l�ika�bc��_����

ε ∈ L(S/G)

(sσ ∈ L(S/G)) ⇔ ((s ∈ L(S/G)),(sσ ∈ L(G))�3_

σ ∈ S(s))

d,e¤�3¥tiu�_j����s��=��l�l ^ �;�axiu��l��&�;_$������s=b��l ��3_�_jin�=b�l�s;����s�� ^ _$��� s;���`_j�~s�p�b�z�iupuik_j�%�¤±��nzm{$����;a���pu� ^�^ �Ws�i̬­b ^ �tu�Ol

Page 27: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � ��������� ����� �� ��������� ��� ���

Z��YZ�� Z���� \]R7N�Um`/a�P T�`yUmRQN7P�©S^Q_Jb��VW _YW P �d,egl��¡����(s�����s;� ^ _�(´µ������b����;�`_7b�lt¥>���Qp�b�_j���;����in�Q���Qs����`_��ts�pn� ^ b��M�l ^ �;�axiuiu���¡�;_(p�bms;���`_j�~sc¬

pub�z�iupnin_��,l�°,� s;����iu���;�jb��`_ml�� ^ ��ts;����� G�3_�l�� p�b����`b�������l¶´µ����s;_�iu���������*���`_������in���

K_j�;pÊw�l��

L(G) 6= ∅�;_

K ⊆ L(G)�¨p�b�yx�`_j�1u;�� s������iu�_j�;�jb �?�����*���`_j����ºp eg�Å¥tiu_�����s;����e¤l��=�l ^ ����axiu��;l��

S_���p5w�l��Wpu�X´µ����s3_jiu���������*���`_v���Vzq��l�s�pn��´µ�;���*���

L(S/G)���in_�����b�pMb�lÏ´µ����s;_�iu���������*���`_v����iu���

K��� "��

L(S/G) = Klo£��X�l ^ ����atin��;l������ ^ ��l�����b¡�3¥tiu�_j���:w�l���i�pu�ºpub����`bc��� K

���_�s����`_j�~s�p�bcz�pu�^ bc�:�jb ^�^ ����_vb�l$p�b�����b���� L

lj ���EN�W PSWYR7N}Z��YZ��*�@b1N�� b�� ` UmR7NQP�©S^7_Yb�� _J`��� ��� �+ ��) �*$ �$ "

G35" + �$��� � �5"

L(G)"� �����$�!

Σu

���*$ $&" "�� 9;"%$ '�+,"�3� 1%:�1��#"%$&"��! 9 � � �����! �769+ � '�+,"29���) � 9 �*) 9�+ �$��� � �5"

K ⊆ L(G)"29� 3$� �����! �76*+ � '�+,"�9��#"� �9;"%)5+,"%$&"��! �9��

KΣu∩L(G) ⊆ K � ��

£��;__j�����'�o��in_�iu���$�;_v��w�l�ika�bcpu���`_�� ��pub�a����i �os�bc_jin���$����p�b ^ �� ^ ���in_�iu���×�l�ika�bc��_����

∀s ∈ K, ∀σ ∈ Σu

isσ ∈ L(G)

bcpu���sσ ∈ K

°,� ��e bcl�_j���,_j�;���*���� ^ ��l���_j��l�_��:��;wxl�����s;�m��e¤�;a������;���;�`_j sb ^�^ b��_����ob��`_ � K

�;_ ^ ��l���_���l�_�3a��������*���`_?in��s����`_��ts�pub�z�pu�

σ ∈ Σu

�]i�p�b=��;wxl�����s;�=��eg�3a��;�����*���`_j?b ^�^ b���_jin���`_ � L(G)b�pu����

�;pupu������in_��;�`b�pn���*���`_mb ^�^ b���_j�;��iu� � KlÑ ºb���vpu�Xs�b�vs����`_j��b�iu�����s;��pub*iu����i �o�Xw�l��Wpu�X�l ^ �;�axiu��l��

���3ax�jb�ik_Êin�`_j�����iu��Qp eg�xs�s;l��������s;� ^ ���iuz�pu�²��e¤l��¡�;a������;���;�`_,iu��s;���`_j�~s�p�b�z�pu����s���w�l�i����jbcin_Ês����`_j��b�iu����p�b¡��� �o��ik_jin���$� ;���º����v�;a��;�����*���`_��iu��s����`_j�~s�p�bcz�pu�; l

� ^ b���_jin�(����s��3_�_��:s�������in_jin���¡����s;���`_j�ts�p�b�z�inpuik_j����p eg�Å¥tiu_�����s;����egl��*l ^ ���axin���l��]����� z�pu�xw�lob��`_^ ��l�_ 3_j�������3_j�;���*iu���;�X���$´µ����s;_�iu���$���;�����lt¥$_��������tu��*���l�inacb��`_jOl� �%� RÑ© $ � ` Z��YZ��~i��=W cOPf`9N�Um`�T �k§�N cÕ§�aK`�©Xe�WYc `x§M© PX`/_���§�`

L(S/G) = K � �����&9b�� �� ���

K+,"8+ �$��� � �5"835129�� �71 "%+�!�)�"

K 6= ∅"�

K ⊆ L(G)� ��+"#"��,9� "�) � 9%) ��"��0: �,9;"%) �

S "%+�!�)�"8+,"

- ��� �� "�����!�#"%$&"��! "�� '��*)!�%+,"�-/"��%$&12"L(S/G)

9 ��� �1$� ��+&%K

9���"� .9;"%)5+,"%$&"��! .9���'( �

K"29� ���71*)�" "� �%+ �;9,+

K = K -�./ �K

"29� �����! "�76*+ � '�+," � �$� � ��� �!���� 0%L(G)

+KΣu ∩ L(G) ⊆ K - �

� �%� RÑ© $ � ` Z�� k1�~i��=W cOPf`9N�Um`�T �k§�N cÕ§�aK`�©Xe�WYc `x§M© PX`/_���§�`Lm(S/G) = K � �2�3�&4�5� �

� ��� K

+," + �$��� � �5" 35129�� �71 "%+&!�)�"K 6= ∅

"� K ⊆ Lm(G)

�.) � 9%) ��"��0: �,9;"%) � � ��� '�+ �6!�) �$�! S "%+

!�)�"Lm(S/G) = K

"#"��,9� "�9�� "� �9;"%)5+,"%$&"��! �9��7'( �

K"29� �����! "�76*+ � '�+," � �$� � ��� �!���� 0%

L(G) ./ �K

"29� Lm(G)

-/"��0$&1�89+K = K ∩ Lm(G) - �

:��K

�3>�+ � �<��$&%879= �<;>=�� ,�>;6.�K? ��=8��+�+&�2=8,��26.( +&( ,#� ��>&>�'9$-�B��� ��,��A@���, =���"�� 6.'CB ,��D= +-(�,��9���<EB����+ �3�A@2,#'F=8���GB ��$$EB%���) �����IH �8+

K�3>�+

Lm(G)B ��$$EB% >#J ( ��=�,���+-(�����+;+-,#'.+-�*>;� �*> ��$&%87�=.�*>�AsEKEB���9���#+5L#��$ > '9� %�+&��+&EB��$&0�'�%

Page 28: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�,v �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

£�� ^ �;���ob��`_Õ�`pn����w�l���pu�Rpub����`b����R����iu�� K���:�bc_jin´ b�ik_ ^ b�²pub ^ ��� ^ ��iu�3_j�:���:s;���`_j�~s�p�b�z�iupuik_j�c�\inp

��_���l��obcin_7bcz�pu�v���º_j���l�a����Rpub ^ pul��p�bc������b ^�^ ���¥tin�×bc_�iu���*��� Kw�l�i¨��in_�s����`_��ts�pub�z�pu�c�t���º�����_j�

wxl��º��egb ^ �tu;Rpu�;]_��������tu��*�� ^ ���;s��������`_j;��l��?l ^ �;�axiu��l���jbc_�iu´ bciujbc��_ K ^ l�in�� ;_����m��z�_j�;��l�l��s��;__j� �o�Ïp�b¡���;p�bc_�iu���&�¨eg���������l���p e¤�������¡z�pn�

C(K)���_���� �o��in���

C(K) = {L ⊆ K | L��_vs;���`_j�ts�p�b�z�pn�

}

� _7bc��_����������¶w�l��Vp e¤�������¡z�pn�Ïaxin���V�;_×s����`_j�~s�p�bcz�pu�c�²b�pu��� p e¤�������¡z�pn�C(K)

b _j��l ���l���l����¡�Å¥�in_�����s;���

∅ ∈ C(K) � l¨ �� ^ pul���¢��� ^ ��l�_������*���`_j����vwxl�� C(K)�;_�zq��������3_Xb������3_

Ks����*����z¢�������>l ^ �;��in��l���,l¢fhpM�;� ���;�l�pk_j�Ww�l�� C(K)���_��_7b�z�pu�W����pubc_jika��;���;��_ �*p e¤� ^ �;�jbc_���l������

��iu �����s;_�iu��� � l���iu��� � lq£��;__j� ^ ��� ^ �iu�3_j���in����i ���Ww�l��>�iMpu�;mpub����`b����� Li

b ^�^ b��_�iu�;�������`_ � C(K)^ ��l�� i ∈ {1,...,n}

��b�pn����∪i=n

i=0Li

b ^�^ b��_�iu�;��_Ïbcl��i � C(K)l�³(b��&s;������w�l����`_���p e¤���������z�pu�

C(K)b������3_�l��¶�;_ºl��=���l�p ^ pnl�����jb����V��pn���*���`_Õ�¢w�l��¡p e¤���V����_j�;�jb SupC(K)

w�l�iÊ���_ºpu� ^ pnl����jb���� ��l��¬ �������¡z�pu�×���

Ks����`_j�~s�p�bcz�pu� l®°,� s;������;�Êinp��3¥tiu�_j�*l�� l ^ ���axin���l�� S

_���p²w�l��*pu�´µ����s;_�iu���������*���`_v���Ïzq��l�s�pn�º´µ�����*���

L(S/G) = SupC(K)���_v� ^ _jin�×bcp ��� "��opu� ^ pnl� ^ �;���*iu�in´�l

Z��YZ��YZ�� � ��P §�T�`yT �k§�N c;ª�cOP $�� `£����*�*�*����l�Wp egb�a�����Watl ^ ���;s��;�����*���;�`_Õ�Mp�b$������b���s7���×s�pub��iuw�l��*��e¤�;_jl����×��e¤l�� �yx_ u;���

s�����iu�_j� � �3_jl���in���*�i�pu�$pub����`b����L(G)

�¨egl�� ^ ���xs��;��� G ^ �;l�_ ;_j��V����_j���;iu�`_ � l�� p�b����`b��������iu���

Kl�£���p�b�����b���� ^ �;l�_ 3_j���l��������������;�¡���>��� ^ bc�_º��b�inv��b����pub ^ pnl ^ b���_������s�b�ºinpM�;_

s������_j�l�in_ � ^ bc�_jin�����×pubÏ���;�s;��i ^ _jiu��� ��l ^ ���xs��;���×�3_¡���* ^ ��s;i �os�bc_jin����Ws�������� ^ �����ob��`_ �Ï����^ ��� ^ ��iu�3_j�;¡bc__j������l������l yx�_ u��*�,lÊ»m���? ^ ��s;i �os�bc_jin��� �;_�����s��in_�� ^ bc�>l�� b�l�_j���×bc_�� �Ï�;_jbc_jElE�;_

G����`_�bc���xs�in��;� ^ b���s���� ^ ���in_�iu��� ^ b���b�pup u�pn�>��l ^ ���x��l�ik_º���;X����lt¥=b�l�_����×b\_j����µa���iu�

�������Å¥t��� � �����X_j�;pupn�X�×b���i u���ºw�l��Wpu�ºpub����`b����X��z�_j�;��lV��in_��;�`b�p � K�g£Rd�{m{$� l

d®�Ws7����ik¥&���`_j���s���� ^ ���ik_jin��� ^ b���b�pup u�pu���;_ ^ ���x��l�ik_���� ^ �����¶���>p eg�;����;�¡z�pn�W������3_7bc_�ms;����ik¬�������v�ob����s7�ob�w�l��>b�l�_�����bc_j����mlvrti²pu�;W�3a��;�����*���`_j�wxl�iQb ^�^ b���b�iu����`_>�ob��� G

��b�iu ^ b���ob��� E���*���p u;a��;�`_ ^ b�W��� p�b

^ ��s;i �os�bc_jin��� Ebcpu���Rs�e¤���_�pub¡s���� ^ ���in_�iu��� ^ b��jbcpup u;pu�ºw�l�i®�;_vl�_�iupuin��;� �

�9l�³(b���s����`_j����iÊs���X�3a��;�����*���`_jW�����_Xb�z���;�`_j����E ^ b���s;�¡w�l�eginpuº���¡����ika����`_ ^ b��b����ina����

b�pu����:s�e¤���_�pn� ^ ��t��l�in_�w�l�i®���_vl�_jinpuiu�,l��in��� �;�`_j������l ^ pul�iu�;l���m ^ ��s�i �osÕb\_jiu���� Ei

^ ��l�a����`_ ;_j��¡s����¡z�iu�������bÕa���s�pn� ^ ��ts;����� l®d®�����x�1u�pn���s������_j�l�in_� ^ b���pu�Vs�����s;� ^ _���l����Rpn�� Gi

�3_Ei

�]����`_&���;?�*�t�1u;pu�;���� ^ �3_jin_��V_jb�iupnpu�,l³(b��ºs;���`_j���p e¤l�� ���;X��z�_jb�s�pn�� ��p egb ^�^ pniusÕbcz�iupnin_j������s��3_�_j�¡b ^�^ ��ts7������_�pub*_jb�iupnpu������X�*�x�1u�pn����z�_j�;��l�

G��l

S/Gl�³Êb����Å¥��;� ^ pu��pubm�*�t����puinjbc_�iu��������p�bmpniu�����Q���Q_j�jbc��´µ�;�_,����p e¤��f­³=���:d�y���� b

b�zq��l�_ji ��l�� ^ ���xs��;��� G���>�Õ�mz��������;_7b\_j²�;_v�W�Xv`�W�����º_j��b����ik_jin���� �¤³Q£R±v�`��� lxrtl��]s��3_]�3¥t��� ^ pu�

p�b��yt�`_��1u��W���ºs����`_��ts�pn��l��Q��e b ^ b�:b�z¢��l�_�iqs�b���pn��Rs�b�pus;l�pu]���;s���jb�in���;:��� ^ bc���;�`_mpn��QsÕb ^ bcs�in_���

Page 29: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � ��������� ����� �� ��������� ��� �mx

��l pu����ius�in��p����×yx�`_j��u��� �$¼v£�¼ ��� l( ���� ;��� inp]����´ b�l�_ ^ b�W���l���;_jin���;�>pubÏ��i � s�l�pk_j�*���p eg�3_7b ^ �����>�*�x����pniujb\_jiu���X��p�b ��in_jin��s;_�iu���$�Å¥ ^ puius;in_��W���>s;��w�l�� ^ ��lt_���lV����ik_v´ bciu����pn� ^ ���xs������ �s;������b��������R�3_mpub¡���x���;puiu�bc_jin���?���;� ^ ��s�i �osÕb\_jiu����:����s;���in_����`_ºl��V�*iu��in�¡l��O��e¤�3¥ ^ ����in����s;��Ol

d®�� ^ �� ^ ���ik_jiu����>l�inacb��`_���¡���`_ ^ ��l�����z���;_¡���&��� ����iu�>������_j��l�s;_jl�����*b�pk_j�;���obc_�ina��� � pub�_j��l�s;_jl�����s��;��_��jb�pniu���Wb �o�Ï�������;��l�iu��Xpu�; ^ ����z�p u��*��:���X_jb�iupnpu����������x�1u;pu��:��z�_j�;�xl� l

B�� B���� � -/.�4�57-94�.1A ��� 032�4�?�>�8 .1A A -F26<=5 A=+ -/.�>@?�8��/<=AZ��YZ�� k �YZ MONQP�©SR=TM§�U,PSWYR7N

d5b�_���l�s3_jl���X���x��l�pub�iu���s�����iu�1u;��� ^ pul�iu��l����l ^ ���axin���l���vb���ts;iu�; ��l�� ^ ��ts;������l���iuw�l�� lfhpnv��z���;�a��;�`_X_j��l�vpu�;m�3a��;�����*���`_j��������;���; ^ b��vpu� ^ ��ts;�����>�;_�b���iu��;��_�s���� ���iu�`_j�;���;�`_ml���pn�^ ��ts;����� l5��iu���i �®l�� �;a������;���;�`_�s����`_��ts�pub�z�pu� ��� ^ ��l�_ ;_�����b�l�_j����iu��w�l��*�e¤iup²�;_�b�l�_j����iu� ^ b��_���l��pn���l ^ �;�axiu��l�� ltrtitl�� ���l�p��l ^ ����axiu��;l��²iu�`_j�;����ik_�p eg�xs�s;l��������s;�:��egl��*�3a��;�����*���`_Õ�`�;pupn����;�jb´µ���s��;���;��_Qiu�`_�������in_j� l���iu���i¢p egb�s;_�iu���*s�����s���l���b��`_j�m����Rl ^ ���axin���l��� ^ ��l�_Rb��*�����;� �>l��?s������oin_ l

d5bv�_j�l�s;_�l����]���x��l�pub�iu�� ^ ������3_Ê���]��iu�*iu��l����®pub�_7b�inpupn�����²�l ^ ����axiu��;l���Ol��v�Õb�������in��®s��]�`b�in���_��jb���l�in_ ^ b�:p�b¡���;s��;��ik_j�W���Xa��;��i ���������� ^ �� ^ �iu�;_���:l ^�^ pn���*���`_7b�in���;:���������$s������oius3_jlob�pnin_���;��_�����pu�;���i��q������`_j��l ^ �;�axiu��l����¢b�pu��l�����in��b��`_vb�iu��i�p egb�pn������ik_j���*�v����yx�`_j�1u;��,l

d5b��_j��l�s;_jl���������s��;�`_j�jbcpuiu���Ww�lob��`_ �*��pupn����_mzob����>�l��ml���������s���� ^ ���ik_jin���$���>p e bcp ^ �obczq�3_��pn��zob�p

Σ�;�V��l��¬hb�p ^ �ob�z¢�;_jOlo°,�V�¨e b�lt_j���;v_�������;���pub �_j�l�s;_�l��������;s����`_��jb�pniu��;�>�� ^ �����l���l����

���;s���� ^ ���ik_jiu������l ^ ��ts;��������� ^ pnl��in��l��,���l��¬ ^ ���xs�������²pu�xsÕb�lx¥ Gi,loc

l���s7�obcwxl��v��l�­¬ ^ ��ts;�����Gi,loc

�;_Xbc���xs�in�>l��¶�l ^ �;�axiu��l��mpu�xsÕb�p Si,loc

l¢d5b�����l������ml � ^ ������`_j�¡l�� �3¥t��� ^ pn�>���W���;s�����¬^ ���ik_jin���V�;�=����lx¥ ^ ��ts;�����;Xpu�xsÕb�lx¥ l¢�v��l��a�� y�����Xl��ºs��3_�_�� �o��l���¡w�l��¡pub����;s���� ^ ���in_�iu���Ï��l^ ��ts;�����W��pn��zob�p G ���¶����lt¥ ^ ��ts;�����;mpn�ts�b�lt¥ Gi,loc

�i = {1,2} � �;_�b��l����;� ^ bc�v����lt¥VsÕbc�ob�lt¥��e¤iu�t´µ������bc_jin���

P1

�;_P2

l,£��;s�i ^ ��lt_ ;_j��?���;������b�puin�� � l��T�����¡z���?w�l���pns�����w�l��$��� ^ ���xs��;����pn�ts�b�lt¥Ql

SS

P P GG1,loc

1,loc

2,loc

2,loc

G 21

�������5�ml ���� ���! "�76*+," � �$��9%) ��"��0: �,9������ 351��2"��! "�#��+ �,9;12"

d®� ^ ����z�p u;���?s;p�b��inwxl��&���&p e¤�3¥tiu�_j�;��s��$��e¤l����l ^ ����axiu��;l�� ����s;���in_����,�obc�� pu�?s�b������&���Ïpub.���� ��� �� �3>�+�'9� ,�'�+-(�� ����$$EB�8+�+ ����+ ��� EB(�>-� �3� , ��' L $&� 6.� �!� +��9%�,�$&(������ ��� � ����'.+ 48+&$-� $-%=8'���%�$&% >-'�$ � �

>�( +-��� �<@ 6.��� ,����2� E����#+-+-���! " $#%#%#<� =�,���+-$&,�� � '.+-,#$-,#�#+&,9� =��& ����,��9� �$ ��$&, BD>' (# ,����9� E)

Page 30: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�,z �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

_j�l�s;_�l����*���;s����`_��jb�pniu��;���®��� �� ^ �������� �&���;lt¥ w�l����_jin���� l � _jb��`_>��������� l�� ^ ���xs��;��� G�3_>l��

p�b�����b����X���;�iu��K�

�ml��ºl���pnpu������`_�pn��Ws�������in_jin����X��e¤�3¥tin_j�;��s��×��egl�� �l ^ �;�axiu��l��>��pu��z�b�p S�®�����`_>p egb�s;_�iu��� ���

s����`_��ts�pn�]�;_(p�b:s���� �����s;_�iu���W���;�b�s3_jiu����5����M�l ^ ����axiu��;l���Êpu�xsÕb�lx¥¨�Õ_���p�w�l�� L(S/G) = K ��9l�d®� ´µ����s;_�iu���������*���`_W��� zq��l�s�pu��´µ�;���*������l ^ ���xs��;��� ��pu��z�b�p G

s;��l ^ pn� b�lt¥ �l ^ �;�axiu��l��pu�xsÕb�lx¥

Si,loc

�����b\¬ _�¬hinp�b�l��i5� ^ _�iu��b�p¢wxl��>s;��pul�i�����p�b�_���l�s3_jl����s����`_��jb�pniu��;� �Z��YZ�� k � k i���WYcOPX`/NVUm`�T�` cÕ§�aK`x©Xe�WYc `x§5©

d®�&sÕbc�ob�p:��e¤iu��´µ������bc_jin��� �;_*��� ����i ^ b���l����$´µ����s;_�iu������� ^ �� ���s3_jin�����obc_jl�����pnpu� Pl²£��3_�_j�

´µ����s;_�iu���¨�t���'�o��in�º���Σ∗ a����� Σ∗

loc

bÕa��;sΣ∗

loc ⊆ Σ∗ � ^ ������3_ � ^ b��_�iu�]��egl��&����_�s�����_j�l�in_��l�� Σ�������;_������*iu������p�b¡��l��¬ s7�obc¾u��������s������c_�s������_j�l�in_��X�l��Σloc

lj ��� NVW PSWJR7NGZ�� k ���W© R�� `/U,PSWJR7N#N�b�P §5© `/_Y_Y`��

� ��� P : Σ∗ −→ Σ∗

loc

"%+�+," !�)�"∀σ ∈ Σ

"� ∀s ∈ Σ∗ :

P (ε) = ε

P (sσ) =

{

P (s)σ9��

σ ∈ Σloc

P (s)9��

σ /∈ Σloc

� �o�¶���W���3_j�����in������l��V�l ^ ����axiu��;l�� ^ ������3_�_jb��`_m�������;_�����in������>pn�Wpub����`bc���X��e¤l�� ^ ��ts;�����G�Miup²�;_����;s��;�jbciu���×���×���3_j�;���*iu���;�>iQs;�?p�b����`b���� ���;�iu��

K�;_���z������acb�z�pu� ^ b��W�jb ^�^ ����_¡bcl

p�b�����b����X��l ^ ��ts;�����c�¢���Wpub ^ ��� ���s;_�iu���Ï�;_����Wp eg�;����;�¡z�pn�W������;a������;���;��_��pn�ts�b�lt¥ Σloc

lj ��� NVW PSWJR7NGZ�� � � � �Vc `�©Xe1b��VW _YW P ���� ���

K) � + �$��� � �5" 35129�� �71 "%+ !�)�"

K ⊆ L(G)�K

"29� 3$� ��'%9;"��0:�� '�+," � �$� �#��� �!���� 2%L(G), P"�

Σloc �9���"� �9;"%)5+,"%$&"��! �9��7'

( �� �*) �� �*) "29 9;1!�)�"�� �2"29 3� 1%:�1��#"%$&"��! 9s ∈ K

�s′ ∈ K

"� �!�*) � �*) 1%:�1��#"%$&"��! σ ∈ Σc "%+ 9 !�)�"

P (s) = P (s′)�sσ ∈ K

"� s′σ ∈ L(G)

��+ ���29s′σ ∈ K ./ � � ��:�"��29;" "� �: �#�$� ��� "�� 9��

s′σ ∈ K"�

sσ ∈ L(G)��+ ���79

sσ ∈ K�

� � �/RÑ© $�� ` Z�� �1�~i ��W cIPX`/NVUm`�T �k§�N cÕ§�aK`x©Xe�WYc `x§5© � ���![ ��� �� ��$�! 3 ���!�#1 ) � + �$��� � �5"�35129�� �71

K� "%+ !�)�"

K ⊆ Lm(G)� ��+."#"��,9� " ) � 9%) ��"��0: �,9;"%) �

S "%+ !�)�"

+,"�- ��� �� �����!�#"%$&"��! "��('��*)!�%+,".-/"��0$&12"�9 ��� K

+Lm(S/G) = K - 9���"� .9;"%) +,"%$&"��! �9���'( �

K"29� �����! "�76*+ � '�+," � �$� �#��� �!���� 0%

L(G) ./ �K

"29� ��'%9;"��0:�� '�+," � �$� �#��� �!���� �%P, L(G)

"� Σloc .

� �K

"29� Lm(G)

-/"��0$&1,+ ��� "��K = K ∩ Lm(G) - �

��Σloc

�3>�+ � J ���9>-�<E0@���� 6.�3>;%#L�%��9�<EB����+&>;, @9>-��$$L � @����3> �9��$ ���<>�'9�2�3$ L (!>��3'�$S

Page 31: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � ��������� ����� �� ��������� ��� �,{

Z��YZ�� k � � � a�PSW � b _YW P �±�� ^ ����������p�b�_���l�s3_jl�������Qp�b ����l����m�ml �t� �ob���Êp�b�w�l��;pupu�,pn� ^ ���xs������R��pu��zob�p G ���_����;s���� ^ ����

�;�¡����lx¥���l�­¬ ^ ��ts;�����;,pu�xsÕb�lt¥ Gi, loc

�i ∈ {1, 2} � l���s7�obcwxl�� ^ ���xs;�����Rpn�ts�b�p Gi,loc

s;����_���l�ik_(l��Pi(L(G))

���_Wb���ts;iu�;��l����� ^ ��s;i �os�bc_jin��� pu�xsÕb�pn� Ei,loc

l®d®���l ^ ����atin��;l���pu�xsÕb�p Si,loc

��_W���������^ bc�:p�b¡���;p�bc_�iu���X� L(Si,loc/Gi,loc) = SupC(Pi(L(G)) ∩ L(Ei,loc))

ld,e bcs;_jin���&���Xs7�obcwxl��Wl ^ ���axin���l�� Si,loc

����_j���;iu�`_�pu� ^ ���xs��;��� Gi,loc

l�� �o�$���ºa�����i �o���:pn�ºz�in���´µ�������&���$p e¤l�_jinpuinjbc_�iu��� ���$p egb ^�^ ��ts7���&����s��;�`_j�jbcpuiu���c�,iupR�;_*����s;��jb�in���Ï���$s���� ^ b������pu�&s;����¬^ ���_����*���`_v��z�_�����l ^ b��vp egb�s3_jiu���Ï�����l ^ ���axin���l����pn�ts�b�lt¥ �*s��;pul�i5w�l�iMb�l���b�in_v�;_��>��z�_j�;�xl b�a���sp e b ^�^ ���xs7����s;���`_j��b�puin��;�,lo£��3_�_��ºa����i �os�bc_jin���?���;s��;��ik_j��p e¤iu�`_����x��l�s;_�iu���*���º����l�a���b�lt¥$s;����s;� ^ _�:�;_��������l�a���pnpu�� ^ ��� ^ ��in�;_j�; l( ���¡l ^ ���axin���l�����;_�������l� S̃i

bc���xs�in���bcl ^ ���xs��;��� Gb�z¢��l�_�iu����`_

�$p�b$� ;��� ���_���ins;_jin��� wxl���s;��pupn� ���Si,loc

�Ïs;������ik_jiu��� ��egb�l�_�����in��;��_���l�Wpu�;>�3a��������*���`_j�b ^ ¬^ bc�_j�;�ob��`_ � � Σ − Σi,loc ��� l¢¼Ê��l�ºpu�;��l ^ �;�axiu��l�� S̃i

b���in���;�`_º���¡��b���i u���>iu�¡l�pk_7b������W�l��ºpn�^ ��ts;����� G

lo �b���R_j��l�:pu�;:sÕb�:pn�ºp�b����`b����K̃��z�_�����l ^ b��:pn�ºs����`_��ts�pn�º���� S̃i

l��:pu� ^ ���xs��;��� G�;_viu��s;pul$�ob���vpn�Xp�b����`b����Kyx�`_j���3_jin�� ^ b���p egb ^�^ ��ts7���Xs����`_��jb�pniu��;�,l¢£��;s�i5���_m�Å¥ ^ ��in��� ^ b��:pn�

pn���*���m�l�ika�bc��_����`�� � ` Z��YZK̃ ⊆ K �

d®�X´µ����s;_�iu���������*���`_v���Ïzq��l�s�pn��´µ�;���*��� ^ bc�vl����>�_j�l�s;_�l����W����s;���`_j��b�puin��;� K̃��;�jb�s;����iu���;���

s;�����*��� ^ _jiu��b�pcpu����w�l��,s��]s���� ^ ���_����*���`_®���jb�����b�p��:s���pnl�i���zt_j����l ^ b��®p egb ^�^ ���xs7���,s��;��_��jb�pniu���KlÑd5b�s�������in_�iu���$���;s���jb�in���W�;_v�l � �b��`_j�W��e¤��z�_j�;�`_jiu���V����s;�>s;��� ^ ����_j���*���`_�� ^ _jiu��b�pq��_mw�l��

pn�Xp�b�����b����K���ik_ � ��������b�p � ^ b��:��b ^�^ ���_vbclVpub����`b���� L(G)

�;_ � p�b ^ �� ���s3_jiu���V³�lj ���EN�W PSWYR7N}Z����� � + �$��� � �5" ���71*)�" "� �%+ �;9

K ⊆ L(G)"29� �3$� +

L(G)� � - � ���0$ ��+ 9��

K = L(G) ∩ P−1(P (K))���P−1

�7" ���2129;"��! "8+ � - ��� �� "����� 35"8+ � ��� ���/"��� "����� � ��:�"��79;"�35"P "%+�+," !�)�"5'

P−1 : Pwr(Σ∗loc) −→ Pwr(Σ∗)

P−1(M) = {s′ ∈ Σ∗|P (s) ∈ M}���

M ∈ Pwr(Σ∗loc)

»m��p�b����`b���� �L(G)

� ³ � ¬h������×bcpo��_�������sml��×pub����`bc����wxl�i ^ ��l�_ ;_����m���;_�����lta�� � ^ b���_jiu�²���vjba�����iu���Ïpu�xsÕbcpu�P (K)

�;_v��lÏp�b�����b����Xd � � l� �%� RÑ© $ � ` Z���� � \]R7NVT�W PSWYR7N T � R a�PXW � b1_ W P ���K = K̃

9�� "� .9;"%) +,"%$&"��! �9��K

"29� � ���0$ ��+D��

·º� ��;_�iu�������jb$w�l�� �i²p�b&���;s����`_��jb�pniujb\_jiu��� ^ �;���*�;_W��e¤��z�_j�;��iu�X����Ws����`_j�~s�pu�;l��� ^ pnl��s�����s�iu;�s;�W��b�iu�&��´ bcin_ ^ b���´µ��iuRb�lt¥$��� ^ �;����

�J�¨egl����W� ^ _jin�×b�pnin_�� ^ bc�_���l ���l���Ra��;��i �o���c�� �.A

Σ − Σi,loc

E��σ ∈ Σ | σ 6∈ Σi,loc �

Page 32: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

q�� �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

� ��e¤l����>b�s;_�iu���&iu�¡l�pk_7b������X���;vl ^ ���axin���l��� ^ ��l�acb��`_�s;������l�in��� ������vz�pn�ts�b�����;�� ��� ^ ��� ^ ��in�;_j�;��l ^�^ pu���*���`_jb�iu��� �¡a����i �o�;�vb�pu��l�����in�jbc��_�pub¡������b��s7���,l

B�� B�� C � -9.�4�5 -�4�.1A��68 <�.�>K.15��68�� 4�AZ��YZ�� � � Z M NQPթ R�Tʧ�U,PSWJRQN

 ºbc���s;�;_�_��×b ^�^ ���xs7����p e¤��z����s3_jik´R���_����×���;s���in���*��i��q������`_j>��ina��Õb�lx¥ ��� ^ ��ts;�����*�;_����*�lt¬^ �;�axiuiu��� �ob���Wpu�;�w�l��;pu�l�� ��ina���b�l ^ b��_�ius�l�puiu�;� i ^ �;���*�;_W��� ^ ���;����������;>����s�in�in���� � ^ b��_�iu���egin��´µ����×bc_�iu�����iu�l��;Q��l���ina��Õb�l � ( l�X����s;� �Xl������3_j��l��²��e¤iu�t´µ������bc_jin����(a����Qpn�v��ina���b�l � ( �`pu���ina��Õb�l

i����in_�����b�pu�;���;��_ ^ ������3_�_j������>s;���`_j��b�iu��������pu��s���� ^ ���_����*���`_����Ws��;pul�i̬hs�i lod,eg��z����s3_jin´

��_m��e¤��z�_�����in��b�iu��i����;v�*�x�1u�pn��:������ika��Õbcliz¢�Õb�l�s;��l ^Ï^ pul�:s�����s;iu�w�l��Ws���lx¥Ï��l$��ina��Õb�l � ( l

 ºbc��:pu�;�_j��b�acb�lx¥?in��_����x��l�s3_jin´µQ��� � � �n{���� ��pn��:b�lt_j��l���:s������in�1u�����`_�l����X�_j��l�s;_jl�������iu�;�jb��­¬s7��iuw�l�� �¡���;lt¥$��ika��Õbclt¥º��l��$��ina��Õb�l$zob��s���� ^ ����X��e¤l��$���x�1u;pu����l ^ ���xs������X�����;p Gl

�3_����X�����l ^ ����atin��;l�� Sl

�3_:l��$��ika��Õbcl&�ob�l�_:s;���`_j�;�ob��`_�pu�m���x�1u�pn�m��l ^ ���xs������Xb�z��_j�jbcin_ Gh

�;_:pn��l ^ �;��¬atin��;l��

Sh

b���xs�in� � ����l������ml|q � l¨£���º����lt¥¶��ina��Õb�lx¥ ���`_ºs���l ^ pu�; ^ bc��l�� s�b��ob�pM��e¤iu��´µ������bc_jin���θw�l�i ^ �;���*�;_m����s;�����_j��l�iu���Wpu���*�t��u�pu����l ^ ���xs��;���>������ika��Õbcl¶�ob�lt_ Gh

� ^ b��_�iu����� Gl

�3_º���yx��s7�������iu���mpu���bcs;_jin����:���;ml ^ ���axin���l��� Sh

�3_Sl

l

θ−1

Gl

GhS

S

h

l

θ

θ

s

(s)

�������M�,lrq�� � �0)!�� ) �7" 35"�9%) ��"��0: �,9�������� � 1��#�$� ��� � !�)�"

Z��YZ�� � � k � R�T%�/_YW c b9PSWYR7N T�`/c aʩSR=U �/T �9cd5b ^ ���;��i u���� �3_7b ^ � ��� �*�t���;puinjbc_�iu��� s;����iu_�� � s�����_j�l�iu�� pn� ���x�1u�pn�=��l ^ ���xs������ ���

��ina��Õb�lVzob� lq°,�¶��� ^ ��s3_7b��`_�pu��vs�����a����`_jin����m��eg�;s��in_jl����W����� � �n{���� �Ñpu���*�t��u�pu����lV��ina��Õb�lVzob���_

Gl = (Ql, Σl, δl, q0,l, Qm,l)lM³M��l���s;�����_j��l�iu����pu� �*�t�1u;pu�*���*��ina��Õb�l ��b�l�_

Gh

� ^ b��_�iu�����Gl

�(inp,´ b�l�_¡��� �o��in��pubÏ´µ����s3_jin��� ��� ^ ���;��;��_jb��`_ pu��sÕb��obcpQ��e¤iu�t´µ������bc_jin��� θl�£��;_�_��×´µ����s3_jin��� ����in_

^ �;���*�;_�_�����p e¤�;a���pul�_�iu��� ��lT�*�t�1u;pu� ���?��ina���b�l �obcl�_ Gh

��� ´µ����s;_�iu��� ���×s;���_jb�iu����¡�3a���pnl�_jin������l ��ina��Õb�l=zobc

Gl

l5£��;s�i�s;������� ^ ����� ������s �?p eg�xs�s;l��������s;�¡��e¤l�� �;a��;�����*���`_W���¡p e bcp ^ �obczq�3_º���

Page 33: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � ��������� ����� �� ��������� ��� q��

��ika���b�l=�ob�l�_�l�in_�� �?s��;�_jb�iu��X�*��_�º�����������;��l��Xp e b�p ^ �ob�z¢�;_m������ika���b�l zob� l�³Ê��l�� T�;_

Σpn��

b�p ^ �ob�z¢�;_�º���; ^ ��s3_jin´µ����;���ina��Õb�lt¥=�ob�l�_W�;_�z�b��� σ ∈ Σ�;_

s ∈ Σ∗ ��pn��sÕb��obcp���e¤iu��´µ����×b\_jiu��� θ�;_v��� ����i®s����*�*�X�l�ik_®�

θ : L(Gl) −→ T ∗

θ(ε) = ε

θ(sσ) =

{

soit θ(s)

ou θ(s)τ ^ ��l�� τ ∈ T

³,pul�_ts�_�w�l��W���>��� �o��in��iu����� ^ �;���ob��*�*���`_�p egb�l�_����×b\_j� Gl

�;_vpub�´µ����s;_�iu���θ�oinp®���_ ^ pul� ^ ��b\¬

_�iuw�l��W����s;����_���l�in���>p�b �×b�s7��iu���W����¹Ï�t����>�;w�l�inacb�pn���`_j�>b�l s;��l ^ pn� � Gl,θ � l¨£��;__j�>�×b�s7��iu���W���¹V�x����X��_G̃l = (Q̃l, Σ̃l, T0, δ̃l, ω, q̃0,l, Q̃m,l)

�����`_mpn���s���� ^ ��jbc��_������

Q̃l, Σ̃l, δ̃l, q̃0,l

�3_Q̃m,l

����`_viu�����`_jinwxl��� ��s���pnpu�;:��lV�*�x�1u�pn�Gl

��

T0 = T ∩ τ0

�;_�p e b�p ^ �ob�z¢�;_���������_jin� Tb�l����*���`_�����egl�� �3a��;�����*���`_ ^ b���_jius;l�puin��� τ0

��ik_�3a��;�����*���`_m�����iupn����s;�X��lÏ�;a��;�����*���`_m�inpu����s�iu�;lt¥ �

�ω : Ql −→ T0

�;_vp�b�´µ����s;_�iu���$��������_jin�X��� ����iu�X´µ������;pupu�;���;�`_�_j�;pupn�ºw�l����

ω(q0,l) = τ0

ω(δ(q0,l, sσ)) =

{

τ0

iθ(sσ) = θ(s)

τi

θ(sσ) = θ(s)τ

d,e bcl�_j����bc_��X������ina��Õb�lÏ�ob�l�_ ^ ��l�_ 3_j����s;����_���l�ik_ � ^ bc�_jin�R����p egb�l�_�����bc_j�º���¡¹V�x����X���>pub´ b��;���&�l�inacb��`_j��� ��_j��lt_:�;_jbc_:���Xp e b�lt_j����bc_j�v���W¹V�x����XbÕy`b��`_�s������*���3a��������*���`_v���X�����_jin��l���3a��������*���`_Riu����i �osÕb\_jin´Ñ������iupn����s;iu��lx¥ s�������; ^ �����×l����3_7bc_]���vp egb�l�_����×b\_j�R������ika���b�l×�obcl�_fl�d5b´µ����s;_jin��������_j��b����ik_jin���¡b���xs�in��� �ºp e bcl�_j����bc_��]���R��ina��Õb�l���b�l�_��;_,��� �o��in�R���¡´µ����s;_�iu���¡��l¡sÕb���b�p��e¤iu�t´µ������bc_jin���

θ � lÊ£��*sÕb���b�p,��e¤iu��´µ����×b\_jiu��� ^ �;���*�;_W��egb���ts;iu�;� �&_j��lt_j� ��;wxl�����s;� s ∈ L(Gl)l����3a��������*���`_×��l l����$���w�l��;��s��V��e¤�;a��;�����*���`_��iu����i �osÕb\_jin´µt ∈ T ∗ l,d®�$s���� ^ ���_j�;���;�`_����

p e b�lt_j����bc_j�(��l>��ina���b�lW�ob�l�_Gh

l�in_Ms��;pul�i`���]p e bcl�_j����bc_��Gl

b�l�_j�jbÕa�����M��l>sÕb��obcp���e¤iu��´µ����×b\_jiu���θbÕa��;s

L(Gh) = θ(L(Gl))l

£�����iu���;������vp eg�Å¥t��� ^ pu�X���Wp�b ����l���� �ml¤���o�Å¥t_��jb�ik_�������� �n{������op e bcl�_j����bc_��Gl

�����1u;�������;lt¥�3a��������*���`_j,iu����i �osÕb\_jin´µ

τ1

�;_τ2

��p e bcl�_j����bc_��Gh

b�������sR���;lt¥��3_7bc_�q0,h

�3_q1,h

l�r�b���(���;_jb�iupnpu���ins�i¢pu���sÕb�pns�l�pn����;s���jb�in���; �¡pub����3_j�����in�obc_�iu�������

Gh

��iup¢���_:´ b�s�inpu�v���ºa���iu��w�l��Xpn�ºs7�ob��������*���`_��e¤�;_jbc_Q���

q0,h

�q1,h

�;_�� & ��pubW���;������bc_jin���×��l?���c_αγ

�ob���Gl

��w�l��ºp�b�z¢��l�s�pn��l���p eg�3_7bc_qh,1�;_º��l�� �*p�b zq��l�s�pn�>�;��_����>pu��v�;_jbc_j

ql,2

�3_ql,3

�;_ºw�l��>p e¤�;a������;���;��_τ2

�jb���u���� ��p eg�3_7bc_vin��in_�i�b�ps�b��mpn����l�pM�;a������;���;��_ ^ ���iuz�pu�W����l�in_��¡�ob��� Gh

��_τ1

lqd®��pu�;s;_���l��m����iu�jbc��_�����m���;_jb�iupnml��p e b�pn�����in_j���������Ws�����_j�l�s;_�iu���$���

Gh^ ��l���jb���W���3´µ������ � �g°,iup xc��� l

���"� �8+-+-� B ,#�F= +&( ,#� �*> +56.%�79��(�� =8, EGEB� >-'�( +��∀s ∈ Σ∗

l

)δl(q0,l,s)!

)9��� ,#$&>δh(q0,h,θ(s))!

Page 34: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

q`� �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

ql,4q

l,0ql,3

ql,2q

l,1

Gh τ1

τ2τ1

τ2τ1τ0τ0 τ0

:

γα β µ

λ

α

qh,0

qh,1

γ

�������®�ml¤� � � ) �*$ �$ "�35"�� � ���2" +Gl, θ - "� �$ ��3��%+,"�3�) �!��:�" ��) � ��) �1!�) ��:���+,"��!

Gh

Z��YZ�� � � � g¨ª�N7P �%$/c ` T�` UmR7NQPÕ© ^7_J`x§M© c� ^ �tu;>bÕa���iu�ºs;�����_j��l�in_Xpn� ^ ���xs��;��� b�z��_j�jbcin_ Gh

��l�� �l ^ �;�axiu��l�� Sh

pul�iÊ���_�bc���xs�in�,l®³M��l��wxl��×s��*���;����in��� ^ l�iu���b���in�X�l��Wpu� ^ ��ts;����� Gh

�5inp,��_>���;s���jb�in����wxl���pn��W�;a��;�����*���`_�¡w�l�i²pu�´µ���`_��3a���pnl���� ��iu�;��_ s�in������*��� �;a������;���;�`_j×s;���`_j�~s�p�b�z�pu����3_ iu��s;���`_j�~s�p�b�z�pu��¨�

T = Tc ∪ Tu

l£��;_�_��m����s���� ^ ���ik_jin��� ��_]zobc����m�l��²s;��pupn�:���vp egb�p ^ ��b�zq�3_,��l���ina��Õb�l*zob�]���*l��*�������¡z�pn�m�¨eg�3a��3¬�����*���`_j:s;���`_j�~s�p�b�z�pu��Q�;_:l��&�������¡z�pn�º��e¤�;a������;���;��_��iu��s;���`_j�ts�p�b�z�pn��]�;_:l��Rpn��s���� ^ ���_����*���`_��l ^ ���xs��;��� Gl

� ^ ��l��¡��� ^ pnl��b�� ^ pn���in��´µ����×bc_�iu�����a���iu�(���¨���m{`��� � lÊ� ^ �~u� bÕa���in�¡���3_j�����in���jb���ºb��¡z�in��l�� _���pu��m�;a������;���;��_�X�in����i ��sÕbc_�in´µ�s����`_��ts�pub�z�pu�;m�3_ºin��s����`_��ts�pub�z�pu�;��opub�_���l�s3_jl���¡���s����`_j�~s�pu�m��z�_�����l��Xb�l×��ina��Õb�l&zobc����_:��ik_j�v_j�l�s;_�l��������º����_jin�m���ºs����`_��ts�pn��s������in_7bc��_�� � ·W£:£ �·Xlt_ ^ l�_�¬�£����`_�����p̬�£�����iu�_j���`_ � � � �n{���� l

��y�b��`_²pu�R�*�t��u�pu��������l�in_Gh

��pub�yx�`_j�1u;��v��l s����`_��ts�pn��l��Sh

�c�`b��jbc��_�iujb��`_²pu�;� ^ ��s;i �os�bc_jin����Eh

��l ��ina��Õb�l �ob�l�_��Ê�;_>��e¤l����×s;��� ^ pu�Å¥�ik_j�*b��*��iu������in����� s;��� ^ b��jb�in���� ����s��;pupu� �Ï� �q��s;_�l������iu���s;_����*���`_��l��ºpu�¡�*�x�1u�pn��iu��in_jiub�p

Gl

l¨d®�¡s����`_��ts�pn��l��Xbc��iujb��`_Xl��Gl

��������l�in_ � ^ bc�_jin����ls����`_j�~s�pu�;l��

Sh

lÑ°,�V� �¨�3_vp e¤�������¡z�pn�X����mb�s3_jiu����:� �q��s3_jl��;��v�l��Gl

��axiubSl

�����`_v��z�_j�;��l��� ^ b��p�b¡´µ����s3_jiu���&iu�`a��;����

θ−1���;�b�s3_jin����:� �q��s3_jl��;�� ^ b�� Sh

�l���pu�X�*�x�1u�pn�X������l�in_Gh

l� �o� ��eg�Å¥ ^ puins�in_����ºp e bcs;_jin��� ��� Sl

�l��Gl

�¨�l ^�^ �������Ww�l���pu��s;���`_j�~s�pu�;l�� Sh

b�l�_j����iu�¡p e¤�;a��3¬�����*���`_

τb ^ �~u��l����&��w�l��;��s�� t ∈ Eh

��� "��tτ ∈ Eh

l,³(b���p egin�`_j������;��i�bciu��� ��l�s�b��ob�pθ−1

pu�s����`_j�~s�pu�;l��

Sl

��� ����ik_�p�b&s�������b������θ−1(tτ)

lÊrtl ^�^ ��������w�l�� t = θ(s)�®�obc���s�� sÕb�Wp�b?s;����¬

�×b������θ−1(tτ)

����ik_vb�l�_j����iu���R_���l��pu�;v�3a��;�����*���`_jmw�l�i � � ^ b���_jiu�����>p eg�3_7bc_ δl(q0,l,s)�o��u����;��_

a����ml��V�3_7bc_mbÕy`b��`_vs������*�X�;a������;���;��_m��������_jin�τl

�ml _��jbÕa��;�������s;�;_�_�� ��� ^ ������b���s�� �;��_���� p egb�s3_jiu��� ����s�����_��ts�pn��������ika��Õbcl ��b�l�_��;_�s;��pnpu�¡��l��ina��Õb�l�zob���`pn�R´µ����s3_jiu���������*���`_]���*z¢��l�s�pn�:´µ�����*������l*��ika��Õbcl�zobcQ�;_]���������m��pu����pn�R_j���;���tu;����l�ika�bc��_��� � �/RÑ© $�� ` Z�� �1� � a�PSW � b _YW P ��Tʧ N�W eQ` bo§ �Vb c ��� �;[ � � �� ) � �!�;9 ��� 9 !�)�"

Gl

9 ��� �) �� ��� �.9 ��� El := θ−1(Eh)

) � + �$��� � �5"�35"89 ��1���� ) � �$ "����� 35" �!��:�" ��)

Page 35: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � ��������� ����� �� ��������� ��� qmq

'��*9�� ��+ ���798+,"�- ��� �� "�����!�#"%$&"��! "�� '��*)!�%+,"�-/"��0$&12"���)��!��:�" ��) '��*9 "29� ���� "��$ ��+ '

L(Sl/Gl) = SupC(El)

Z��YZ�� � ��� \]R7N�cfW cIPXb N�Um`���W ��©Sb�© U ��W ��§�` �egb ^ �~u�×pn�Ï_��������tu��*� ^ ���;s��������`_Õ�Qpu�&´µ����s3_jiu���������*���`_���� zq��l�s�pu�$´µ������;�V��l ^ ��ts;����� Ghs;��l ^ pn� �?���� �l ^ ����axiu��;l�� Sh

�¨eg�;_ ^ b�X� ^ _jiu��b�p � L(Sh/Gh) ⊂ Eh � l5£��;p�b×axiu�;��_W��l=´ b�ik_Xw�l��p e b�s3_jin��� ��l l ^ �;�axiu��l��>��l ��ina���b�l z�b�>s;���`_j��b�iu�`_Wpu�*s���� ^ ���_����*���`_W��l ^ ��ts;�����*��l ��ina��Õb�l�obcl�_flq��iu���i �¢p e¤iu�`_�������ius;_�iu���V��e¤l��=�;a������;���;��_>b�l=��ina���b�l zob� ^ ��lt_����`_j��bc¾����;�ºp e¤iu�`_�������ius;_�iu���Ï�i̬�¡l�pn_7bc�����X��� ^ pnl��in��l��:�;a������;���;��_����i �¨�;���;��_�vb�lV��ina���b�l$�ob�l�_ � �o��l���*�,l � � l

τ2c

τ1c

τ0

τ0

τ0

τ0

τ0

τ0

τ0

q8,l

q7,l

σα β υ

γη

ϕ

ν

�������®�ml ����� " "%$ � +," 3� 1� ��$ �9 � �$�� "����$� �7"29

£�����iu���;������Ïp e bcl�_j����bc_��Gl

��� p�b �o��l����T�ml �9l� ºb���Ïs;�;_Vb�l�_�����bc_j� pn��$���;lt¥J�;_jbc_jql,7�3_

ql,8

����`_>����>�;_7b\_j ^ b��_����ob�in���; ^ l�iuwxl¨egl����?iu�`_j�;����ins;_�iu��� b�l ��ina��Õb�l �ob�l�_>���*p e¤�;a��;�����*���`_s;���`_j�ts�p�b�z�pn�

τ2c

��m_j�jbc��l�in_ ^ b��Ql����ºin��_������ius3_jiu���×���mp e¤�;a��;�����*���`_�s;���`_j�ts�p�b�z�pn� σb�l?��ika��Õbcl&zob�

� atiubθ−1 � lc ºb����s;�RsÕbc τ1c

����bº���`b�pn���*���`_Êiu�`_j�;����ik_Õ� s��Rw�l�i ^ �;l�_ 3_j����� ��obc��_(sÕb��Ê��������l��ob�ik_j� lfhp,���_ �$����_j�;�Xwxl���s;�;_�_�� �in_�lobc_�iu���=��� ^ ��l�_�� ^ �������`_j�;�>w�l�� �obc���pu��sÕbcW������;_jbc_j ^ b��­¬

_����ob�in���; l5°,pupn����_ ^ b���s;������;w�l����`_�pub$��b�iu��� ^ ��l��Wpub�w�l���pnpu�¡pn� p�b�����b�������� zq��l�s�pn� ´µ�;���*��� ��l��ika���b�l��ob�l�_���eg�;_ ^ bc�� ^ _�iu��b�p � L(Sh/Gh) ⊂ Eh � l�� �o�����:��Õb�pniu��;�(s;�;_�_��R� ^ _�iu��b�puik_j� ��� "���bÕa���in�L(Sh/Gh) = Eh = θ(SupC(El))

��inp(´ b�l�_ ^ ���xs�������� �&l���� �� ^ b��jb\_jiu��� ����W�;_7b\_j ^ b���_j����b�iu���� � �n{���� lÑ»m���W´µ��in:s��3_�_j� ^ ��ts;����l����W���Õbcpuiu���c������l�v��z�_���������ms;��wxl�iM�;_mb ^�^ ��pn��p�b�s������iu�_7b���s����in����b���s7��inw�l��,l�£��Xs�����s�� ^ _ ^ �;���*�;_����º����b�puin��;��p e¤� ^ _�iu��b�puik_j�:bcl?��ina��Õb�l&��b�l�_Rs;���*���mpu���*���`_j��pn�º_j���;���tu;���Xl�inacb��`_®�� �%� RÑ© $ � ` Z�� �� ��� "��! 8) � ��) �*$ �$ "

Gl

3�) �!��:�" ��) '��*9 � � �����("� Eh ⊆ L(Gh)

� ���: � 35" ���21*)�" "� �%+ �;9 "� �����9���%� >�(�"���( 79�<0�'�� � � EB,.6.@3� � ��'.+-, EB��+-�

Gl

�3>�+/'�� ���%� �8+/0�' J ( �:��� =8,#�#+&( �3��+;�2��> 6�J %8+ � +&>;�2��$-+-���2��(�$-�*>

Page 36: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

q�� �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

�����! �76*+ � '�+,"�� � + ���795'θ(SupC((θ−1(Eh))) = Eh

d,e¤��z����s3_jik´���pn��zob�p¢atin�� ^ b���p e¤l�_�iupuinjbc_�iu��������p�b�_���l�s3_jl������in����b���s7��inw�l�����_m������s>���������l�in���p�bÏ_jb�iupnpu�¡�����s;���`_j�~s�pu�;l���>yx�`_j���3_jiu��¡�;� ^ ��ts;���ob��`_ �Vl���������s;��� ^ ��in_�iu��� ��� ����lt¥ ��ika���b�lt¥��iu�;�jb��s7��iuw�l��; lm£�� ^ ������b��`_ s��3_�_�� ���;s���� ^ ���ik_jiu������� ^ �;���*�;_ ^ b�$��� �`b���b��`_jiu�&p eg� ^ _jin�×b�pnin_�����l���_j��l�_�b�l���ika���b�l��ob�l�_ l²£��;__j�$�������i u;���&���$���jb=��Õb�pniu��;�&w�l��$�iRpub ����_jin���T���&s;�����in_jb���s����iu�;�jb��s7��iuw�l������_²a����i �o�;���µp�bº���;s�in�iu���*���vs;���`_j�~s�pu� ^ �iu�mbcl���ika���b�l �ob�l�_]����s�����_��jb��iu� ^ bc]s;��pnpu�wxl�iM�;_ ^ �iu���bclV��ika���b�lVz�b� � l

B�� B���� � -9.�4�5 -�4�.1A��68 <�.�>K.15��68�� 4�A 2�8�� -/.�8���4�<=A ºbc�� �g£��ob����$�5pu�;�bÕacb��`_7b�����v����mb���s7��in_j�;s;_�l����;m���;s��;��_��jb�pniu���W�;_m��iu�;�jb��s7��iuw�l������`_m�;_j�W�3¥�¬

^ pu��ik_j�;�� l� m��lt¥×��ina��Õb�lx¥*��iu�;�jb��s7��iuw�l��;Q���`_Rs������in����������l��×��ina��Õb�l�zob�]s����`_j�;�ob��`_Ql�� ^ ��ts;�����Gl

s;��l ^ pn� �*����lt¥Vl ^ �;�axiu��l��ºpu�xsÕbclt¥ S1,l

�;_S2,l

�;_ml��¶��ina���b�l �obcl�_�s;���`_j�;�ob��`_ºl��¶���x�1u�pn�b�z�_��jb�ik_

Gh

s���l ^ pu�*bÕa��;s×���;lt¥ �l ^ ����axiu��;l��� S1,h

�3_S2,h

lÊd®� ��ika��Õbcl zobc>�;_>�¡l���i,��� ���;lt¥sÕb��obclt¥ ��egin��´µ����×bc_�iu���

P1

�3_P2

_7bc����iuWw�l��*pu��W���;lt¥ ��ina��Õb�lt¥ ���`_����puin�� ^ b��Wl�� _j����iu�i u��*�sÕb��obcp®��egin��´µ����×bc_�iu���

θl

S1,h

S

θ−1

1,loc

,locS2,h

S

θ−1

2,loc

,loc

G2,l,loc

G1,h,locG2,h,loc

G1,l,loc

G

G

h

θ

P1,h

P1,l

P2,h

P2,l

�������5�ml|v�� � �0)!�� ) �7" 35" �����! "�76*+," � �$��9%) ��"��0: �,9������ � � 1�� �$� ��� � !�)�"�3$�,9� "��� '�)�12"

d5b _j�l�s;_�l���� ^ ��� ^ ����� ^ �;���*�;_v������iu_���inz�l�����pn��v��i��q������`_j�;m_ �cs7����m���>s;���`_j�~s�pu�W�����i������t¬_7b�pn���*���`_X�;_Xa�����_jius�b�pu�;���;�`_fl®d,e¤l�_jinpuiu�bc_jin���Ï�����l ^ ����axiu��;l���W���;s����`_��jb�pniu��;X�ob����l�����_j�l�s;_�l������iu�;�jb��s7��iuw�l��V���¶�*�t��i �o� ^ b��p�b ����_�iu��� ���¶s;�����in_jb���s��V��iu�;�jb��s7��iuw�l�� ^ ���;��;��_���� ^ ���s;�����;� ¬���;��_ l¢ ����� ��*��p�b ����_jin���Ï���>��������b�puik_j�X�;_ms���������a���� ^ ��l���s7�obcs�l��=���;����;lt¥V��ina��Õb�lx¥ lqd®���l ^ ����atin��;l���¡����s7�obcwxl��×��ika��Õbcl ���`_�������s�� ^ _jin�×b�lx¥=���l�>pn��W� ;���;�s�������in_jin����Xw�l����ob���l����W_j�l�s;_�l����W�in� ^ pu���*���`_:����s��;�`_j�jbcpuiu��� l¨£�� ^ �;���ob��`_mp e¤l�_jinpuinjbc_�iu��������s��;__j�W_���l�s3_jl���>�� ^ �����l��ºl������`y ^ �c_j�1u;��¡´µ����_j�W���¡�����¶s���� ��ius;_�lob�pnin_j���;��_����>pu��m�l ^ ����axiu��;l���Xpn�ts�b�lt¥Ï���>s7�ob�w�l�����i̬a��ÕbclT��iu�;�jb��s7��iuw�l�� lÊ�v��l�>���;axin�����������>�l��Ws��3_�_j�×b ^�^ ��ts7�����M�;_¡pubÏ��pult_jiu��� b ^�^ ���_j�;� �$s��3_�_j������_j�ius;_�iu���¨���ob����pn�Xs7�ob ^ ik_j����l�inacb��`_fl

Page 37: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � ��������� ����� �� ��������� ��� q`�

B�� B�� � � 0�+�5Q? 4 �98�0�+

 ºb����s��3_�_��>��s;_�iu���V����l��bÕa����� ^ ���;��;��_��¡pu�;ms;����s;� ^ _�����Wzob������Wp�b�_j���;����in�>��l¶s�����_��ts�pn�^ bc���l ^ ����axiu�in��� b�in���itwxl��:��i��q������`_j�;]�_j�l�s;_�l����;]lt_jiupniu�b��`_(p e b ^�^ ���xs7���R��yx�obc��inwxl��,l`d®��_jb�z�pu��b�l�mlk���g£��ob��������*���`_j��� � ^ b���_jiu�M��e¤l�� �3¥t��� ^ pn�Rw�l��Rpu�;,b ^�^ ���xs7����,���;s��;��_��jb�pniu����,�3_,��in���jbc��s7��inwxl���^ ������3_�_j�;�`_¡��e¤��z�_�����in�����;��*�t�1u;pu�; ^ pnl� ^ �;_�in_��w�l��?s;��lt¥ ��z�_�����l� ^ bc��p egb ^�^ ���xs7���×s;���`_j��b�pui̬��� ���Xl

PP

PP

PP

PP

P

¹V�x��lrx_���l�s3_fl £��;�`_j�jbcpuiu��� ¹Ï�t��l�p�b�in���  m��s��;�`_j�jbcpuiu��� ½miu�;�jb��s7��iuw�l��

³,���xs��;���G = [32,176] G = [32,176] G1 = [4,16] Gl = [32,176]

G2 = [4,12] Gh = [1,3]r ^ ��s�i �osÕb\_jiu��� EB = EB1 ∩ EB2 EB1 = [3,29] EBl,loc = [3,14] EBl = [3,29]

EB = [9,78] EB2 = [3,30] EB2,loc = [3,12] EBh = [3,6]¯o����s3_jiu���������*���`_

K = [128,496] KM1 = [64,288] K1,loc = [8,20] Kl = [64,288]�;�Vz¢��l�s;pu�º´µ�;���*���KM2 = [64,304] K2,loc = [8,16] Kh = [3,6]

����� �M�mlk��� � �*$ � �$�#�$�,9 ��� 9%) �8) � "#" "%$ � +,"�35"29�3$� ��1��7"��! 9 �2129%)5+ ��$ 9

d®� ^ ���z�p u��*�����>p�b*_jb�iupnpu�����;º���x�1u;pu�� ^ ��l�_X������s� 3_j���>�×b\¾u_j�iu�W�;�=����s;��� ^ ���b��`_Xpu� ^ ��c¬s;�����¡�3_ �c��l=p�b� ^ �;s�i �osÕbc_�iu���¶���pn��� ���;X_���l�s3_jl����X�*�t��l�p�b�in�����o����s��;�`_j�jbcpuiu���c�¨��in���jbc��s7��inwxl��¡��l��in����b���s7��inw�l�����in_���iuz�l���� l¨�v�Õb����*��in��ms;��Xb ^�^ ���xs7���; ^ ���;����`_����`_�w�l���pnwxl���Xiu��s����`a��;��iu�;�`_jXw�l������l� ^ ��lta����������l����;�v�;�Ï_�����in ^ ��iu�`_j���,lm°,�&s;�Xwxl�i�s�����s��������p�b��_j�l�s;_�l����X�*�t��l�p�b�in���c�`����s;���`_j��b�puin����X��l&��iu�;�jb��s7��iuw�l��X��in_���iuz�l����c�p e bcs;_jin���*�iu��l�pn_jb������m���m_���l�Rpn��Rl ^ ���axin���l���:�l��Rpu� ^ ���xs��;���º��pn��zob�p ^ ��l�_:�;�����;�������;�Rl��z�pu�xsÕb�������lV�yx_ u;�����

�/lmd®�;vs;����s;� ^ _�m��bc_j������bc_jinwxl���Rl�_�iupniu��; ^ ��l�a����`_�����������Wp�b ^ ���l�a��>�3_mpub�a��;��i ��sÕbc_�iu���$��ik´�¬��s�iupn�,l�£�eg�;_mpu�XsÕbcv������ b � p�b�������×b�pnin_�� ^ ��l���pu�;:_���l�s3_jl����v����s;���`_j��b�puin������3_m��iu����b���s7��iuw�l�����iu�_j�iuz�l��;����µz � p�b������$s���� �oius3_jlobcpuin_��º�ob���vpn�XsÕb������pub¡_j�l�s;_�l����W�*�t��l�p�b�in������µs � p�b�s;�����in_jb���s��:��iu����b���s7��iuw�l��R�obc��,pu�;�sÕb�,��iu����b���s7��iuw�l��R�3_,��iu�;�jb��s7��iuw�l�����iu�_j��inz�l��;� �

q9lvpn��´µ����s3_jin�������;���;��_v�;�Vz¢��l�s;pu�º´µ������;�X��e¤��_ ^ b�:_���l ���l��:� ^ _�iu��b�p l

���������9> =��B+&� @9� �*��' � J ��'.+&��'�$ � J � �9�#> =8, E �2��$&%B>&� ��$&,���,#>-( +&( ,#� 6.� >�+-$&'F= +&'�$&� �9( %3$&��$$= ��(!0�'��B6.(�>�+-$&( @�'�%�� ��'.=��'.+&$-�*>/>�+-$&'F= +&'�$-�*>�� � � �IH �8+5� J �8=.�<EB����� '.+&( ��(�>-% �*> +/+&$-,#� >�( EB��� � �2,#'�$�EB,���+&$-�3$ � J ( ��+&%�$&48+�6.�0=8�8+-+-� ������$&, = ��� �9��$$&������,�$-+;��'.= >�+-$&'F= +&'�$-�*> 6.%#=�����+-$ ����(!>�%3�3> ,�' ��(�%�$ ��$ = ��(�0�'��*>

Page 38: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

qmv �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

���� !#"Ï"&%Ê'*),+$-[A�2MU�254��*0$-

d,egb ^�^ ��ts7���&�_7bc_�iuw�l��?�;_ l����Vb ^�^ ���xs7���&���×yx�`_j�1u;��¶w�l�i���� ^ ���&�l���l��T�;����;�¡z�pn�&��egin�t¬´µ������bc_jin����W���;p�bc_�ina��; � p e¤�;_jbc_¡s;��l���b��`_ ��lTyx_tu��*�$�;_�������_¡p egb�s;_�iu��� ���?s����`_��ts�pn�?���_ ���;�����iu����� ^ �;�����;���*���`_�����p e¤��in_j����iuw�l���������;a������;���;�`_j l¢ ºbc���s��;__j� ^ b���_jin�º����l� ^ ������`_j����m���;lt¥´ b���inpupn��º��� _j��bÕa�bclt¥ �� ^ p�b �Õb��`_W�ob���>pu� sÕbc�����*���*s��;__j��b ^�^ ��ts7���,lM¼Ê��lt_>�¨e b�z¢���� ����l�>�3a��c¬wxl�����*pu���_��jbÕacb�lt¥�zobc���*�l��*pn�� b�lt_j����bc_j�; � �3_7bc_� ��� iu��iu_jb��`_ ^ b���_jius;l�pui u�����*���`_��l��*pn��b�l�_j���×bc_���º��iu����b���s7��iuw�l���Ol®�m��l�Xb�z¢����������º�;���l�ik_j�¡pn��Xb ^�^ ���xs7���;Wz�b���;��X�l��Xl�����´ b��*iupnpu�����´µ������b�puin��*��]_j�tu;���� ^ b�����l�� ^ ��l��:p e¤�;_�l��������;�rt°]  �Ñpn��v±v�;���b�lt¥Ï���W³Ê�3_j�i l

B���� �~B �4 -90�� >E-9A � A - ��.�<=2�8�5 >E- �Z�� k �YZ�� Z �&§�PXR � b9PX`/c�U�_Jb cfc W ��§�`/c

£����*�¡l������*���`_*b ^�^ ��pn���&yx�`_j��u���Ï���$s�����_��ts�pn��l�� ^ b�����;_j��l�����e¤�;_7b\_ �¤±��nz�xcz � ��� ¼Ê�� {��$� �� " >¹y{,q$� ��)"X�ob������ �®s;�;__j��b ^�^ ��ts7��� �� ^ ���� �l��Wp eglt_jiupniu�bc_jin���¶��e¤l�� b�l�_����×b\_j��s�pub��iuw�l�� ^ ��l��p�b����x����pniu�bc_jin���¡��l ^ ���xs��;��� G

�µ_j�;pow�l�������l�²p egb�a�����]��� ����i ^ ��l��²p e b ^�^ ���xs7����s��;��_��jb�pniu��� ^ b�����,q � �;_v��� ^ �����insÕbc_� Pi

^ ��l��:pu�;: ^ ��s�i �osÕb\_jiu���� l³Êb������ �o��ik_jin�����,l�� ^ ������iusÕb\_ P

���_×s;�����_j��l�in_��l���p e¤�� ^ b�s��V��eg�3_7bc_�×���Vp egb�l�_����×b\_j� G�;_

s�������� ^ ����� ��l����Qs����`_��jb�in��_���l���p e¤�;_jbc_Ê��l¡yx�_ u��*�,l�¯o�����*��pnpu���*���`_ P���_�l����Q´µ����s;_�iu���>��� ����iu�

�l��Q_���pupn�Xw�l����

P : Q −→ {0, 1}

P (q) =

{

1�i

qjb\_jiu�´ b�in_Rp�b ^ �� ^ ��in�;_�� P

0�iu�����

d®� ^ ������iusÕb\_ P���_ºs�����_���l�ik_ � ^ b��_�iu�v����pub�s����¡z�iu��b�iu���Vpn����inwxl��W���� ^ �����insÕbc_� Pi

��� ��s��b�lt¥�� ^ �;�jbc_���l������Rpubmpn����iuw�l��Qzq�x��pn�����������\pu� �v�;_ � � Pi∧Pj � �cpn� ����l � � Pi∨Pj � �;_,pubm���;�`bc_�iu����¬Pi � l ��in�������`_j�;����l>pu��®�~u���pn��®���²p e b�pn�mu�z�������� �Q�t��pn���egb ^�^ puiuw�l��;�`_Êl��5pu�; ^ ���;��ius�bc_j�� ^ ��in����ik_j��;���iu�_j��inz�l�_�inaxin_�����t�tu;��pu�;v���> m��¹Ï�����`bc���o�;_�s,l

d,e¤�������¡z�pn�¡���;º�;_jbc_jXb\_�_j�;iu����b�z�pu�;R(G, P )

���_�p e¤�������¡z�pu������º�3_7bc_�º���; ^ ��s;_jb��`_�pu� ^ ���Ŭ��ius�bc_

Pl�d,eg�Å¥�in_�����s;�>��e¤l��Ï�l ^ ����axiu��;l�������s;���in_��>w�l���p eg�3_7bc_:in��in_�i�b�pÑ��� ^ ��s3_j�Wpu� ^ �����insÕbc_ P

�;_wxl¨e � ^ b��_�iu�º���*�¨egin� ^ ���_��¡w�l���p²�3_7bc_��bc_jin´ b�injb��`_�pu� ^ ������iusÕb\_ P

p e¤�ts;s�l�����;��s�� ����_j��l�_W�;a��;���3¬���;��_(iu��s;���`_j�~s�p�b�z�pu�

σ ∈ Σu

� u;���²a�����l��¡�3_7bc_Ê���; ^ ��s3_7b��`_²b�l���ixpu� ^ �����insÕbc_ Plc£��3_�_j�Q�������i u;���

s�������in_jin�����®b ^�^ �;pu�;� Σu

¬hiu�`acb��i�b���s;�¡��l ^ ���;��ius�bc_ P�¨��_>b���b�pu����l�� �&s��;pupu�����*pub&s����`_j�~s�p�bcz�iupnin_j�

�ob���vp egb ^�^ ��ts7���X��yx�ob��*iuw�l��,l°,�¡���Q���3_j����b��`_�w�l���pn��Ê�;_7b\_j(�bc_jin´ b�injb��`_

P�\p e b ^�^ ���xs7���]_jbc_jinwxl���s�����_���l������pubvs;��� ^ pu�3¥tik_j�

����sÕb�pns�l�p�s�b��,��pnpu�R�3axin_j��pubº�������;�jbc_�iu����s;��� ^ p u3_j�:���:p eg�;����;�¡z�pu�:����,_j��b ���s3_j��in����,�¨eg�3a��������*���`_jOl°²��s;� ��;��?�;pupu� ^ ��l�����b�in_���;�¡z�pn��� ^ pul� ^ �;�_�iu���;��_�� w�l�� p e b ^�^ ���xs7���¶�tyt��b���inw�l��¶s;� ^ �����obc��_^ ��l��]pubºs�����_j�l�s;_�iu���*��l ^ ��ts;�����v����l�²���_�����,_j��l ���l��²_���inz�l�_7bciu��������p e¤�3¥ ^ pu���iu��������p e¤�� ^ b�s��

Page 39: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � ��������� ����� ����������� �V� q�x

��e¤�;_jbc_j�w�l�i®s;����¾n_��jb ^ in�����*���`_vbÕa��;s>pn�X�����¡z����X�����*�t�1u;pu�;:�×b���i ^ l�pn��Ol

Z�� k � Z�� k �&§=PXR � b�Pf`9c ��W ��©Sb�© U �VW ��§�`9c ºb��� � ¹ W�`�����3_ � W¹¶�mq���pn��=b�lt_j��l��� l�_�iupniu��;�`_¶l��}´µ������b�puin��*�=��� ��� ^ ���;��;��_jbc_jin������l

^ ��ts;������iu�� ^ iu������� rx_jbc_j�;s7�ob���_j �¤½�b��tz�x�� �Êp e bcl�_j����bc_��*��iu����b���s7��iuw�l�� � ½�¯,r�¹ � � � "��#� ��� ��� ��+�) �!� " 9� �$ "!$ � ��� � �#"29 � � �R½�{mq��mw�l�i ^ ������3_×l����V�� ^ �����;�`_7bc_�iu��� ^ pul� s�����s�in��¶����×r�°²  l�³Êb�����'�o��ik_jiu�����²l�� ½�¯,r�¹ �;_&l��Jb�l�_j���×bc_�� � �3_7bc_� �o��in?�ob���?pu�;wxl���pºs;���_jb�iu��×�;_jbc_j ^ ��lta����`_ 3_j���V�jb � ���;?�����¨e b�lt_j���;?b�lt_j����bc_j�; lQ¯o�����*��pnpu���*���`_ l��J½m¯,r�¹ �;_×��� �o��i ^ b���pu�V�t¬hl ^ pu�;_�(K1, K2, ..., Kn,R)

��,+K1

�;_�l������_j�l�s;_�l����>���>��ina���b�l¶��b�l�_ ^ �;���*�;_�_jb��`_�l������*�t����puinjbc_�iu���b�z�_j��b�in_��º�;_v�����Ï���;_7bciupupn���º��lÏ�yx_ u;��� lq£��W��ina���b�lÏiu��s;pul&pu�;�b�l�_��������ika���b�lt¥$�����*�t����puinjbc_�iu���Ki

�l��w�l�egb�lt¥ ���;����in���W��ina���b�lt¥Km,...,Kn

�����`_�p e¤�� ^ b�s;����e¤�;_jbc_j���� s;���`_jiu�;�`_�wxl������;��;_7b\_j�����iu��b�iu��� � � lÊd®��¡�_j�l�s;_�l����;

Ki

����`_����;�b�l�_�����bc_j�;>������_�p e¤�� ^ b�s��×��eg�3_7bc_� ^ ��l�_ ;_j��?b�l��c¬�*���`_j� ^ b���p e¤iu�`_j�;���jb\_jiu��� ��e¤l����������¡z�pu� B

��eg�3_7bc_� ^ b���_jins�l�pniu���¡b ^�^ �;pu�����b�s;���c¬ �;_7b\_j l(d®��l���;s���ik_jl���X�×b\_j���;�×bc_�iuw�l��º�;_m������s�l��$w�l�in��_�l ^ pn� Ki = (Qi, Bi, Σi, δi, Q0,i, qm,i)

bÕa��;s���

Qi, Σi, δi

����`_Xpn��ºs;��� ^ ���b��`_jXs�pub��iuw�l��;º����Wb�lt_j����bc_j�; �?�3_7bc_��� �?�b�a���iu��p e¤�������¡z�pn�������;_jbc_j;�op e¤�������¡z�pn�X����v�;a������;���;�`_j��3_vp�b�´µ����s3_jin���&����_j�jbc���ik_jiu��� �

�Bi

��� ^ ���;����`_�� p eg�;����;�¡z�pn� ��� _���l� pn��¶��b�s;���c¬ �;_7b\_j¶��� Ki

lm��l���ika���b�l�pu� ^ pul�¶zob��Km,...,Kn � Bi = ∅

��

Q0,i

��_ºp e¤�������¡z�pn�>����º�3_7bc_��iu��in_jiub�lt¥?���Ki

lq³Ê��l��i 6= 1

s��3_º�;����;�¡z�pu� ^ �;l�_�s;���`_j�;��iu�^ pul�iu��l���:�;_jbc_j�in��in_�i�b�lt¥�s7����iu�in:���$´µ����s3_jiu���Ï���Wpub�´µ����s3_jiu��� Ii

^ ���;����`_���� ^ pul�:pn��iu� ��

qm,i

�;_mp e¤�;_jbc_:��b���w�l���l���inw�l�� ^ ��l��:s7�ob�w�l�� Ki

ld5b*´µ����s;_jin���

R = (Yi,Ii)i∈J

bÕa���sJ = {1 ≤ i < m | Bi 6= ∅}

sÕb���b�s;_�����in��>p�b ��iu�;�jb��s7��iu���;_pub¡s���� ^ ���in_�iu���×���`_j��>pn��:_���l�s3_jl���� Ki

bÕa��;s���

Yi : B −→ 2Ki+1, Ki+2, ...,Kn�;_&l���� ´µ����s;_�iu��� w�l�iXb���xs�iu� � l�����b�s���c¬h�3_7bc_

b ∈ Bp eg�;����;�¡z�pn�¶���;&_j�l�s;_�l����;Kj

� bÕa��;sj > i � b�s3_jika����;&�in�¡l�pn_jb����;���;��_���� b

l�d5�����w�l��pn�?yx�_ u��*�&_j��b����ik_j�&�obc���l����×bcs����\¬h�;_jbc_

b�(_���l�_j�; pu����_j�l�s;_�l����;�bc���xs�in���; �

b����`_

bcs;_jika��;����;_viu��in_jiub�puin��;��]�ob����l��Ï����pu�;l�����;_jbc_j�in��in_�i�b�lt¥ ��

Ii

�;_,pubm´µ����s3_jiu�������'�o��iujb��`_²p eg�;����;�¡z�pu�Q����(�;_7b\_j�in��in_�i�b�lt¥�b�s;_�ina��;�pu�����w�l���p e¤�ts;s�l��������s���¨egl�� �3a��������*���`_�´ b�in_��;a���pul��;�Xpu�¡�yt�_ u;��� �ob���Xl�� �×b�s;���c¬ �;_jbc_

bl∀b ∈ Bi

�¨p�b�´µ����s;_jin����;_���� �o��in� ^ bc� Ii(b) : Πj∈Jb

Q0j −→ 2Σi�(�,+

Jb

���_�l�� �;����;�¡z�pu�×�����in����ius;��j 6= na����i �Ñb��`_

Kj ∈ Yi(b)l

rtl���p eg�Å¥��;� ^ pu�X����p�b ����l���� �mlrxt�op e b�lt_j����bc_j�m��iu�;�jb��s7��iuw�l�� ^ ������`_j�>���s���� ^ ���������w�lobc_������ika���b�lt¥

K = (K1, K2, K3, K4)lÊd®� ��ika��Õbcl �ob�lt_

K1

�*�t����puin��¡pn� s���� ^ ���_j�;���;�`_���pu��z�b�p���l�yt�_ u;���m�;_Rin��s�pnl�_²_j��lt_j��Qpu�;Q�_j��l�s;_jl���������l�­¬ ��b�s;���`_j�;

K2

�K3

�;_K4

ltd,eg�;����;�¡z�pu�m����Q�×bcs����\¬�3_7bc_�

Bb=���;lt¥ s���� ^ ��jb��`_� {b1, b2}

�,�,+b1

s�����_�iu�;��_*���;lt¥��_j��l�s;_jl�����K2

�;_K4

�3_ �,+b2

�������/��%�+&� + �*> +56.( +/,�$ 6.(��9��(�$&��>#J (��1��� =3��$ � = +&%�$&(�>-��0�' J '���� >-��'9� �<� =8+-( L ( +&%

Page 40: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

qmz �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

b

b

1

2

K

KK2

K1

a

b

c

bb

d

c

K2 K3 K 4

2

4

f

f

f

K33

4 5

6

7

8

9

10

11

12

13

b c

g

�������®�mlrx���� " "%$ � +," 3� ) � ��) �*$ �$ " � � 1��#�$����� � !�)�"

s����`_jin���`_¡l�������l�pn���_j�l�s;_�l����K2

lMd®����wxl���pn����ika���b�lK1

�;a���pul��*a�����>pu�*�×bcs����\¬h�;_jbc_b1

�5�l���ts;s�l��������s��v���

b��l

c��pu�;²b�l�_j���×bc_���

K2

�3_K4

����`_Qb�s;_�ina���²�;_²in��in_�i�b�pniu��;Êiu�¡l�pn_7bc�����*���`_fl�rtl���ts;s�l��������s�� ���

bp eg�3_7bc_ºiu��ik_ji�bcp®���

b1

�;_(q3, q10)

b�pu����ºw�l���l��X�ts;s�l�����;��s�� ���cs��3_��;_7b\_���_

(q3, q12)l�³Ê��l��,b�zob������������;�,pu�Q�×b�s;���c¬ �;_jbc_

b1

��s7��b�w�l���_j�l�s;_�l����K2

�;_K4

���Y1(b1)

����ik_,bÕa���iu��;a���pul��;�X�ob���:��� ^ ��� ^ ���X�3_7bc_ ���ob�p¨�3_�bc__j���������Xp eg�xs�s;l��������s;�º���Xp e¤�;a������;���;�`_ b

l�d5b¡_j�l�s;_�l����K4

��_ml��Vb�l�_����×b\_j� ���;_jbc_j �o��iu�s�pub��iuw�l��Xs�e¤���_¬ �\¬h��in���X��� ^ ��l��axl¶���W��b�s;���c¬ �;_7b\_j l

£���´µ����×b�pniu���>b&�;_j� �Å¥ ^ pu��ik_j� ^ ��l��Xp�b?�yx��_��1u��×��� s;���`_j�ts�pu��l�� ^ b��Xp egb ^�^ ���xs7����_jbc_jinwxl��,l£������*� ^ ��l��Êpu�;Ê_j��bÕa�bclt¥ ^ ���;����`_��� ^ ���;s��;�����*���;�`_Õ��pubm�_j�jb\_j����iu�]���Rs�����_��ts�pn���Rzob��:b�pu����M�l��p�b×���c_jiu���¶��e¤�;_jbc_jºin�`_j�����in_���3_X���¡ ^ �;s�i ��sÕbc_�iu����m��s;��in_���º��l�º´µ������W��� ^ ������iusÕb\_j P

lq� �o�=������Õbcpuiu���5p�b�yx�`_j��u�������Qs;���`_j�~s�pu�;l���;�\inp`���_(���;s��;�jbciu���Q���]���;a���pu� ^�^ �;� Kf

p e bcl�_j����bc_��,��w�l�inacb�pn���`_�

K���ms;���`_j����b��`_:b�l�s;l��×��b�s;���c¬ �;_7b\_ ^ l�iu]��egb ^�^ pniuw�l��;�]pn��,_j�;s7����inwxl����s;p�b��inwxl�������m�yt�`_��1u��

� ¹���`��� l

·º�T���3_jin��������b ���&p egb ^�^ ���xs7���?���%�g¹���`���Rw�l��$pn�?���x�1u;pu�×��l ^ ���xs��;���$�`b������×����puin�iuz�iupuik_j�^ b��W�jb ^�^ ����_ �Ïl�� �*�x�1u�pn� ^ ���x��l�ik_�bÕa���s×����¡bcl�_j����bc_����s�pub��iuw�l���Ol�£�� ^ �;���ob��`_��Ê��l ´ b�in_���lsÕb�pns�l�p����

Kf� s��;__j�Qb ^�^ ��ts7������� ^ �;���*�;_ ^ b�M����� ^ pnl�Ê���Qs;���`_j��l�������Mpu� ^ ���z�p u��*�]�¨eg�Å¥ ^ pu��iu���

s����¡z�iu�obc_���iu��(���,p eg�; ^ bcs��²��e¤�;_7b\_j lÕ ºb���5l����,�Å¥x_j�����iu���>���s��;�`_j�� W¹¶�mq���pu�;5b�l�_���l��Êb ^�^ puinw�l����`_pu� ^ �iu��s;i ^ ����������s;��� ^ ��in_jin��� ^ b��(���;s��;��_��jb�pniu�bc_jin���¡����´ b ����� ��s�b�pus;l�pu�;�(l�� l ^ �;�axiu��l��,��pu��zobcp� ^ b���_jin�X��egl�� ���������z�pu������l ^ ���axin���l����pn�ts�b�lt¥ �yx��_����;_�iu�� �$s7�ob�w�l�����ina��Õb�l ��iu�;�jb��s7��iuw�l���������x����pniu�bc_jin����lx£�� ^ �����ob��`_Õ�Ñs��;:_j�jbÕacb�lt¥?��� ^ �;���*�;__j���`_vb�s3_jl��;pupn���*���`_ ^ b�:���W��b��jb��`_�iu��w�l��p egb�s;_�iu��� s�����s����*in_jb��`_j�$����*�l ^ �;�axiu��l��?pu�xsÕb�lx¥��l��*pu�Ï�� ��*� ^ ���xs������V��e¤��������������� ^ bc�l��z�pu�xsÕb����X��lV�yx_ u;���Ws�����_��ts�pn�,l

Page 41: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � ��������� ����� ����������� �V� qm{

B�������� �#< �/A=>�4�� 2�A���A -/.18°,� ^ b���b�pup u�pu�X����Xb ^�^ ���xs7�����wxl�i(���zob���;�`_X�l��mp�b _j���;����in�����;Xb�l�_����×b\_j��v�;_�pu�;�p�bc���`b����;

´µ������;pu;��pu�*±������b�l ���׳M�;_j�i]bÏ�3_j�*�3¥ ^ pu��in_j� �obc��>pn� s����`_j�Å¥x_j�*����pubÏ�yx��_��1u��,l(°²� � �q�;_�� ^ b���b ^ l�iujb���s������¡�����s;��i ^ _jin���=pu�W´µ������b�puin��*�W±v�o³J��;�¡z�pn� ^ ��l�a���in������*����in��� �×p egin��s�����a�����in���`_��b ���l�����l����x�1u�pn�&b�l�_�����bc_j� �=�b�a���iu��p eg�Å¥ ^ pu��iu���Ts;���¡z�in�obc_���iu��×���$p�b¶_jb�iupnpu�*��e¤l�� �*�x�1u�pn�s;����_���l�ik_ � ^ b��_�iu�®���]p�b:s����¡z�iu��b�iu���X��� ^ pul�iu�;l���Ol  ºb���Ms��3_�_j� ^ b���_jin��� ^ pnl�_ s�_5w�l��]��� ^ ���;��;��_�����;�Ï���;_7bciupu:s7��b�s�l����W����mb ^�^ ��ts7���;�l�_jinpuiu�b��`_Rpn��v±v��³²�����l�:������b�����������pu�;:���jbc���� ^ ��in��s�i ^ �;l�_�iupniu��; l�³(b��Mb��obcpu����in�,bÕa��;sQpub ^ b��_�iu�,�l��Mpn��Mb ^�^ ���xs7����M��yx�ob��*iuw�l��;�������l�(b�z¢������������5��egb�zq�����pn���b ^�^ ���xs7����*s��;�`_j�jbcpuiu���; ^ l�iu��;���l�in_j�&pn�� b ^�^ ���xs7���� ��in_���iuz�l����; l��@���c_j���$s;�����ob�in��b���s��c�b�l�s�l����&�_j�l�s;_�l����$��in���jbc��s7��inwxl��&��eg�;_ ^ �� ^ ����;� ^ ��l���p�b yx�`_j��u���Ï���&s;���`_j�ts�pu��l��� ^ b��¡±v�o³M�b�pn�����wxl��>pn��:�*��sÕbc��iu���;:��e bc�����;�`bc_jin���t¬ �����b������;�`bc_�iu��� ^ ��l���jb�in���`_��e y ^ � ;_������ r�£�{,z$� l

Z�� k � k �YZ �ha�aM© R�U ��`/c Um`/NQP�©Sb _YWYc � `9cd®�� ^ ���;��in����²_j��bÕa�bclt¥�l�_jinpuiu�b��`_]pu��Q±��o³, ^ ��l��QpubW�yx��_��1u�������s;���`_j�ts�pu��l���]����`_:s;��lt¥ ^ ���Ŭ

���`_j�;]��b�����)"W¹¶½�{�� ����l �¤½�"p{���� l�£��;�_j��b�acb�lx¥ ^ ���_����`_,l��,p�b���� �o��ik_jin��������±����Õb�lx¥�����³M�;_j�is;���`_j�ts�pu�� � ±v�o³]£Q_ � w�l�iÑ����`_Q�����±v��³²Qs���� ^ ���_jb��`_²���� ^ p�b�s;��]���vs����`_j�~s�pu� ^ �����*�;__7b��`_ �>����s;���`_j�ts�pu��l�����Å¥x_j����������egb�l�_�����in��;����l �¨egin��_������iu���pu�W´µ�jb���s7��iu����*���`_X���¡s��;�_7bciu���;�_j��b����ik_jin���� ld®�?s;���`_j�ts�pu�&���_Õ� ^ b���b��obcpu����in�×bclt¥T�_j�jb\_j����iu������&s����`_j�~s�pu� ^ ���;����`_����� ^ ���s��;�����*�*���`_Õ�,zobc��l��¡p�bÏ´µ�����¡l�p�bc_�iu��� ��e¤�;_7b\_j¡in��_������in_� l,£��;��;_jbc_j¡in�`_j�����in_�����`_ ius�i]�3¥ ^ �iu�*��¡��l�¡´µ������������b���w�lobc����Xin��_������in_� l¨fhp(�egb���in_º������sc��� ^ b��_�iu���¨egl�� �*�t�1u;pu�¡��� ±v�o³]£Q_W��� ^ ���;��;��_jb��`_�pn� ^ ��c¬s;�������;_vl��Ï���������z�pu������ ^ ��s;i �os�bc_jin����:�Å¥ ^ ��iu�*���;����l��pub�´µ�����*�X�����×bc��w�lob����;:iu�`_j�;����ik_j;��������3_j�;���*iu���;�:p e¤�3¥tiu�_j����s�����e¤l��Vs;���`_j�~s�pu�;l�� ^ �;���*�;__7b��`_�����s�����_���l�in���Xl��Ï���jb ^ ���������×bc��w�lob����;��� ^ ��l��axl×���vp eg�;����;�¡z�pn�v���m��b���w�lobc����²iu�`_�������in_jOl� ºb���]s���s�b������vl���s����`_j�~s�pu�c�`s�����_jik_jl�����e¤l���;����;�¡z�pu����� ^ pub�s��;:����s����`_��ts�pn���o��;�jb yx�`_j���3_jin��,lÑfhp®���jb ��ik_�� ^ _jin�×bcpqi���,lvpn��Q�×b��w�lob����;:bc_�_���in���ob�z�pn��]��� ^ l�iu:pn����b���w�lob�����iu��in_jiub�po�����_R��i��q������`_j:���;:�×bc��w�lob����;in�`_j�����in_���

�/lvinp¨�;_vpu� ^ pnl� ^ �;���*iu�in´ ^ ���iuz�pn����sceg�;_�¬ �\¬ ��iu��X��egin�`_j�����in_ ^ b����egb�l�_j���v�×bc��w�lob����; ld®� ^ ����z�p u��*�º��e¤�;_jbc_j�in��_������in_��b �;�`b�pn���*���`_��;_��W�3_jl���iu�X�ob����� �:£ p{mz$� lo ºb���ms;��:_j��b�acb�lx¥

p eg�;����;�¡z�pu������X_j��b����ik_jin����X���_W�s�in����� ��� ���;lt¥ �������¡z�pu��W��in ���in��_����p eg�;����;�¡z�pu�������_j�jbc���i̬_�iu����vs�����_��ts�pub�z�pn��v�;_Xp eg�;����;�¡z�pu�W���;�_j��b����ik_jin����viu��s;���`_j�ts�p�b�z�pn��Olq»v� ��b���w�lob����¡b�s;s����inz�pu� �

��;_×b�pu��� s�����iu���;���Vs����*���$s;���`_j�ts�p�b�z�pn�&�i���� ^ l�iu�s��Ï�×bc��w�lob����Vb�l�s;l�����b��wxl�b����Ïiu�`_j�;����ik_��e¤���_mb�s�s;���iuz�pn� ^ b��:pn��´µ�jb���s7��iu����*���`_v��e¤l�������;w�l�����s;�>����_��jb����in_�iu����R�����$s�����_��ts�pub�z�pn�� l�d®��b�lt_j��l��������_�������_����Ww�l��¡�iMp e¤���������z�pu�W������×b��w�lob����;�b�����in��inz�pu�;���_�s����`_��ts�pub�z�pu�>b�pn�����l��s;���`_j�ts�pu��l��:�3¥tiu�_j���;_v���_v� ^ _jin�×bcp l

���.�*'���E ��$ 0#'2��"����3>�+56.( +5� =#=8�3>&>-( @���� >�(:6�����'�(!>;��� EB��$&0�'9��"���( �9( +&(����1( � ��=.(�>�+-� '���� +&$&��� �#=8+-,�(�$&� EB���2����+5L���$ >5=8�E ��$ 0#'2��"��

Page 42: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�`� �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

d®�� ^ �� ^ ���ik_jiu����¡pu�; ^ pul������s;���`_j�;×��e¤l�_�iupuinjbc_�iu��� ���ϱv��³ ^ ��l���p�b �yx��_��1u��¶s;����s��;�����;�`_p e¤l�_jinpuiu�bc_jin���Ï��� p�b×_j�������iu�¡���;�������iu���� ^ ��l��X�yx��_����;_�iu���Wp�b×�_j��l�s;_jl����*����s����`_��ts�pn� � �±��º��� � l ºb���]s���s�����_��3¥x_j�c�`pu� ^ ���z�p u��*�:���:p�bº�yt�`_��1u������_]��e bc��l������]p e¤�3¥tin_j�;��s�����e¤l��*�l ^ ����axiu��;l�� ^ b�����;_���l��,��e¤�;_jbc_,_j�;p�w�l���pu��´µ����s;_�iu���������*���`_²��� z¢��l�s�pn��´µ������;�:���; ^ ��s;_���pu� ^ �����insÕbc_ P

l�d5bº_j�������iu�����º�����in���� ^ �;���*�;_m��e¤��z�_j�;��iu�ml��¶�*�x�1u�pn��±��o³������`_mpu�W���jb ^ �������>�×bc��w�lob����W���_Xpuin��ik_j�Xbclt¥�×b��w�lob����;,bc_�_���in���ob�z�pn��M���; ^ ��s;_jb��`_ P

l�d5b��_j��l�s;_jl����R����s����`_j�~s�pu�Q���_,����b�puin���� ^ b��Êp egb�� �����s;_jin������ ^ p�b�s;��:��ik_j�;R���Xs�����_��ts�pn��:in_jl�������;�Vbc�����`_:����:_j��b����ik_jin���� ��s;���`_j�ts�pu���Ol�³Êb��:�3¥t��� ^ pn�X�l��p e¤�3¥t��� ^ pu�>����p�b �o��l���&�ml|z��q�Å¥x_j�jbcin_º��� �g» �Õb��`��� �¢_j����iu ^ p�b�s;��º����s����`_j�~s�pu�¡£����5£:�×�3_W£�q?����`_b ���l�_�����mb�l$�*�t�1u;pu�X��l ^ ��ts;�����Wb �o�$��e¤iu�`_�������iu�������;��×b��w�lob����;vin�����;�iu��b�z�pn�� l

p2

p5

p8

p7

p4

p10

p11

M1

M 2

t1

t2

t3

t4t5

t6

t7

t8

C3

C1

C2

p1

p9

p6

p3

R

�������M�,lrz�� � " "%$ � +,"�35"�9 ���! � �29;" � �$��� 3 ��"� ��1������ " 35"29 �71$�$����� 9

Z�� k � k � k �haVaM©SR=U ��`/c T �/Um`/NQP�©Sb _YW c � `/c ºbc��&pu�;&b ^�^ ��ts7���� ^ �����;�`_j���; ^ ����s;�����;���*���`_��Rpu� s�b�pus;l�p����=p�b �_j��l�s;_jl����=���=s;���`_j�ts�pu�

����s;���in_��vw�l��:p eg�;����;�¡z�pn�R����Ê_j�jbc���ik_jiu����(��iu�;��_���z���;�acb�z�pn��Ol` ����_��jbÕacb�lt¥¡���`_,�;_��R����b�puin���(�l������m_j�l�s;_�l����;����;s��;��_��jb�pniu����m�ob���vpu�;�w�l��;pupu�;ms;����_7b�in�����_j��b����ik_jin����:���W����`_ ^ b�v��z���;�acb�z�pn��� ·X :��{mv�� l²£�� ^ �;���ob��`_Õ�,��b��� s��&s�b���,p eg� ^ _jiu��b�pnin_j�����Ïpub¶_���l�s3_jl���$���$s����`_j�~s�pu�×��� ^ �;l�_ ^ b�_j��l ���l��� ;_������`b���b��`_jin�,l

Page 43: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� ����� �E� � �9����� ���

d®��R_��jbÕacb�lt¥ ^ ���;����`_���v�ob���Rpub���;s;_�iu��� ^ ���s;�����;��_��>l��Rpub�yx�`_j�1u;�� ^ b��:±����Õb�lx¥&����³M�;_j�is;���`_j�ts�pu������`_>�;_����3_j������l� �Ïl����*_���l�s3_jl���×��in_j�iuz�l���� � �½�{���� lÊd5b$yx�`_j�1u;��?���×s�����_��ts�pn� ��zobc�� b�pn������l��&l��J�;����;�¡z�pu�¶���=�l ^ ����axiu��;l���$pn�ts�b�lt¥�wxl�iXb���in���;�`_$s�����s;l�������*���;�`_&�l��&pn�^ ��ts;����� G

l`d,egb�s;_�iu����s;����s�l������;�`_j�v���:_j��l�²s;��²�l ^ ����axiu��;l���]�l��]p eg�3_7bc_�s���l���b��`_]��l ^ ���xs������v�;_���;��� ^ b���l��=s�b��ob�pÊ���¡s;������l���ius�bc_jin��� �µa���iu� ����l����×�mlr{ � l¨£���sÕb��obcpÊ���_�����_7b��*�*���`_ ���;axin_����pn��:s�������b������;:s������oius3_jl��;pupu�;:�;_vpu�;:�ik_jlobc_�iu����:����z�pu�xsÕb����,l

Procédé G

Cannal d’information

S SS1 2 n

�������M�,lr{�� � �0)!�� ) �7" 3$�,9� ��� '�)�12" 35" �����! �76*+,"

£��ob�w�l���l ^ �;�axiu��l��,pn�ts�b�p S �;_]b���xs�iu� �ºl�� ���l�­¬ ^ ��ts;�����:�3_,����*�����×bciu���Q��eg��z���;�acbc_jin����3_V��� s;���`_j�ts�pu� ���_V����_j���;iu�`_ � s;� �*�t��u�pu� l:d®� �l ^ ����atin��;l��¶��pn��zob�pm���;_������in��� � ^ bc�_jin�&���p eg�;����;�¡z�pu�*���;¡�l ^ ����axiu��;l����pn�ts�b�lt¥ ��e¤���_ ^ b��� ^ _jin�×bcp � p e¤� ^ _�iu��b�p���pn��zob�p²��e¤���_ ^ b�>p e¤l���in������;�� ^ _jiu��b�lt¥=pu�xsÕb�lt¥ � lʳM��l��>������������p�bV�_j�l�s;_�l��������×s;���`_j�ts�pu� ^ pul� ^ �;���*iu�ina����5iup²�;_¡������s���;s��;�jbciu��������pnl�i�b�� ���iu�������ºl����W�_j�l�s;_�l����W���Xs��x�����iu�ob\_jiu���?��pu��zob�pu� � �º½��mq�� lÑ£��3_�_��W�_j�l�s;_�l����^ ������3_²������� ^ b�,iu�`_�������iu���:�yx_j�;�×b\_jiuw�l��;���;�`_Q����²�;_jbc_j ^ ��_j�;��_�iu�;pupu�;���;�`_,�ob����������;lt¥ �3_Q������s��������������pu�Xs�����_��ts�pn�X��pu��zob�p ^ pul� ^ �����*iu�ik´�l

��� � ' L )�1;0ÏA®43' L

 ºb���×s��3_�_�� ^ b���_jiu�$����l�?bÕa����� ^ �����;�`_j�=l�� �3a��;��_jb�iupv���Vp e¤�������¡z�pn�V�����_��jbÕacb�lt¥ zob���l��Xp�b�_���������iu������p�b×�yt�`_��1u��×����s;���`_j�ts�pu��l�� ^ b��Xl ^ �;�axiuiu���=�;� ����l�Xpuin��ik_7b��`_mb�lt¥=b� ^ ��s3_j_��������iuw�l��;v�3_vjb���vb�z¢��������:pn�� ^ ����z�p u;���;:��egin� ^ p�b��`_7b\_jiu����l

� pub×zob�������s��3_�_j�¡_���������iu�c�qpn���b�lt_j����bc_j�; �?�3_7bc_�º�;_�pn��ºpub����`b����������_º�;_j��lt_jiupniu�����b���^ pnl��in��l��Wb ^�^ ��ts7���;���yx�obc��inwxl��� lÊd,e b ^�^ ���xs7���*s��;��_��jb�pniu��� ^ �;���*�;_>��eg��z�_j�;��iu��pu��´µ����s;_jin�������Ŭ�*���`_º�;�=zq��l�s�pn�>´µ������;��� ^ _jiu��b�p®��b�iuv���� b ^�^ pniusÕbcz�iupnin_j�������_j��bc��l ��;_�_�iu� ��p�b�s;��� ^ pu�Å¥�ik_j�W���s�b�pus;l�p5��l�� �×p eg�Å¥ ^ pu��iu���Ïs����¡z�iu��bc_j��in�������¡p eg�; ^ bcs����¨eg�3_7bc_� l®£�� ^ �;���ob��`_�inpM�;_ ^ ���iuz�pu�W��eg��zt¬_�����in�����;X���x�1u�pn�� ^ pul�º��b���i ^ l�pub�z�pu�;���� ����s;��� ^ ���b��`_Xpu� ^ ���xs��;�����;_ �c��l=pu�;º ^ ��s;i �os�bc_jin����Ol

Page 44: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� �������K� �V�6����� ����� �V��� ����7��� ����@����� � �/��� � ��@������

dMbW_���l�s3_jl���º���x��l�pub�iu��R�egb ^�^ l�iu��b�iu��iÑ�l��Ql���������s���� ^ ���ik_jin��� ����Q ^ ��s�i �osÕb\_jiu����]_jb�����inQw�l��p�b��_j��l�s;_jl���������s;���`_j��b�puin��;��acb ^ pul��pu��in�×���$�ºzob��b��`_��l��:l����º����s;��� ^ ��in_�iu������l ^ ���xs��;���,lod5b_j�l�s;_�l�������iu�;�jb��s7��iuw�l��]l�_jinpuin��,l�����b�l�_����Qa���iu�]���]�in� ^ pni �os�bc_jin���X��� ^ ��� ^ ���b��`_(l����Rb�z��_j��b�s;_�iu�������� ^ �;s�i �osÕbc_�iu���� � �*�x�1u�pn�Q��l���ina��Õb�l�zobc��\���x�1u�pn�Q��l¡��ina��Õb�l���b�l�_ � l�°,� ����p egb ^�^ ��ts7���Q��iu�;�jb��­¬s7��iuw�l��:��in_���iuz�l����Ql�_jinpuiu� ��p�b�´µ��iuÊpu�� ^ ��in��s�i ^ �;(���;,b ^�^ ���xs7����,���;s��;��_��jb�pniu����(�;_,��in����b���s7��inw�l���b �o�Ï����s�l��¡l�pu���:pn��vbÕacb��`_7b����;���������;lt¥Vb ^�^ ��ts7���� l

³,pult_ s�_$w�l�� ��e¤l�_jinpuiu���&s;��Vb ^�^ ��ts7���;V����s��;�`_j�jbcpuiu���c�v��iu����b���s7��iuw�l�� ��l ��iu�;�jb��s7��iuw�l�� ��in�¬_j��inz�l��;���(l����&b�l�_����×a���iu���3¥ ^ pn�����;�?���_�p e¤l�_jinpuinjbc_�iu���=��egb ^�^ ���xs7������_7bc_�iuw�l���Ol�d,e¤l�_jinpuiu�bc_jin��� ����b�l�_j���×bc_���v��iu�;�jb��s7��iuw�l��;����������¡���;��*�t��u�pu�;v_��tu;�puin�inz�pu�;:������s;� �*p�b ����_jin���¶������b�s���c¬h�3_7bc_ l³Ê��l���_7b��`_�iupuX����iu� ^ pui �o���`_ ^ b�Wp e¤�;_jb ^ �*�����yt�`_��1u�� ^ l�in�w�l��*s���pnpu�Ŭhs�i,����s��;�in_j�*_j��l ���l���W������;a���pu� ^�^ �;�>p eg�; ^ bcs��*��eg�3_7bc_� l5d®��>±������b�lt¥ ����³Ê�3_j�i �®w�l���pnpu��w�l��*���ik_�p�b&s�pub��� l�_jinpuiu���c������`_b�l��iº���;×´µ������b�pniu��*����� ^ lt_j�� ^ ��l�� ^ ���x��l�in���Ï����&�*�x�1u�pn��*s�p�bciu��*�;_×��ins7����?����&yx�_ u��*����� ^ ���x��l�s3_jin����l®£�� ^ �;���ob��`_Ws�����_��jb�in���;���;��_Wbclt¥=b ^�^ ���xs7���;Wz�b���;����l��Xp e bcl�_j����bc_�� �?�;_jbc_Õ�¨pu����x�1u�pn� �o�ob�p®��l ^ ��ts;�����W���l�ms;���`_j�~s�pu�����_�_j��l ���l��� ^ pnl��s���� ^ puinw�l��X���V±v��³�w�l��>pn�����x�1u�pn�iu��ik_ji�bcp���l ^ ���xs���������;l�p lq³(bc��s��>w�l���pn���_j�jbÕacb�lt¥V���Wyx�`_j��u����z�b���;º�l��vpu�;�±��o³���lVpu��mb�l�_��c¬�×bc_���v��iu�;�jb��s7��iuw�l��;m���`_ºz¢�Õb�l�s���l ^V^ pul�m���s��;�`_j�w�l��>s��;lt¥Vl�_jinpuiu�b��`_�pu�;mbcl�_j����bc_��� ���3_7bc_���pu��²_j��bÕa�bclt¥ ^ ���_7bc��_Q�l��Q���;Rb ^�^ ���xs7����Q����s;���`_j��b�puin��;��]����`_R�*��in��,�����¡z�����lx¥×�3_��*��in��²b�z¢��lt¬_jiuOlÑ·º�&���3_jiu�;������b ���Õb����*��in��Rw�l��X�i¨pu�Xs�����s�� ^ _����X�*�t���;puinjbc_�iu����l�_jinpuiu���obc��:p egb ^�^ ��ts7��� ^ b��b�l�_j���×bc_���Q�����_j�X��i � s�iupn�m�¨e b ^�^ ���;������iu��� ^ ��l��Qs�����_7b�in��:b�lt_j����bc_jins�in����]���ºpub>s�������b�������� l��^ ���xs��;��� �;_7bc��_ ^ ��� ��l s����*�*�¡l�� ���������jb\_j��l��W�¨eg�3a��������*���`_j � �Mp�b×�*�;_����t��������p�b?�yt�`_��1u��×���s����`_j�~s�pu�;l�� ^ b��5�l ^ �;�axiuiu���>b:��� ^ �������`_j��l����]bÕa�bc��s��;�Qs;�����in������b�z�pn�]�;�>�ml�_j���×bc_�iuw�l��² �in�s;�tu;_��,ld²egb ^�^ ����_R��b ���l��]���ºs;�;__j�m´µ������b�puinjbc_�iu��� b ^ �����in²����_7bc���*���`_Q��egin�`_j���x��l�in���v�;_����macb�pniu���;�]pn��^ ��in��s�i ^ b�pu�; ^ ��� ^ ��in�;_j�;Q���vpubXs����*�×bc�������`��z������acb�z�iupnin_�����s;������b�����b�z�iupnin_��Q�3_��_7b�z�inpuik_j�,lcfhpo��e¤��_������s ^ bc:�;axiu���;�`_�����´ b�in����l��Ïs7����ik¥×���`_j��Xpu�;:b ^�^ ��ts7�����_jbc_jinwxl���R�3_���yx�ob��*iuw�l������l&����s;��������X´ b�iu��Xl��Vs7����ik¥?���`_j��>pn��:��i �¨�;�����`_�v´µ����×bcpuiu���;Qlt_jiupniu�� l

Page 45: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��q

� � ����'7%�)�� �

� �#"�%�'�� � !�" $ �w !�" !� � � � � %�'�� ��� �#$ � � %

d®���rxyx_tu��*����ml�_j���×bc_�iu��,���m³,���x��l�s;_�iu��� � rx�º³ � ����`_QsÕb���b�s;_�����in��; ^ bc�]pn��l��²s3yts;pu�v����atin�w�l�iQ����s;��in_�pu�;¡��i��q������`_j�;�b�s3_jinaxik_j���b���ts;iu�;�� �¶p eg�Å¥�in_�����s;�?��lTyx�_ u��*�&��� ^ l�iu�p e¤�3¥ ^ ���;�iu������X���&z¢�����iu� �l��w�l�e ������$���;�×bc��_tu�pn���*���`_fl�dMb¡pniu�_j������:´µ����s3_jiu����Rw�l��X����ik_�b��l�����:l��Vrt��³_���l�_vb�l$pu����� ����s���s;yxs�pn�����Xatin����_vin� ^ ����iu�����ob��`_j�(�

� »v� �yx_ u;��������ik_ 3_j��×b ^ _j� � ^ ��t��l�iu��� l�����w�lob��`_�in_j�*z�in��� ��� �o��iu� ^ �;���ob��`_¡��� lt_jiupnik¬�bc_jin���¶�;� � ^ ��t��l�s;_�iu��� ������in�ob�pn� �`�q�×bciu�iup5����ik_ºbcl��i ;_����¡s�b ^ b�z�pu���������;_����ºpn� ^ pnl�pn������_���� ^ ^ ���inz�pu�>�ob���ºs;�¡�*�t��� l¨ ml��jb��`_Xpub ^ ���iu�x������� ^ ���x��l�s3_jiu�����qpn���yt�_ u;�����;_� ^ _jin��in�� ^ ��l�� ^ ���x��l�iu��&��� w�lob��`_jik_j���(wxl�b�puik_j�&�;_ ��s;l���ik_j�$��;pu��� pu�;��3¥tiu���;��s��;��;s������c¬�*iuw�l��;:�;_v��������;:pu�;�`b�pu�;:���$axiu��l��;l����

� d5b*s����*�×bc�����W��egl�� rt�º³J����ik_ºbc��l������mpu�;m´µ����s3_jin����v���¡����b�s;_�iu���¶b�lt¥V���3´ b�iupnp�b���s;�����lt¬��b�in����m��l=����p�b ^ b��_�iu��� ^ �;�jbc_�ina��c�¨a���iu��� ^ ��l��ºpu�; ^ pul���;a���pul��;X����p�b?s;������b���������pnpu�Ŭ�� ��*� �

� d®�?�yx_ u;���&����s��;�in_j�$��e ;_����×_����_j�$�;_������pn�×pn����¡���?����Tin��_jb�pupubc_jin��� ��lTpu������e¤� ^ ����b\¬_�iu��������X��b�iu�`_����ob���s�� � ^ ���3a����`_�ina��;m��l&s�l���bc_jika��� � ����lÏ�;��s������Xpu��������X���x��i ��sÕbc_�iu����]��l�yx_ u;������lÏ����s7�ob��������*���`_jv��� ^ ��t��l�s;_jin��� �

� d5b ^ ��t��l�s;_jin���Ï����in_ ^ ��l�a���iu� 3_j���b���� 3_j�����3_����p�bc��s��;� ^ ���iu�x��iuw�l��;���;�`_Õ��pn� ^ pul���in� ^ pu�3¬�*���`_����jb ^ iu���;���;��_��3_v &�����*���`_ ^ ���inz�pu� l

£������i �¨�;���;��_���º´µ����s;_jin����º���`_�l�_jinpuin����;�� ^ ��l��º������yt�_ u;���;Wiu� ^ pu�;��¢�ob���X���� ^ �;��in�t���;��i �¨�;���;��_��� ^ ��l��Xpu�;�w�l���pnpu�;Wpn�����z���;s;_�in´µ���� ^ ���������`_¡����pub&´µ����s;_�iu��� �$b��l����;� l(£��� ^ �;��in�t���;s;������� ^ ���������`_ � ��������x����*���$´µ����s3_jiu���������*���`_ �¡�ob����pu��w�l���pn�pn��*��z����s3_jik´µ � bc_�_���iu�������c��3_ ������s&pn��¡s;������b���������(��i��Qu�����`_ �;_ ^ bc�´µ��in���ika���������`_ l²³Ê��l������� yx_tu��*��*s�����_jik_jl��;����^ pnl��in��l��¡���l��¬ yx_tu��*����,pub¶�ik_jlob\_jiu��� ���_ wxl���puw�l��3´µ��iu¡_��tu;¡s���� ^ pniuw�l����×�ob����pub¶���;�l���&�,+s7�obcwxl�� ���l��¬h�yx_ u;��� b ���� ^ ��� ^ ��¶�*�t���,lQ£���s;i����;s����ik_j� b�pn����*��e¤iu���_j��l����;��_�����pu�Ï��ina��Õb�l

�����/,#'9> ��$&%IB %�$&,��2> �#E �9� ,��#��$ � � +-�3$ EB� 6.��E ,.6.� 6.��B ,#�F= +&( ,#�����<EB�3�#+ 0�'�( ��,#'9>B>��#E @���� �9� '9>B"#%���%3$&��� 0�'��EB, 6�� 6��<��$-,.6.'D= +-(�,���A ��( E ( +-%�� �!� ��$&, 6�'F= +&( ,#�2E ) EB,.6.� 6�J ��$&$-4�+ A ��( EB( +-% ��'�= ��$&$-4�+&> E ) EB,.6.�<6.� E ��$ = ���������

Page 46: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� ���6� �K� �V�6� � � ���@��������� ��@�y�*� �� ���� �#��� �����������6�@�y�� �

yx_tu��*�=��egl�� �l�ikaxim���;?��ika��Õbclt¥ l�z¢�������������� ^ ��l��×l����V���;iupnpu��l����$��in��Ï��� s;�����;������s��=���p e¤�������¡z�pn�,l

d5b ^ ��in����;��s;��� ^ _j�]��� ^ pnl��in��l��5���x����M���]´µ����s;_�iu���������*���`_M��e¤��_ ^ b� ^ ��� ^ ��� �mp e¤�;_�l����]����yx_tu��*������ ^ ��t��l�s;_jin����l ���Õbcl�s���l ^ ����yx_tu��*�����yx�ob��*iuw�l��;º���`_X���;º´µ����s;_�iu����º��l ^ �obc�����i��q������`_j�;��ol��$bÕaxiu���?�;_ ^ ��;axl ^ ��l��R���;s���pnpu���;�xa���pu�;�R�;_:bc_�_������iu�;�tl��&��iu_���inz�l�_j�;l�������in_���iu�_j��i̬z�l����X���� ^ ���x��l�ik_jm�×b�inºb�l���i,������b������;�º����p egb�������`_X�3_X���;��������pub?�������ob�in�,l l lqd®��º´µ����s3_jin����^ ��l���pu�;�w�l��;pupu�;ºpu�Wyx�_ u��*� b×�3_j������������b�pu�;���;�`_ �Vs;��� �;l=s������_jik_jl��;��_ºpu���*�x���>������in�ob�p5���´µ����s;_�iu���������*���`_fl�¹¶b�in�pu�*�ts�pu�×��lTyx_tu��*�����3_¡���?�b s����*��b������c�M���?�egb���� ;_�� ^ b��p �R�Êi�l�����Õbcs;_j�;l��(_����¡z¢����� ^ b������c��pn� ^ inpu��_��]����in_ ^ ������(p egb�axin���>_���l�_������� ��*���� �b����s;�R���x���]����´µ����s3¬_jiu���������*���`_m�������jb����c�qpn�� ^ ��in����ik_j�;:�;_º������sWpu���´µ����s3_jin���� �×b��l���������������_ ^ pnl�mpn��v� ;���;��pu�Xs�����´µ���_v���; ^ b���b����;�� ^ b��:�3¥t�;� ^ pn����eg�;_ ^ pnl��l���� ^ ��in����ik_j�ºpn����w�l��Xpu�;l��Raxiu�����_m�;� ��;l�l l l

°,�=b�lt_j����bc_jinw�l��>s;���`_jin�xl����¢p e¤�;_jl��������;º�*�t���;����W´µ����s3_jiu���������*���`_���_ºb�l��i(l����¡����b�puik_j� ld5�;X�3¥t��� ^ pn��ºpn�� ^ pnl�ºiu� ^ pu�;������_ºp�b ^ �iu�¡���=s;��� ^ _j�¡��� ^ pul�iu�;l��� ^ ��in��_�º����´µ����s;_�iu�������3¬���;��_ ^ ��l���pu�;��yt�_ u;���;W����� puin���Õbciu���;m��l p e¤�;_�l����¡����p�b���Õb�s3_jin��� ���¡�yx_ u;���; �×���;º���`_j����;��ius����`_jin��l���Ol¨d®��s7�ob��������*���`_����>�*�t��� ^ �;l�_�������s ;_j�� ^ ����a��xw�l�� ^ b���pu��s7�ob��������*���`_��¨eg�3_7bc_z���l�w�l�� �¨egl����=���`_j���� � ��in�s;���`_jiu��l�ik_j� � ��l ^ b��&pn� ��� ^ b�����*���`_Ï��e¤l��J���l�iupº���3_j�;���*iu��� ������puiu����� � ��� "�� � ����������� � ��l �;� puin����� lq ml ^ ��in�`_����>atl��¡���¡pub�s�������b������c�ql����>´ b��;��� ��� ^ ���;�����������s;��� ^ _j�$s��; ^ ��������� u;����*���_����Vs;����_���l�in��� ^ pnl��in��l��*�*�x�1u�pn���s�����_�iu��l� s��������; ^ �����obc��_s7�ob�s�l�� �Ïl�� �*�t���*���*´µ����s;_jin�������;���;�`_��;_>�����*�;__j��*�;� ^ p�b�s;�*l�� �*��sÕbc��iu�������*�l�inaxi,�������x�1u�pn��X�3_�����zob�s�l�pn���*���`_���e¤l�� �*�x�1u�pn� �?p egb�l�_����,l®£��;_�_��*b ^�^ ��ts7�����;_W��ik_j�¡�¡l�pn_ji̬h�*�t��u�pu��;_vs�����_jik_jl���pn�XsÕb����e¤�;_�l����W�obc_jl�����p®�����yx_tu��*��v��yx�ob��*iuw�l��;v�`yxz��iu���;�� r� º½ � l£��:s7�ob ^ in_����R�;_,s;����_�in_�l��:����_�����in ^ b���_jin�� l� ºb���,pub ^ ����*i u��������l� ^ ���;��;��_�����²pu�;(_j��bÕa�bclt¥���²p�bRs������¡l��ob�l�_���´µ�jb�� ��b�iu�

��l��5pu�;®���x���;®���,´µ����s;_�iu���������*���`_5���;(rx�º³Vl\£��;Ê�yx_ u;���;Ê�3_7b��`_

����²b ^�^ puius�bc_jik´µ ^ ��inaxinpu����iu��;� s��;__j� ^ b���_jin�����_²p�b ^ pul�,in� ^ ���_jb��`_j�]��l s7�ob ^ ik_j��,l��v��l� ^ ������`_j��������l�in_��:������;s�������� ^ b��_�iu�Q����lt¥�_j��b�acb�lx¥�����b�puin��;�b�l���iu�����:p e¤��w�l�i ^ ��q�r�³ �µ�ob���,pn��s�b������:���Rp�b_j���;����in�º±�� � ^ l�iu]����l��_������in������ ^ b��]l���� ^ �������`_7b\_jiu���?����Rb ^�^ ��ts7���;��¡l�pn_ji̬h�*�t��u�pu��iu�l�������p egb�l�_j���×bc_�iuw�l��ºs;���`_jin�xl��W�3_v����p e¤�;_jl����X�����r� º½ol

� �� . '�8&-�A 8$- Z\' L )Q2543' L$L -�E - L 2 -R2 B×!��

��� B��~B ��A����� �

d®� Xl�iu���?��e � _�l����&���;*¹V�x��������ϹVb���s7���;��;_ ��e¤����� 3_j�� �°]¹ ¹V� � b �;_�� ^ ��� ^ ��� ^ b��p e¤�º º°²³q���;���X{,z�� �¤�� º°�z�� � lÕfhp�s�����_�in_jl��]l��W��l�iu���,���jb ^ ��iuw�l��,_���l�s3_jl��� ^ ������3_�_jb��`_5���,��� ����iu��.� � �3> +&$&� L ��'�= 6����!� =�, EGE '��2��'.+&%�B $ �����3��(!>���>�'�$;���3> EB, 6��3>;6.� B ,��F=8+-(�,������#EB����+ B ,#$ EB�3�#+ >-'�$ �����������?(���+-��$ ;

�2� +-(�,��2��� '�� ���9>-�<E0@�� ��,�$&(�"�(��9��� 6.�<0�'9����( +&% =3��$;(���> ��$&�����9����+ � �3'�$&> $ � =�( ���*> 69���9> ���3> +-$ � L ��'.=?6.% � � ���F=8(���� >�'9$ ���� ����� C � � J �3>�+ ��,�'9$&0�'�,#(F@�(����?0�' J � �#����+ $-%*����(�>-%/'���� @�( @�� (�,�"#$&������(��5>-�&L�,#'�������+ �8=��9��'9> +&( L#��)6=8�8+-+-���9��$-+-(��/$&�3>�+-�'9��(�0�'��#EB����+5B $&��������(�>-���

Page 47: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � � �3��@���� � ��� ������� �����@�y�� � ��� �/��� ���

� ^ b��_�iu�v��e¤l��=sÕb����;acb��_hy ^ �¡pu�;���i �¨�;�����`_���*�t���;������×b��s7����m�;_���e bc���� 3_jº�¨egl����¡�×bcs7��iu���>��l��e¤l�� �yx_ u;���&��� ^ ��t��l�s;_jin��� bciu��iQw�l��?pn�� ^ b���b����;¡��e¤l��T���x��� �¶l��Tbcl�_j��,l(£��?��l�in���×�;_�;p�b�z¢����� ^ ����������ina����*���`_Rpn����²���vp�b�s�����s�� ^ _jin���×�3_Q�����s7����ik¥*���;��*�t����²����s;��jb�in���� �>pub��*iu��;�V�x��l�ax��W��lV�yt�_ u;��� l

d®� �°Q¹¶¹V� ^ ��� ^ ����_j���iuv´ b��*iupupn������ axl������¡s�pub�����Xpu�;���i �¨�;���;��_�X���x���;º���¡��b���s7�����3_º��egb���� ;_����� ´µ����s;_�iu���V����p eg��z ���s;_�in´,�¨egl�_�iupniujb\_jiu���Ï����p�b ^ b���_jiu�W� ^ ����bc_jika�� � ³Vl ·�l � l¨d5b�´ b��*iupnpu���³,���xs�����l����;(��e¤����� ;_Ê���]p�b ^ b���_jiu�²� ^ ����bc_jika�� �W��������l ^ �²pu��M�*�t���;5s�������� ^ �����ob��`_ � ��l>���;acb��`_s;������l�in��� � �¶l�� �;_jbc_¡�¨e b���� 3_¡z�in��� ���;_j�;���*iu��� � in��in_�i�b�p(��l ����� � lÊ£��;__j�×´ b��*iupnpu�¡s;��� ^ ���;��� pu�;�*�t������ ���,�Ê����� ;_ ��b�����;_jbc_ iu��in_jiub�p ��� � �X���Ê����� ;_ ���;�×bc�����&��� �o�����&s3yxs�pu����� �¶��qR��m���� 3_�������b������W��b���:�;_jbc_viu��ik_jiub�p �`� � �m�:������� ;_���z�_j�;�xl ��� �¡�X���ѳ,��� ^ b��jb\_jiu��� ^ ��l��:�����*iu��;�Ï���l�_��Xb ^ �~u�:���3´ b�iupnp�b���s;� ��� ����vR�ѹViu��³Vl ·�l��ob���:�;_7b\_�iu��ik_ji�bcp �×�3_ �¡��x��o¹Ïiu���³�l ·�l���b����3_7bc_:���;_j�;���*iu��� � � a���in� �o��l���>�9ln� � l�d5b¡´ b��*iupnpu� ��³²��ts;����l���������X´µ����s;_jin�������;���;�`_ �?����������l ^ �pn�� ���x���;*���V��b���s7����*��� ^ ���x��l�s3_jiu��� � � ¯��,�]³,���x��l�s3_jin������������b�pn���`� � ¯,���]¹¶b��s7��������^ �� ^ bc�jbc_�iu��� �*�3_ ��¯ qR�x¹¶b���s7����R���ms�p s�_jl��� � � �3_����m���;��p�b���� � �>¯(�:�t¹¶bc��s7���;R����a����i �os�bc_jin����obc�� pu�$������������� �`� � ¯,���]¹¶bc��s7���;×���&a��;��i �osÕbc_�iu��� �ob���*p eg�������� �T�;_ � ¯EvR�]¹¶b��s7��������_���_ � � l �Xl�b��`_ �¡p�b�´ b��*iupupn� �¡³,���xs�����l����;:���º���3´ b�iupnp�b���s;�����ºp�b ^ b��_�iu�v� ^ ���jb\_jina�� ���t�;pupn��iu��s�pult_pn��$���x���;Ïpniu�;$b�lt¥J���3´ b�iupnp�b���s���&in�`_j�������Ï��l yx_tu��*���viupº;e b���in_$���;V�*�t���� �  ��,�:�m��� ;_��e¤l��������s;����� �= X���, �iub��������_jins×�;_ �c��lT_j��b�in_����*���`_¡���&���;´ b�inpup�bc��s�� � �;_��= �qR�,³,��t��l�s;_jin���_���l�_v���W� ;��� �ml¢£���v_j����iuR´ b��*iupnpu������>�*�x��������W����`_ ^ ��in����¶s;��� ^ _j��w�l�� ^ ��l���l���� ^ bc�_jin�s;������b������ � ³Vl £�l � �;� �;�������iu�$�;_*�;���;_jbc_*���$s����*��b������;� l²d5b ^ b��_�iu�$�`b�l�s7���$��l �°]¹ ¹V�^ ������3_����V�� ^ �����;�`_j���×pu� ^ b�jb����Ï���Ïp�b ^ b���_jin�Ïs;���*�×b������$������*����������iu� � l������;×�*�t���;^ ���s;�����;��_�Rpu�����w�l��vp�bW³Vl £�l ^ b�����;�?����������iu�,lx ��;�� u;s7�������� ^ ��in��_�iupnpu���� ^ ������`_j�;��_���i��q�����;�`_j^ bc�jbc���� ^ ���iuz�pn�����e¤l��V�*�x��� ��p egb�l�_j��,l

d5bT������b���s7��� �¨egl�_�iupniujb\_jiu������� p�b ����iupnpu� W°]¹ ¹Ï� s;����iu_�� ��e bczq���� ����pn��s;_�iu���������$pu�;�*�t���� l�_jinpuin��� ^ ��l�� pub s;����s;� ^ _�iu��� ��l��yx_ u;���Ï�;_ � �l ^�^ ��iu�*��� pn�� ���x���;*in��l�_jinpuiu��Ol�°,�t¬l�in_��¶iup�´ b�l�_×���;_������in������pu�� ^ b�jb����; ^ ���iuz�pn��?�;��_���� �*�x����×b�iu��imw�l��¶pu��×s�������in_jin����*���^ bc�jbc���,lq£�����_7b�in��������Ws��;ms;������ik_jin���� ^ �;l�a��;�`_ ;_�����iu� ^ pnius�ik_j�; l X�������jbcpu���*���`_��od®� �°]¹ ¹V��;_������l�ik_j�¡_j��b����´µ�����*����� �±v��¯Ê£R°,¼ ^ ��l��Xyx��s7�������in�����pn��X��i �¨�;�����`_�X���jbc´µs;�;_�X ^ ��s�i �Ñb��`_pn�Xs���� ^ ���_j�;���;�`_:����p�b�s�������b������ ^ ��� ^ ��� �*s7��b�w�l��>�*�x���º���X´µ����s3_jin�������;���;��_ l

 �e¤l�� ^ ��in�`_R���ºaxl���� ^ ����bc_jin�������;p¨pu� W°]¹ ¹V� ^ ��lt_ ^ b��jb\¾u_j��Xbc__j�jbcs;_jik´5sÕb��:inpqs;�����_jin_�l��Xl����l�iu��� ^ �;���*�;__7b��`_>��eg�3axin_j�;��s;���_jb�iu����>´ bcl�_j�;���l ��l�z�pniu����×s;����s;� ^ _�iu����lMfhp]��_���egb�iupnpu��l���X_j�~u�l�_�iupniu��]b�l ^ p�b��>iu����l�_���iu�;p lc£�� ^ �����ob��`_²�����l�_jinpuiu�bc_jin�����l��Ê����,�yx_ u;���;�s���� ^ ���_jb��`_ ^ pnl��in��l����b�s7��in���� ^ �����������;��in��lt¥ ^ ���z�p u;���;Qs�b���pubWs;���*�×b������m��l?yx_tu��*�ºb�l���iqz�iu�;�×w�l��º�b ^ bc�_jin�� ^ ����bc_jika��R���`_,_j��l ���l���(s�����iu���;���;��,s������*�R���;,���`_jik_j��,l���iuw�l��;,�;_,in����inaxin�iuz�pu��Ol fhp���e¤��_²������s^ bc ^ ���inz�pu� ^ bc�:�3¥t��� ^ pu��������in_�iu����l����Rl����Ws;���*�×b������Xpu�xsÕb�pn������pub¡s����*�×bc�����X��pn��zob�pn����l�yt�_ u;��� l²°²����lt_j���&pn� W°]¹ ¹Ï�@��eg�;_*zob��$�l�� b�l�s�l�� ���x�1u;pu��´µ�����*��p lMfhpR���$��in ^ ����$bciu��i��egb�l�s;l��T�*��sÕbc��iu�������?acb�puin�obc_jin��� ���� bcpn_j�;���obc��s��; ^ ����inz�pu�;�� bcl�_j���iu�bc_jin��� �3_¡acb�puin��in_�������

Page 48: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��v ���6� �K� �V�6� � � ���@��������� ��@�y�*� �� ���� �#��� �����������6�@�y�� �

F4<marche devérification

dans le désordreA6<mise P.O. dans état initial>

A7<mise P.O. dans un état

A5<préparation pour remise en route après défaillance

D2<Diagnostic et/ou traitementde défaillance>

d’assurer la sécurité>

A4<arret obtenu>

état initial>

A2<arret demandé

en fin cycle>

A3<arret demandé dans un état

vérification dans l’ordre

F1<production nominale>D3<production tout de meme>

Production

energie

hors

commande

Partie

>

A : Procédures d’arret de la P.O. F : Procédure de Fonctionnement

D : Procédure de défaillance de la P.O

F2<marche de

préparationF3<marche de

cloture>

F6<marche de

test>D1<Marche ou arret en vue

F5<marche de

déterminé>

déterminé>

A1<arret dans ^

^

^ ^

^

^

^

^

�������q�9ln��� "�� � � ���'�� ) � 35" 3� � ) 35" 35" � ��35"29 35" � �$� ����"29 "� 3� � ������ �9

s����*�¡l�_jbc_jin��� ���&�*�x��� � ��lT���?���s7���;��s7���Ï�����z�pu�xsÕb����; lÊd5b ���s3_jin���T�l�ikacb��`_j� ^ �����;�`_j�$l����^ ��� ^ ��in_jin���?axiu�b��`_ � ^ bcpuiu�;� ��s��;m���3´ b�l�_� l

��� B�� � � � ��.�035���A��68 <�.�>K.15��68�� 4�A A -F> � ��-9.�>�57-98�0@+� ^ b��_�iu�º���;�s���ik_jinwxl����´µ����¡l�pn���� ^ ���;s��������*���;��_Wl��Xpu� �°]¹ ¹V�>��pu�;º_j�jbÕacb�lt¥ ���¡_j��u���

��� � �Qiup {c���¨���`_ ^ ��l��R��z���;s;_jik´M��� ^ ��� ^ �����Rl��Ï�*�x�1u�pn�����;:���x��������X�×bc��s7���;:��egl��¶rx�º³ z�b����l��:l�����b ^�^ ��ts7������iu�;�jb��s7��iuw�l��X�3_:�l��:p eglt_jiupniu�bc_jin������e¤l��$��l�_jinp¢´µ�����*��p��xpu�;:b�l�_����×b\_j�� �¡�;_jbc_j���;_������*iu��iu_���Ol

�5acb��`_¡_j��lt_Õ�Ms���>_j�jbÕacb�lt¥ ���;������b�puin����`_�pu� W°]¹ ¹V� �ob���¡pubV�*��l����?��+Tp�bV�*�x����pniujb\_jiu���atin��>��e bcl�_j���m´µ����s;_�iu�����w�l��¡pub*s;���*�×b������ � ��;l�pu�>b�z¢���������W�ob���mpu� W°]¹ ¹V� � �¢pu���´µ����s3_jin����������b�iu�`_����ob���s�����s;������l�ik_j� ^ b��]p e¤� ^ ���jb\_j��l�� �µyx��� ^ _�iuw�l�� � �x�l�ikatiÑ��� ^ ���x��l�s3_jin�����3_R���;_�iu���*�������x�������eg�Å¥ ^ pu��ik_7bc_�iu��� ^ ��l�a����`_�b�l��i 3_j���×�;_jl���iu�;�� ^ b��>p egb ^�^ ��ts7��� ^ �� ^ ������ l,³Ê��l��¡s7�ob�w�l��´µ����s;_�iu���¨��l��×�*�x�1u�pn�R��iu�;�jb��s7��iuw�l�����i �¨�;���;��_]�;_Qs������_j�l�in_ l`d®�m��ika���b�l�pn� ^ pul�]z�b���`pn�:��ina��Õb�l������_Ês�����_�in_jl��]���²_���l�Mpu�;®���x�1u�pn��;�Õ��l ^ ��in�`_5���]axl��]���²p�bR´µ����s;_jin���Xs������in���������� ���;Ês;��� ^ ���b��`_j��pu�;���;�`_7b�in����&��l rx�º³Vl�»v�J��ina��Õb�l��v��� ���x����pniu�bc_jin�����;_$pu�=���l�pn_jbc_&��� ���;lt¥J� ^ ����bc_jin����� �q��s;_�l����;&�l��*pu�;×�*�t��u�pu�; ���¶��ika���b�l � ( �²l����V� ^ �;�jbc_�iu��� ���Ïs���� ^ ���ik_jiu��� w�l�i ^ �����*�;_��������������l ^ ���Wpu�;X���x�1u;pu�����l ��ika��Õbcl in��´µ���iu��l��X�;_>l���� � ^ ���jb\_jiu��� �¨e b�z�_j��b�s;_�iu��� w�l�i ^ �;���*�;_Wb�l��ina��Õb�l ��� ( ��egbÕa���in��l�����atin�in���$puiu�*in_����m��l¶s;��� ^ ����_j���*���`_����;ºrx�º³ ���W��ina��Õb�l � ( ��������l ^ ��b�l ��ika��Õbcl � l]³Ê��l��×w�l��¶pn�V��ina���b�l ��� ( ^ l�iu��VbÕa���in��l����Vaxiuiu��� b�z��_j�jbcin_j�Ï��l ��ina��Õb�l � �²l��

Page 49: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � � �3��@���� � ��� ������� �����@�y�� � ��� �/��� � x

���;_�iu������b�iu��&����in_*bc��l������*p e¤iu�`_����´ bcs��&���`_����Ïpu���rt��³ ���$��ina��Õb�l � ( �3_×pn�&��ina��Õb�l ��� ( � a���in��o��l����>�9l � � l

SAP Composé

SAP Composé

de niveau i

+1de niveau i

de niveau i

SAP2 Composé

−1

SAP1 Composé

de niveau i −1

SAP Composé

de niveau i

CommandeSignialisation

Niveau

Niveau

Niveau i+1

i

i−1

détections dechangement d’états

changement d’états

commande de

gestionnaire

gestionnaire

�������¨�9l ��� � �0)!�� ) �7" � � 1��#�$� ��� � !�)�" "� �76*+," 3�) �5"29� �����!���$� �7"

d,eg�;����;�¡z�pn�V���;��*�x�1u�pn��������_����;×b�lt_j����bc_j�; � �3_7bc_������iu ���3_j�����in��iu�_j�; l²d,e bcl�_j����bc_���� ^ �����;�`_7b��`_ºpn�>s;��� ^ ����_j�;���;��_��o��l ^ ��in��_v����axl����¨egl����W´µ����s;_jin��� ^ b��_�ius;l�pui u����c����e¤l�� rt��³ �����ika���b�l �Qs;��� ^ ���&��_*��zt_j����l � ^ b���_jiu�����$p�b s���� ^ ���ik_jin��� b��yx��s7���������V����*b�l�_����×b\_j�������rt��³ ���:��ika���b�l�� ( l�d²e¤iu�`_�������ius;_�iu��������s�����_7b�in��,�;_jbc_j²s;��� ^ ����]b�iu���i�w�l��vp�bº��� �o��ik_jin������e¤�;_7b\_js;��� ^ �����_j�jbc���ik_j��in���� ^ ������3_�_����`_����>�*�t����puin��;�:pu��vs�����_��jb�in�`_j��v���W��;s�l��in_j� � �3_7bc_�min�`_j�����in_���l�s����*�¡l�_jbc_jin����,��z�puiu��bc_j��in���; � l�d,e b�lt_j����bc_j�v��l�s���� ^ ���_j�;���;�`_Qs;�����_7bc_�����l$rx�º³T���v��ina��Õb�l�Ñ���_�������sXl����ºa��;���in���&���;��l�ik_j�X���ºpub¡s���� ^ ���ik_jiu���×b��yx��s7���������>�����b�l�_�����bc_j�;����X��ika���b�l � ( ld®� ���x�1u;pu�¡��l ���;_jin�����obciu�����;_W��z�_�����l � ^ bc�_jin�X��� s��*���x�1u;pu�¡�����l�ik_��;_W��e¤l�����b�z��_j�jbcs;_jin������;��;_7b\_j�s7����in�iu� ^ b���pu�Xs�����s�� ^ _j�;l�� l

� p�b����iujb��`_&pn� �°Q¹¶¹V� �T��e bcl�_j���?´µ����s3_jin����?w�l�� p�b s;���*�×b��������]zob���� �l��&l�� ��l�_jinp´µ������;p �qs��;__j��b ^�^ ��ts7�����;_�_j�~u�Wiu�`_j�;����jb��`_��,lM�O_��jbÕa��;��Wp�b&�*�t���;puinjbc_�iu��� ����W ^ ��s�i �osÕb\_jiu�������:��s;l���ik_j������pupn��l�_�iupniu��Q���� ^ �iu��s;i ^ �� ^ ���xs7����²���:pub�yx�`_j�1u;��v����pu��in(���:s;���*�×b��������b��� ^ ��l��b�lt_7b��`_>bÕa���in�Xp�b ^ l�in�jbc��s��*��� p�b?_j�������iu� ±�� l5°,� � �¨�3_�pub$����_jin���=���*s����`_j��b�iu�`_��*���*��s;l���ik_j�^ �� ^ ����;�V�;_�zq��b�l�s���l ^ �*��iu���� ��ins7��� � w�l��¶pub=����_jin��� ���V ^ �;s�i �osÕbc_�iu���X�,pub ^ ��� ^ �iu�3_j�$���s;���`_j�ts�p�b�z�inpuik_j�:��e¤�3¥tiu�_j�Xbciu��i ^ bcR�;_:pn��z�pn�ts�b����v��l?�����t¬hz�pn�ts�b����m����pub�s����*��b������v��� ^ ��l�_ ^ b� 3_j���?a����i �o�;�,l² �� ^ pnl��p�b¶�_j�l�s;_�l����$��in���jbc��s7��inwxl��&iu� ^ �����&�;_�_j�~u� ���;_���ius3_jika�����inp���e¤���_ ^ b�^ ��;axlÏ����s����*�×bc�����X�*�t��l�p�b�in������lÏ����s��;�`_j�jbcpuiu��� l

Page 50: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��z ���6� �K� �V�6� � � ���@��������� ��@�y�*� �� ���� �#��� �����������6�@�y�� �

��� B�� C � 0�+�5QA �6-F26A ?�> .1A=5 0�+���:�46.�>K-98�0�+ 26A ?�> ��>K.9-98�A&0�� <�.�>E-�8���Ad®��Q����lx¥×��s3_jiu���� ^ ���s;�����;��_��� ^ ������3_�_j�;�`_R���m�egb�s�s;�������;��l���l�������� ^ ���;��;��_jbc_jin���?s;����s�in��

����,�*�t����(���Q´µ����s3_jin�������;���;��_(�;_,�;�`b�pn���*���`_(��� ^ ���;����`_jin�,wxl��Rpu�;l��(�Å¥ ^ pu��ik_7bc_�iu��� ^ �;l�_,bc��l������l���� s��;�_7bciu���¡s;������l�in_j����� ^ iupn��_7b����,l¢fhp��egb���ik_�b�pu����º����s;����s;�;a���iu�X���;W�_j��bc_j�;��iu�;º����´µ����s3_jiu���t¬�����*���`_ ^ ��l��&��� ^ ��������� ��l���� ^ �;s�i �osÕbc_�iu��� ^ bc�_jins�l�pni u;��� ��l ^ ��l��&����b���in� ��l���� in_�lobc_jin���iu� ^ ���3atl��?�×bciu����s;l ^ �;�jb�z�pu�,l�d5�×s7����ik¥ ��egb���� ^ _����¡l���� ^ ��puin_�iuw�l��*���&s7�ob��������*���`_ ���&�*�t����^ �;l�_ ^ ������3_�_����:��e y ^ b���a�����iu���`�bW�*iu�R��� ��l�ax������� ^ ���ml��²pu�:s;����s�� ^ _Q����p�bX���;s���� ����l��jb\_jiu����l

³Êb��_jb��`_����*s��*s�����s�� ^ _Õ�Mpu�;W_��jbÕacb�lt¥ ��� � ¹Vb�z {mv$� ^ �� ^ ����;��_>l����*�*�;_j���t����pu����in�¡��egb�iu��� �p�b ���s;��� �o��l��jbc_�iu��� �����yx_tu��*�� lR£�eg�;_&pub ���s;��� �o��l��jbc_�iu��� ���¶pub ^ bc�_jin�V� ^ �;�jbc_�ina��Ïw�l�i��;_s�����iu���;���;�=ius�i l²°,pupu�Ïs������in_j� � ��� ����iu��pu������x���;×���V�×b��s7���¶l�s�s;���in´µ$�3_?pu�; ^ ��ts;����l�����b���ts;iu���; ^ ��l��m´ bciu����_j��b���in_j�;�mpn���yt�_ u;���¡��������=�;_7b\_�s;��l��jbc��_�a����ºl�� �3_7bc_���z���;s;_jik´ � �o��l�����9lrq � ld,e¤�������¡z�pn�>����v���x��i ��sÕbc_�iu������ ^ �;�jbc_�iu������pupn�� � ����b�puin���� ^ ��l��vbc__j��in������Ws;�;_m�;_jbc_���z����s3_jin´s������_jik_jl��vl��?s�����b���in�>���v���;s���� �o��l���bc_jin����lt£��ob�w�l��m�s��;�ob��iu�W����l�pn_��m�¨egl������l�in_j�v��e¤����s;pu�;��s7���3¬���;��_���������x���; l¨fhp ^ �;l�_ ;_�������� ^ ���;��;��_�� ^ b��Xl�� s7�����*iu�=��b����l������_j��l�s;_jl����*b���z¢������s;���`_j������`_$s7�ob�w�l��=� ��l���s�b��jbcs;_j�;��in�� l����3_7bc_?���=���x���V��� ��b���s7��� lRd5b _���l�s3_jl��� b���z¢������s;���`_j���_¡��p�bczq������ � ^ b���_jiu�W���?pubV ^ �;s�i ��sÕbc_�iu��� ����¡�*�t��������?s7�ob�w�l��?�;�`_jin_����Ê����¡s;���`_j��b�iu�`_j�;¡���s���� ^ bc_�iuz�inpuin_��:����:�*�x����R�3_:���;:�s��;�ob��iu��R���X����s;��� �o��l��jbc_�iu��� l�d®��:� �Wl���R���X��� ^ b���_:�;_ ���ob�p��� �o��iu����`_,��� ^ ��s3_jika����*���`_(p e¤�;_7b\_Ês;��l���b��`_(�3_(p eg�3_7bc_5��z ���s;_�in´o���Q���s���� �o��l���bc_jin����l d®�]s7����ik¥W�¨egl���s��;�ob��iu�����_�b�pn����Q���;_�����l&�ob���Rs��3_vb���z��� � ^ bc�_jin�Q�¨egl��&��l?��� ^ pnl��in��l���s��in_tu����;R��e¤�;acb�pnlobc_jin���s����*��� ^ b��:�3¥t��� ^ pn�Wpn�º_j�;� ^ ��*iu��in�×bcp¢���W���s;��� �o��l��jbc_�iu������p�b¡��;s�l��in_��W��lVpn�Xs��,&�_ l

état actuelétat objectifMode i,2,1

Mode i,1

Mode i,n,1

Mode i,2,j

�������q�/lrq�� � �*929 � �5" 35"8+ 1� �$ � �� )�"%+Ea

% + 1� �$ ��' �/"��� � -Eo

�ml ���;p �$����p eg�Å¥ ^ pu��ik_7bc_�iu���¶����>���x���� ^ ��l��Ws�������l�iu�� l�� �yt�_ u;���c�Ês;��>_��jbÕacb�lt¥ �*�;__j���`_���&pul���i u����vp�bW����s;��jb�in���X��pub�z¢���jbc_�iu���*���º�*��s�b���in��*������ºs7�ob��������*���`_:���º�*�x����Olorti¢��l ^ ��iu�`_��� axl�� ��pn��zob�p�p e¤� ^ _�iu��b�puik_j� ^ ��l�_ ;_����=�;_�l���in��� �3_?w�lob��`_ji �o���c�Rpu�; ^ ���z�p u��*��&b�l���ina��Õb�l�pn�c¬sÕb�p �µ��l=�*�t��� � ��egb�l�_�����injbc_�iu���V����s7�ob��������*���`_�����s���� �o��l���bc_jin��� ���_����`_W����� ���;���pnl� l¨�m��_����s����`_j�iuz�lt_jiu��� ^ ��lt_�b ^�^ ���_j�;�:�ob����s;�Ws�b�����Ww�l��;puw�l��;m�;pu���*���`_�v���W�� ^ �����,l

Page 51: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � � �3��@���� � ��� ������� �����@�y�� � ��� �/��� ��{

� � B�� � < - ��03260@?�0�:�8�A � � � � �#* d®��?_��jbÕacb�lt¥�l��&p�b ���3_j���x����pn����iu�¶£��Xrt³q��f�¹ � £�����s�� ^ _jin���J���iu�_j��� ���;Ïrxyx_tu��*��$���

³,���x��l�s3_jin�����ml�_j���×bc_�iu��²����fh����l��_j��in�º¹Vb���l�´ b�s;_�l���i u��� � ���`_Q����z�l�_�� �Wp�b �o�×����Rbc�������;m�f{mz��b�lV��;iu�¶��l d5b�z¢���jbc_���iu��X��e¤��l�_����×b\_jiuw�l���fh����l�_���iu�;pupn�W���¡d®iupnpu� � d5� Xf�r � l¨°,pupn��bÕa�bcin_ ^ ��l��m��zt¬��;s;_jik´�iu��ik_jiub�p�p�b ^ �iu�=���Js7�ob�����=���=p�b _j��_jb�puik_j�Ï��lJs;yxs�pn�=���=s�����s�� ^ _jiu�������=p�b s;���*�×b��������e¤l�� rt��³Vl¨d5�;º������z����;lt¥¶_��jbÕacb�lt¥V���¡���s7���;��s7��� w�l�iÊ���`_º�;_��¡�*�����;º�ob����s��¡s�b������(� £��l {�� � �� ����i {���� ���¤¼M����{`� � ��� �����t{mz$� ���¤d�y9{m{$�M���`_ ^ �����inv��� ^ �� ^ ������vl����>iu�`_j�;���jb\_jiu���V���;m´µ����s;_jin����v���l��a���iupnp�b���s����`l ^ ���axin�iu���×�;_Q��b�iu�`_j�;�ob���s;�m��b���]p�b���iu�;�jb��s7��iu�v���vp�b�s����*�×bc�����,l`fhpnQ����_Q����b�pu�Ŭ�*���`_ ^ �����*iu�l���� ^ ��in������Ïs���� ^ _��X����p�b¡ &����3_j�W���º´µ����s3_jiu���������*���`_��;� ^ ��b���W��e¤�3¥ ^ pu��in_7b\_jiu���^ bc��p egb��*��pniu����bc_jin��� ���?pub¶��in ^ ����iuz�iupuik_j�c�¨���?pub �Ñb�z�iupuik_j�c�®���?p�bÏ�×bciu�`_j�;�ob�z�inpuin_����;_����×p�bV���s;lt¬�in_j�×������yt�_ u;���; l]³(b����i�pu��>_j�jbÕacb�lt¥ pu�; ^ pul�����s;���`_j;�,p�b¶_j��u���$���$�mbc_j��b�puin�? ºb�������l���b�l�¤ ºb��o���$� ^ ����_j�W�l��vp�b ���;_jin���¶������*�x������;_�����Viu�`_j�;���jb\_jiu���Vbcl¶��;iu�V����pub ´µ����s;_jin���Ï�l ^ ����ati̬iu��� � �o��l�����9l¤� � l®£���º_��jbÕacb�lt¥ ���`_ ^ ��l��º����l�º����lx¥ b� ^ ��s3_jXin��_��������b��`_j��®pub×sÕbc�jb�s3_j���iu�bc_jin������;R�*�t���;������×b��s7������;_:��egb���� ;_�R��e¤l���� ^ bc�_R�3_:p�b ^ ��in��m���&s���� ^ _��º���ºpub>s;��� ^ bc_jinz�iupnin_j�:�����*�t���� l

Recouvrement

Gestion des Modes

Pilotage

Supervision

Planification/Ordonnancement

Commande

Partie

MAINTENANCE

Surveillance

Partie Opérative

�������q�/lg� �����! 1$�$� �$ "����� 35"8+ �A�5"29� "����� 35"298$ ��35"29

d5b=sÕb���b�s;_�����injbc_�iu��� ^ �� ^ ����;�Ï�� ^ ����$l�� p e¤iu���;�&wxl��Vpub ^ �;��s�� ^ _jin��� ���$p e¤�;_7b\_ � ��l��*�t��� ���e¤l�� yx_tu��*�$��� ^ ����� ��l ^ ��iu�`_����&axl��Ïb���� ^ _j�,l²d5b=���;�×b��s7���$s������iu�_j� �=���;s���� ^ ������;�,�����b���i u�����iu����� ^ �;���ob��`_�� ^ ��l���s7�ob�w�l�� ^ ��iu�`_�����axl�� � ��l$´µ����s3_jiu��� � ��s7��b�w�l��>�3_7bc_v�;�¶���l��¬ �;_7b\_js;�mw�l�i¢���������m�obciu��b���s;� �W����]´ b���inpupn������v�*�t���;��`�3_R���;Q�3_7bc_� ltd5��_7bcz�pu��b�l?�/ln�v�l�ikacb��`_����������

Page 52: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� ���6� �K� �V�6� � � ���@��������� ��@�y�*� �� ���� �#��� �����������6�@�y�� �

l��V�Å¥t��� ^ pu�����;v��i��q�����;�`_jv���x����:�3_v�;_7b\_j ^ ��l�acb��`_ ;_j������ �o��iu l¯Ñb��*iupupn�� ¹V�t���� � _jbc_j¬�¹¶b�in�`_j����b���s�� ¬Q¯Ñ����s;_�iu���������*���`_ ¬Q�v���Vrtiu����i �os�bc_jik´ � ¹¶¯5¬h�� �¬Q�v������b�p�� ¹¶¯M¬ � �¬Q m������b���� � ¹¶¯5¬h� �¬Q½v����vrx���axins�� � ¹¶¯M¬ �� �¬�¹¶b�iu�`_����ob���s�� ¬Q�v���Vrtiu����i �os�bc_jik´ � ¹ ¹&¬h�� �¬Q°,jb�in � ¹ ¹$¬ � �¬]fh�`_����a����`_jin��� � ¹ ¹$¬ i �¬�¹¶b���s7��� ¬Q�v���Vrtiu����i �os�bc_jik´ � ¹ ¹Vb\¬h�� �¬�¹Vb���l���p � ¹ ¹V�v¬ � �¬]����� ;_ ¬Q�v���Vrtiu����i �os�bc_jik´ � ¹V��¬h�� �¬ � _jbc_v ��;_������in����� ¹V��¬h� �¬ � _jbc_�fh��in_�i�b�p�� ¹V��¬hi �¬Q½v����:¼M�����iu��� � ¹V�v¬ ��_ �¬Q³,���x��l�s3_jiu��� ¬Q¯Ñ����s;_�iu���������*���`_ ¬Q�v���Vrtiu����i �os�bc_jik´ � ³²¯M¬ �� �¬Q�v������b�p�� ³²¯M¬h� �¬Q m������b���� � ³²¯M¬ � �¬Q½v����vrx���axins�� � ³²¯M¬h�� �¬�¹¶b�iu�`_����ob���s�� ¬Q�v���Vrtiu����i �os�bc_jik´ � ³]¹$¬ �� �¬Q°,jb�in � ³]¹$¬h� �¬]fh�`_����a����`_jin��� � ³]¹$¬hi �¬�¹¶b���s7��� ¬Q�v���Vrtiu����i �os�bc_jik´ � ³]¹¶b\¬ �� �¬�¹Vb���l���p � ³Q¹Ï�v¬h� �¬]����� ;_ ¬Q�v���Vrtiu����i �os�bc_jik´ � ³¢�v¬h�� �¬ � _jbc_v ��;_������in����� ³¢�v¬h� �¬ � _jbc_�fh��in_�i�b�p�� ³¢�v¬hi �¬Q½v����:¼M�����iu��� � ³q�v¬ �`_ �

����� �¨�9lk���! ��$ ��+�+,"2983�) $ ��35"�3� "#" � + ��� ��$ "����� 3�) � � �£��;R���x���;������_Rl�_jinpuiu��]�ob����pu�v���x�1u�pn�m����:s���� ^ ��jbc��_��w�l�iq��� ^ �������`_j�c�o�l�ikacb��`_Rs7�ob�w�l��

���x�����cp e¤�;_jbc_(��b���,pu�;w�l���pt��R_j���l�a��Rpu�Rs;��� ^ ���b��`_��*�t����puin�� lcd®��´µ������b�puin��*�]s7����iui����_,pu�:rxyx��s3¬£��ob��_(�¤�m��� {mv��]������_�pu�;���b�s���c¬h�3_7bc_� �µpu��Ws�����_���pupubc_jin���� � �;� ^ b���b�pup u�pu�;�s�������� ^ ���������`_ bclt¥���x����Ê����´µ����s;_jin�������;���;�`_ � a���in�%�o��l������/l � � l ¼Ê��l��pu�;(�*�t���;Ê���`_,������sRb�s3_jin´µÊ���¡�� ��*�²_j��� ^ s��vwxl�io����s;���in_��ml�� �3_7bc_]�����x¬h�in����i �osÕbc_�in´ ^ ��l��,s7�obcwxl��m�*�t����b �o� ������� ^ b�²�����;_j���l�a����]�ob�������W�;_jbc_j������ s;��� ^ bc_jinz�pu�; l� m��lt¥ �3_7bc_�W���`_W��in_�Xiu��s;��� ^ bc_jinz�pu�;��i,p e bcs;_jikacbc_jin���¶iu�¡l�pk_7b����������s��;W����lt¥ �;_7b\_jº_j��b���l�ik_Xl�����in_�lobc_jin���¶����b��`_jinwxl����*���`_�iu��s;�������s3_j��� ³,��t��l�s;_jin���t¬­¹¶b���s7���3¬¹¶b���l���p��3_*³²��t��l�s;_�iu���t¬ ����� ;_�¬­½v����¡¼M�����iu��� �;� �� ��*�×_���� ^ ^ b����Å¥��;� ^ pu� � l,d5b=����_jin���T���s���� ^ bc_�iuz�inpuin_�� ^ �;���*�;_����X���3_j�;���*iu���;�:p�b�s;�����������s;�>������;_jbc_j:��e¤l��$�*�t��� ^ b��:�jb ^�^ ���_ ��s��;lt¥��egl�� b�l�_����$�*�t��� l,d5b s;��� ^ bc_jinz�iupnin_��*����*���x���� �;_*� �q��s3_jl��;�¶����´µ����s3_jin��������*s����`_��jb�in��_���

Page 53: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � � �3��@���� � ��� ������� �����@�y�� � ��� �/��� �t�

in� ^ ����;�� ^ b��ºpu��s�����s;� ^ _���l��Ol5 ºb����s;��s����`_j�Å¥x_j� p�b?���;_�iu���=�����*�x����º�;_Wb��l����� pu�����w�l���pn�^ bc�jbc���>�¨egl��V���x�������W´µ����s;_�iu���������*���`_ i

� l��¶b�l�_j��>�*�x���j���´ b�in_��;��_����>pu�;m�3_7bc_�ms;��� ^ b\¬

_�iuz�pn�� l

�� ��

����

Modèle de composant : SRI

PA−ht PA−ns

PA−dPA−i

PM−ns

PM−a

PF−n

PF−ns PF−hs

PF−d

PP−e

PP−p

PP−ns

repare/

def2/

repare/

fns and not PA_ns/

fns and not PA_ns/

fns and not PA_ns/

def1/

signal ans, pns, fns, mns

pns and notPA_ns/

fin_pp/

pns and notPA_ns/ PM_ns/ans

Prod and not

ad and not Pm_nsand not PF_ns andnot PP_ns/

ai/aht/mns

aht/mns

Ma and notPA−ht

mns and notPa_ns ans not

PA−d/pns, fns

ai/pns, fns

ai/pns, fns

ans and notPM_ns

ad/aht/mns

fin_d/

prod and notPM_ns/ans

�������q�9l ��� � " "%$ � +,"�35"8$ ��3��%+," 35" ���*$ �!�;9 �$�! �3�) ��� � �%) � � � �

»m��¹V�t��u�pu��¯o����s;_�iu��������p���e¤fh� ^ p�b��`_7b\_jiu��� � pu�;���;�`_7b�in��� � ¹¶¯(f­° � ^ ������3_(�¨eg�Å¥ ^ ��iu�*���Êpu�;(��ik´�¬´µ�;�����`_���,s���� �o��l���bc_jin����Ê�;_�a�����iu����,���Rs���� ^ ��jbc��_������b�puinjb��`_Êp�bm´µ����s;_�iu���¡�������;�jb�pn����l��yt�_ u;����3_jl���in�,lM£������x�1u�pn���;_>pu�;W�*�x�1u�pn������*s���� ^ ��jb��`_W����`_>l�_jinpuin��� ^ ��l���s;����_���l�in���*l�� �*�x�1u�pn����?´µ����s;_�iu������� ^ ���;��;��_jb��`_Õ�²����b�pu�;���;��_ ��l��´µ������?���¶r�yt��s�£��ob���_Õ�,pub ��iu ^ ����iuz�inpuin_������Ïs;�;__j�´µ����s;_jin��� �3_ pu�� bcpn_j�;���ob\_jina��� ^ ���iuz�pu�� � s���� �o��l���bc_jin����¡�3_�a��;���in���� � l²d5b s�����_j�l�s;_�iu�������&pub^ bc�_jin�>�3_7bc_�����s;�¡�*�t�1u;pu�����;s����ik_j�¡���������¡z����lt¥Vs�b�pus;l�puv�;_ºa����i �os�bc_jin����v���¡s������������s;��b �o��������3_j�;���*iu���;�:p e¤�;_7b\_:��e¤l��¶�yt�_ u;��� � ^ b��_�iu�R���Wp eg�3_7bc_����W���s�����_�in_jl�b��`_j l

£��;__j� ^ ��� ^ ���ik_jin��� ^ �;���*�;_º����s�����_���l�in����������*�x�1u�pn���_j�tu;��ius7���;��¨�;�¶_j�;���*��m��egin��´µ����×b\¬_�iu����º´µ��l�����in��;�®�l��Wpu���yt�_ u;���*���x���;puiu�,l5£�� ^ �;���ob��`_�s��;__j� ��ins7������×b�� u;��� l����*s���� ^ pn�3¥tin_��in� ^ ���_jb��`_j������ �*�t�1u;pu�;���l�� �=p�b �*iu��×��� ^ b��jbcpup u;pu�����&�����¡z�����lx¥����x�1u;pu�� �=�3_7bc_� l²£��;s�i�;��_��jbc¾u���¶l��������¡z���¶in� ^ ���_jb��`_×���¶a��;��i ��sÕbc_�iu����;�Q�3_&��e¤�3¥ ^ ����iu����&�l��?pn��×_��jb����in_�iu������²���s;������ik_jiu����X���*s���� ^ bc_�iuz�inpuin_��,l¢¯(in�ob�pu�;���;�`_�pu����*�t��u�pu�;X����`_W_j�;pupu�;���;�`_���ius7����Wwxl¨eginpu����;�������`_

Page 54: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� ���6� �K� �V�6� � � ���@��������� ��@�y�*� �� ���� �#��� �����������6�@�y�� �

s��;__j�>b ^�^ ��ts7���W_��tu�v��i � s;iupn� �*lt_jiupniu��� lt� ���lt_j�����w�l��Ws��3_�_j�>b ^�^ ���xs7���>�;_ ^ l�����*���`_ml����>b ^ ¬^ ���xs7�������>s;����_���l�s3_jin���¶���;��*�t��u�pu�; ^ b���pu��s�����s�� ^ _j�;l����3_�w�l�egb�l�s;l��=���;sÕb���iu��*�X��� ^ �;���*�;_���¶pn��×s;�����_j��l�iu���¶b�l�_����×b\_jiuw�l��;���;�`_fl²�m��l�×��;_jin����������������Õbc������iu��*p e¤iu���;�$��e bc� ���iu�������Ï�����;_7b\_j���in_�������$�in����i ��sÕbc_�in´µ ^ ��l��:pub ��Õb�pniu�bc_jin���×����pub s;��� ^ bc_jinz�iupnin_��v�;�`_j���W�*�t���; l

��� B�� � ���3+ - ��� �/A 2�AG? 0�8��F2�A��/46. ��A=8�? ?�>�+�5QAd®� ������l ^ � ·º����b���iu�bc_jin��� �3_ £�������l�ik_j� ����¶rxyx_tu��*��V��� ³²��t��l�s;_�iu��� � ·�£:r�  � ��l d5b\¬zq����bc_j��iu���*��e¤���obcpnyx��?�3_���e¤���s7��in_���s;_�l����×���� r�yt�_ u;���;�� d®���ºr � _��jbÕacb�iupnpu� ��� ^ l�iu ^ pul�>��� � �b����l��]l������_j�l�s;_�l����m��iu�;�jb��s7��iuw�l����;_����x��l�pub�iu��R���vs����*��b������c�`�l���a���inpupub���s����3_�l ^ �;�axiuiu���

� r�bc� z�x�� � � «����1zm{�� � � £���� {���� � � � ��{mq$� � �g£��obm{`��� � �g½v�;_ {mv$� � ����b�� {�x � l  ºbc�� � ��b�� {�x ��s;�;__j�Rb ^�^ ���xs7���b&b�zq��l�_jin� �?l������_j�l�s;_�l������;� bc��z���¡��l=s7�ob�w�l�� ��ika���b�l=s���� ^ ���_��¡l��=���������z�pu���������x��l�pn����s7�ob������Õb��`_,�����in��´µ������bc_�iu����5bÕa���sR���;��*�t��l�pu��5���Q��ina��Õb�lx¥¡in��´µ���iu��l���M�;_�pn�Q�*�x��l�pu�²���Q��ina��Õb�l�l ^ ���iu��l�� l5£��obcwxl������x��l�pn�>in��_tu�����¡l��=l ^ �;�axiu��l��Xs;�����_jin_�l��¡���¡_�����in��;pu���*���`_�ºw�l�i(���`_�pu����x�1u�pn�¡������;´µ�������s;���5pu�����x�1u�pn�¡�����_j�jb\_j����iu���;_�pn�¡�*��_j�;l��º��e¤�3¥ ^ pn��in_jbc_jin��� �µa���iu� �o��l���×�/lrv � l£��*��������iu���X�;_Ws7�ob����� ��egb ^�^ pniuw�l����Xpub×_��jbc_�����in����� �l���a��;iupupub���s;�¡iu� ^ ������ ^ b��Xp e¤� ^ ���jb\_j��l��º�;_��� ���pn��s3_jiu���������Xp eg�;����;�¡z�pn�¡����X´µ����s;_jin����X����l��a���inpup�bc��s��c�¨��� s�������b��������;_�����l ^ �;�axiuiu���wxl�i®���;ax������_�_��jb�ik_j���Ql���������lta���pnpu�ºin��´µ����×bc_�iu��� l�£��;R´µ����s3_jiu����:����`_�pub�s����*��b������c��p�b¡�� ^ �iu���p e¤l������;��s��c��p�bº���3_j��s3_jin�����`pu����iub�������_jins��cpu�:�l�inaxio�;_Qp�bº���;s�in�iu����l�d®�vpn��s3_j��l�� ^ ��l���jbº_j���l�a����]�ob���� £ ���

+������l����Ryx�`_j��u�������;����'�o��in_�iu����(���Rs;��(´µ����s;_�iu���� ^ ��� ^ �����;²b�l¡��;iu�¡��l�������l ^ �Q����_j��b\¬

a�bciup ����l�_����×b\_jiu�bc_jin���º���;�r�yt�_ u;���;�r'&���M����¯o����s;_jin�������;���;�`_ � �µ�Xr�r�¯ � ���Qp eg�Å¥�����l ^ ���*���`_^ ��l��ºp�b?±���s7������s7�����;� ³,��t��l�s;_jinw�l���� �±v³ � l�d®���*�t�1u;pu�>���¡���3´µ�������s;�*�� ^ ������`_j�*p e¤�������¡z�pu�����²_j��b�in_����*���`_j,����l��a���iupnp�b���s��3¬ s����*��b������Rw�l�e¤iup���_ ^ ���iuz�pn�R��egb ^�^ pniuw�l����²�;� ^ �������s;�m��e¤l�������;´ b�inpupub���s�� l²£��Ï���x�1u�pn�&���_�z�b���Ï�l��*pu�$s;����s�� ^ _���e bcs;_jikaxin_j�&�3_×�b �_j�l�s;_�l����Ï���Ïs����*�×bc�������_����;�����iuw�l��,l]£���b�s�l����V���Ïs��;*b�s;_�inaxin_�������_×�� ^ ������`_j�;� ^ b�� l�� �t¬ l ^ pu�3_ s�����_j�l�in_ l�� p�bpuiu�_j�����;X´µ����s;_�iu���� ^ ���;����`_���� ^ ���;s��������*���;��_�b�in���i�w�l�� l���pu��X������l��s��; ^ �`yx�inwxl���W���������^ b��ºpn���*�t��l�pu���3_X�l��ºpu�; ^ ���x��l�ik_jv_j�jbc��´µ������; ^ b���s���X������l��s��; � ^ b��º�Å¥t��� ^ pu�¡pn���t¬ l ^ pn�;_� s;���*�×b��������Ñ���3_j��s3_jin�����Ñ�l�ikaxi �o���;���l���s;��� ^ ���x��l�ik_��}s�b��jb�s3_j�;��iu��l�����b�s3_jikatik_j�W���Ws����*�×bc��������$´µ����s;_�iu���������*���`_�� ^ _�iu��b�p � lt� ^ bc�_jin�R����s����*�t��u�pu�c��pn�Xs�����s;� ^ _���l�� ^ ��l�_mb�pn����R��pn��s;_�iu���������pu�� bcs;_jikaxin_j�;���� ^ ��s3_7b��`_*pu�;¡s�����_��jb�in�`_j������×´ b�z��iusÕb\_jiu�����5s�e¤��_�¬ �\¬ ��iu��?pu�;¡s�����_��jb�in�`_j���pniu�;�� �p�b ^ ��pnin_jinw�l������ ^ ��t��l�s;_�iu��� ���×p eg�;��_���� ^ ��in�� � ^ ���x��l�in��� _j��lt_������ ;���c�®_j��pn�����;�>s;����_7b�in����>���3¬´ b�iupnp�b���s;��Ol l l � bciu��ivw�l��Ïs��;pupn��*puiu�;�� � pub ´ b�z���insÕbc_�iu������l ^ ���x��l�ik_fl]£��3_×�;����;�¡z�pu�V��egb�s;_�inaxin_���s�������� ^ ����� b�l$�*�t��u�pu������_j��bc_j�;��iu� l

£��;²_��jbÕacb�lt¥¡s����`_jin��l����`_Q��eg�3a���pnl����²bcl*��in�*��l������l ^ �v·�£R Xr �g£R Xr ����� � �`�×b�in(p eg�Å¥t_�����iu���wxl�i,����l�Xin��_�������� ^ b��_�ius�l�pui u;���;���;��_ºb?�;_�� ^ ��� ^ ����;� ^ b���½v��s;_����W¹V�;����� ��b�l=��iu� ��l d5b�z¢�c¬�jbc_���iu��?��e¤��l�_����×b\_jiuw�l������ X��������z�pu� � d®� � �g¹V���`��� l�°,��� �q�;_ pu�;l��¡��z ���s;_�in´m���_ ��eg�3_j�;�������s���lx¥=��������b�� {�x �(�;� ^ ���;�ob��`_º�;�=s���� ^ _��>pn����*�x����m������b���s7������3_º��egb���� ;_�º�ob����pu�;ºb�s3_jikati̬_j��X��l ���x�1u;pu���������3´µ�������s;���;_X�;� ^ ��� ^ ���b��`_Xl����¡�*�;_����x���>´µ������;pupn�W���¡yx�`_j�1u;�� ���¡pn��iuv���

Page 55: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � � �3��@���� � ��� ������� �����@�y�� � ��� �/��� �,q

����������������������������������������������������������������������������������������������������������������������������������������������������

����������������

��������

������������������������������������������������������������������������

����������

���

��������

�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

����������

������������

�������������

�������������

������������

����������������������������������

�� !�!!�!"�""�"

##$$

%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%%�%�%�%�%�%�%

&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&&�&�&�&�&�&�&

'�''�'((

)�)�)�)�)�))�)�)�)�)�))�)�)�)�)�))�)�)�)�)�))�)�)�)�)�))�)�)�)�)�))�)�)�)�)�))�)�)�)�)�))�)�)�)�)�)

*�*�*�*�*�**�*�*�*�*�**�*�*�*�*�**�*�*�*�*�**�*�*�*�*�**�*�*�*�*�**�*�*�*�*�**�*�*�*�*�**�*�*�*�*�* +�++�+,,-�--�--�--�--�--�-

.�..�..�..�..�..�.

/�//�//�//�//�//�//�//�//�//�//�//�//�//�//�//�//�//�//�//�//�/

0�00�00�00�00�00�00�00�00�00�00�00�00�00�00�00�00�00�00�00�00�01�1�1�1�1�11�1�1�1�1�12�2�2�2�22�2�2�2�23�33�34�44�45�55�56�66�6

Modèle de Modèle de

stratégie

Commande

Diangnostic

Détection

Décision

Reprise

Urgence

Suivi

Niveau inférieur

Niveau superieur

Module

Module Module

SUPERVISEUR

Module

Acquisition/Orientation

O

P

E

R

A

T

E

U

R

référence

�������87/lrv�� � " ���2129;"��! ��$ "����� 3� ) � $ ��3�)5+,"�35" 9%) �0:�"���+�+ �$� �2"� ���*$ $ �$� 35"

9;:=<;>@?BADCECGF@HJIB?K?MLON=?P9;:=QR?M<;>SAD9;ADTUH lV FWQ=<XAE9X?P?BHYIBTUZ[QJL\?KNJ?B9OZ]TSN=?B9^9;?P_`FaAEL^?BHYF � TU:bLcF@HdLOCfehgBCEgBZ[?BHdLiZ[TbN=?P?MHYIMTU:=<X9OF@:jHbkl:=Q=CD?mL

N=gMIB<;AE>aF@HdL[CD?B9]F@ImL\AE>SAnL\gB9oN=?j<Xgm_pgB<;?BH=IM? lrqrs F@IB:JH=?tN=?M9uF@ImL\An>bAnL\gM9[H8evgmLcF@HdL]QwF@9[IBTUZ[QwFaLXADx=CE?yFz>@?BII s FaIB:=H{N=?B9PZ[TbNJ?B9B|8IB?BIMA}IBTU<;<X?B9;QRT@H=N � <;gBQwFa<;L\AE<KCD?M9 qJ~ F@IMLXAE>SAELXgB9�N=:{Z[TbN u CD?�NJ?W<XgM_pgM<X?MH=IB?[N=?� � F@Z {�x � 9;:=<�CE?B9 ~Sx Z]TSN=?B9�N=g � H=AE9�NwFaH=9�CE? P�����Y�]la� ?rH=TU:b>U?BCECD?M9�IMTUHdL\<XF@ADHdL\?M9�TUHdL�gMLXgrN=g � H=AE?B9F � H�N=?WCDAEZ]AnL\?B<^CE?�H=TUZ�xJ<X?�N�evF@ImL\AE>SAnL\gB9 l�q ?mLXL\?o?��bLX?BH=9;ADTUH{F�_`F@AnL�IM<XT@�EL\<X?�CD?�HJTUZ�x=<;?WN�e�FaIML\An>SAEL\gM9N=? qJ~ � {mz ?MLOCE?KH=TUZ�x=<;?KN=?KL\<XF@H=9XAnL\AETUH=9 ��~U~Sxb~,l

V FWZ]gmL s TSN=?PN=?P9;�SHdL s1u 9X?�<X?MLX?BH�:=?�<X?m>bAE?BHdL � <\F � H=?M<OCE?KZ]TSN u CD?KN=?P<Xgm_pgB<;?BH=IM?�?MHYAEH�LXgB�U<XF@HdL9;:=IBIM?B9X9;AE>@?BZ[?BHdLoCD?M9�Z[TbNJ?B9�N=?�Z]F@<XI s ?B9�?mL�N�evF@<;< LX9B|�CD?M9�IBT@H�LX<\F@AEHdL\?B9�N=?[9XgBIM:=<XAnL\ga|�N�ehgBIMTUCDTU�@AD?@|N=?tQ=<XTSN=:=ImL\AE>SAnL\gt?mL�N=?���:wF@CEAELXg@|�Q=:=AD9�CD?B9]< u �UCD?M9uN=?�Q=<;ADTU<;AEL\gjN=g � H=AD?M9�QwF@<]CD?�IMTUH=IB?MQJL\?M:=<B|r?ML?MH � HuCE?B9r<;gB�UCDF@�U?M9�N=?�<XgMIB:=<;9XAE>SAnL\g � � �U:J<X? 7/l x � lJV ?OZ]TSN u CD?ON=?�<;gM_pgB<;?BH=IM?�gML\F@HdL�Z[TbNJgBCDAE9Xg^QwF@<�:=HF@:bL\TUZ]FaL\? � gML\FaL\9M|�IM?B9�<\F � H=?MZ]?MH�LX9�9;:=IBIM?B9;9XAE_p9�IBTUH=9;AD9 L\?BHdL � AEH�LX?B<;N=AD<;?�NJ?B9OgMLcF¡L\9OADH=N=gM9XAE<\F@x=CE?B9M|9Me�F@QJQwF@<X?MHdLcF@HdL�F@ADHJ9XA � :=H=?PN=gMZ�F@<;I s ?PN=?P9;�SHdL s1u 9X?�9;LcF¡L\AD��:=? l

� :YQRTUAEHdL�NJ?�>S:=?�N=?�CDFWN=g � HJAEL\AETUHyN=?B9�Z]TSN=?M9ONJ?�_pTUHJIML\AETUH=H=?MZ]?MHdL¢|£IB?mLXL\?�F@Q=QJ<XTSI s ?�:bL\ADCEAD9;?LX?BCD9���:=?BCE9¤CD?B9�Z]TSN=?B9�N=?iZ]F@<XI s ?M9¥?ML¥N�e�Fa<X< L\9¤AEH�LX<XTSN=:=AnL\9�QwF@<¥CE? P���t�Y� ld� CECD?r?M9;L}N�eh:=HoF@QJQRTU< LAEH�LXgB<;?B9X9XF@HdLiNwF@HJ9rCD?O9X?MH=9�T + ?BCDCE?�IMTUZ[Q=C u L\?OCD?B9}L\<XF¢>@Fa:b�]N=? �v� F@x {mv�� ?MH�IBTUHJ9XADNJgB<\FaH�Lr:=H=?�?BHdL\AnL\gF@:bL\TUH=T@Z]?�NJ?�9;:=<;>@?BAECDCGFaH=IB?�k¦IBT@Z]Z]F@H=N=?�NwF@H=9^CGFWQ�TUCDAnL\AE�S:J?�N=?P�U?M9;L\AETUHyN=?B9OZ[TbN=?M9 l

Page 56: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� ����� ������� � � ���� ������������� ��*������ ���� �#��� ��������������������

Modèle de référence

intégration de modes de marches et d’arrets

Modèle de référence réduit

synthèse 1

synthèse 2 productivité, qualité

Modèle de référence réduit

Modèle de référence réduit

Modèle de référencefinal

synthèse 3

synthèse 4récursivité

priorité

Sécurite, écologie

�������R7/l x���� 1%$ �$� ����" ��� ���!�;9;12" �!�*) � + � 9 � �! � �29;" 35"8+ ���,9�35" 9%) �0:�"���+�+ �$� �2"

� ��� � � �"!�#$��!&%'�)(�*�+�,-�)(�("!�. !�(/+0!1+325476 8:9 ;=<?>

@ TU:=9�F¢>@TUH=9KN=g � � gM>@Tb��:=gWNwFaH=9�CD?�I s F@QJAEL\<;?�Q=<;gBIMgBN=?MH�L�IM?B<;L\F@ADHJ9�L\<XF¢>@Fa:b�YAD9X9;:=9�N=?�CfehgB��:=ADQ�?qBADC N=: V���E la� F@H=9¤IM?BCD:JAnk¦IMA�H=TU:=9¥gm>UTS��:=?B<;TUH=9¤IB?M:b�WQ�TU< LcF@HdL¥9;:=<�CE?B9¥Z[TSN=?B9�N=?r_pTUH=ImL\AETUH=H=?MZ]?MH�LB|F � H�N=?�9XAnL\:=?M<�H=T@LX<X?�Q=<XTUQ�TU9;AEL\AETUHyNwF@H=9�:=H=?�Q�?B<;9XQ�?BImL\AE>@? s AE9;L\T@<XAD��:=?�CDTSI¢FaCD? lF@ TU:=9�Z]TUHdLX<X?B<;TUH=9�S:J?OCDF�Q=<;TUx=CDgMZ�F¡L\AD��:=?�N=?iCDF��U?B9 L\AETUHWN=?B9¤Z[TSN=?B9¥?M9;L}:=HJ?iQ=<XTUxJCDgBZ]FaLXAD��:=?�N�e�FaCEL\?M<XHwFaH=IB?i?mL¤��:=?iCGF9;LcFax=ADCEAEL\grQR?M:JL}� L\<;?^QR?M< � :J?�QwFa<�CDFK<X?BI s ?B<XI s ?�N=?M9�gmLcFaLX9�NJ?�<XF@IBIMTU<XN=?MZ]?MHdL lG@ TU:J9�QJ<XgB9;?BHdL\?M<XTUHJ9F@ADH=9;AwCD?M9}LX<\F¢>aF@:b�oNJ? � :J9;LcFaQ s F @ TU:=<;?BCE_`F¡L s �H@ TU: {�x�� Q=:=AD9}IM?B:b�[N=? A F@Z[AD< qrs F � � �vqrs FJIJI � lSV ?B9L\<\F¢>aF@:b��9X:=<OCGF�9 LcF@x=AECDAE9\F@x=AECDAnL\gON�e � xRNJ?BC s F � ADZ "Ks F¡LcF@x �)"Ps FJIJI � HJ?�9;?B<XT@H�LOQwFa9Ogm>UTS��:=gB9�I¢F@<^ADCE9QRTU< L\?MH�LO9;:=<^N=?B9OZ]TSN u CD?B9�L\?BZ[Q�TU<X?MCD9iN=?M9 AJ�}� ?MLO9XT@<;L\?MHdL�NJTUH=IPN=?PH=T@LX<X?PI¢F@NJ<X?PN=?KL\<XFz>aF@AEC l

����� �~B 032 �=? A}2�A �/46. ��A=8�? ?�>�+�5QAV ?B9�LX<\F¢>aF@:b� NJ? � :=9;L\F@Q s F @ T@:=<X?MCE_`FaL s �H@ TU: {�x�� 9BehADHdL u �U<X?MHdL]N=F@H=9WCGFtL s gBZ]FaLXAD��:=?uN=?y<;?mk

I s ?B<;I s ? �KA gMIB:=<;AEL\gML�QRgM<\FaLXADTUH=HJ?BCDCE? � ADHJAEL\AEgB?oQwF@<ON¤<XAEI @ AE?BC �P@�Qm{d7�� l�V Fj9XgMIB:=<;AEL\g]TUQ�gB<\F¡L\ADT@HbkH=?BCECD?PIBTUHJ9XAD9 L\? � Q=<;?BH=NJ<X?�?MHtIMTUZ]QbL\?�CGFo9XgBIM:=<XAnL\g�F � HY�S:8ev?MCDCD?PL\<XF@AELX?KCD?M9�<;AD9X��:=?M9�IM<XAELXAD��:=?M9^LXTU:JL?BH�Fa9X9X:J<\F@HdL�CDFWIBTUHdL\AEH�:=AELXg�NJ?�CDFoQJ<XTSN=:=IMLXADTUH � lR� F@H=9OIB?�IBTUHdL\?��SL\?@|�:=H=?�N=gm_`F@ADCECGF@H=IM?�?B9 L�Q�?B< � :=?IBTUZ[Z]?K:JH=?�Q�?B< L\:=<;xwFaLXADTUHyN=:jZ]TSN=?KN=?K_pTUHJIML\AETUH=H=?MZ]?MHdL�HJTUZ]AEHwF@C |bNwFaH=9^CD?B��:=?MC�?B9;L�F@9;9X:=<;gB?�CGFQ=<XTSN=:=ImL\ADT@H ldV ?B9}TUx � ?MIMLXAE_p9¤N=:WL\<XF¢>@FaADCJNJ? � :=9;L\F@Q s F @ TU:J<X?BCn_`FaL s T@H�L}gmL\g^N�evF@Q=Q=CEAD��:=?M<¤CGF�L s gBTU<;AD?

:�� � ,���+-$ ��(�$-�#EB����+ � ��� >�%=8'�$&( +&%�) 0�'�( �3>�+;>-,�' L#����+ ,#����,#>-%�� � ��� ��$&, 6�'F= +&( L ( +-%�) �!� >-%#=�'�$&( +&%5,���%�$ � +&( ,#�����3� ���/�3>�+6�,��F= '��9� =8, EB��,#>&����+-� 6�J � EB%���(�,�$ � +-(�,�� 6.� ���B�9$-,.6.'F=8+-( L ( +&%���+56.�<�!� 0�'9��� ( +-%#�

Page 57: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � � � ���� ���� � ��� ������� ������������ ��� ��������� ��� �J�

��� QRTU:J<KCfehgML\:JN=?oN=: Z[TSN=?�H=TUZ[ADH=F@C�?mL�NJ?[Z[?ML;L\<;?W?BH{Q=CGF@IM?W:=H{Z]gMI¢F@H=AE9XZ[?�N=?o9X:J<;>U?MADCECGF@H=IM?N=?M9�Q�?B<;LX:=<Xx=FaL\AETUH=9�?mLW:=H=?�9;L\<;:=IMLX:=<X?�NJ?uIBTUZ[Q�?BH=9XFaL\AETUH Q�?B<;Z]?mLXLcFaH�L�N=?u�dF@<;N=?B<�CD?]Z]Tz�U?MH N=?Q=<;TbNJ:=IMLXADTUH{TUQ�gB<\F¡L\ADT@H=H=?BC¤LXTU:JL�?BH Z]Fa�DLX<XAE9\F@HdLPCD?M9�<;AD9;�S:J?B9�?MH=IBTU:J<X:=9 l¥V FYN=gMZ�Fa<XI s ?]Q=<XTUQ�TU9;gB?IMTUH=9XAE9;LX?�NJTUH=I � IBTUH=9;ADN=gM<X?M<O:JH=?P9;L\<;:=IMLX:=<X?�IBT@H=9;LXAEL\:JgB?PN=?KL\<;TUAD9iQwFa<;L\AE?B9 � � �U:=<;? 7/lrz ���

� :JHjQJ<XTSIBgBNJg�IMTUZ]Z]F@H=NJg@|� :JHj9;:=Q�?B<;>SAE9X?B:J<�H=T@Z]AEHwF@Cf|� :JHjZ[TSN=:=CD?�N=?P9X:=< >U?BAECDCDF@H=IB? l

d’événementsobservation

controlables etincontrolables

inhibitiond’événementscontrolables

SurveillanceModule de

(MS)

S

Supervision nominal

Procédé commandé

G

^^^

��������79l|z � � "�%)!�� ) �7" � 3 ���� 12" 35"8+ � 9%) �0:�"���+�+ �$� �2" %&+ � ���*$ $ �$� 35"� 9%) ��"��0: �,9������ � �*$ � ����+,"

V ?B9KN=?M:b� QwFa<;L\AE?B9�QJ<XTSIBgBNJgWIBTUZ[Z�FaH=N=gmkl9X:=Q�?B< >SAD9X?M:=<�H=T@Z]AEHwF@C�IBTU<;<X?M9XQ�TUH=N=?MH�L � CDFuZ]TSN=gBCEAnk9XFaL\AETUH � IMCGF@9;9XAE�S:J? � NJ?OCDF�L s gMTU<XAE?@|UZ]F@AE9¥CDAEZ]AnL\gB?rF@:oZ]TSN=?�HJTUZ]AEHwF@C

�CD?M9¤gM>@gBH=?MZ]?MH�LX9rN=?^QwFaH=H=?

?mL�N=?j<XgMQwF@<XFaL\AETUH H�eh� 9;TUHdL�QwFa9]Q=<;AD9o?BH IBTUZ[QJL\? l}V ?YZ[TbNJ:=CD?�N=?j9X:J<;>U?MADCECGF@H=IM?YIMTUZ[QRTU< L\?yCD?M9_pTUHJIML\AETUH=9�NJ?WN=gMLX?BIMLXADTUH � TUx=9;?B<;>aFaLXADTUH8|�N=?WIBT@Z]Q�?BH=9XFaL\AETUH�?MLP?MH � H{N=?W<X?MIBTU:b>b<;?BZ[?BHdL l�V Fu_pTUH=I�kLXADTUH NJ?uN=gMLX?BImL\ADT@H � TUx=9;?B< >@F¡L\ADT@H ?B9;LoI s F@<X�UgM?�N=?�9XAE�UHwF@CE?B<�CfehTbIMIB:=<;<X?BHJIB?uN�eh:=H=?�NJgM_`F@AECDCGFaH=IB? l�V FIMTUZ]Q�?BHJ9\FaLXADTUH Q�?B<XZ[?ML�N�evF@9;9X:=<;?B<�CE?W_pTUH=IMLXADTUHJH=?BZ[?BHdL�N=gB�@<\F@N=g l�V ?o<X?MIBTU:b>b<;?BZ[?BHdL�NJgBIBT@:=CD?[N=?CDF�<;gBQwF@<XFaL\AETUH l�V ?B9�< u �UCD?M9�N=?ON=ADF@�UH=TU9 L\AEIO?mLrNJ?�N=gMIBAD9;ADTUH8|S9;TU:J>@?BHdLiADHJIBCD:J9X?B9�NwF@HJ9rCGFP9X:J<;>U?MADCECGF@H=IM?9;TUHdL�IMTUH=9;ADN=gM<XgB?M9�IMTUZ[Z]?�QJ<XgBNJg � H=AE?B9 lC T@:=<oCfehgML\:JN=?yN=: Z[TSN=?�H=TUZ[ADHwFaCf|�CD?B9WZ[TSN u CE?B9W:JLXADCDAE9XgM9�9XTUHdL]N=?B9[F@:bL\TUZ]FaL\?M9 � gmLcFaLX9 l}V F

IMTUHdL\< s CGF@x=AECDAnL\g�TU:PCD?¤H=T@Hbk¦x=CETbIBF@�U?�QR?M:J>U?MH�L�N=TUHJI L\<;?}gML\:JN=ADgM9�9X:=An>@FaH�L�CE?B9�Q=<;ADH=IMADQ�?B9�N=?¤CDFrL s gMTU<XAE?��� IBCDF@9X9;AD��:=? l@V F�Z]TSN=gMCDAD9XFaL\AETUH�N=:WZ]TSN=:=CE?�NJ?i9X:=< >U?BAECDCDF@H=IB?�H=gBIM?B9;9XAELX?iL\TU:JL�N�evF@xRT@<XNWN�eh?BH=<;ADI s AE<CE?[Z[TSN u CE?[NJ: Q=<;TbIMgBN=g�Fz>@?BI]CD?B9�gM>@gBH=?MZ]?MHdL\9�N=?]QwF@H=HJ?]?mL�N=?[<XgMQwF@<\F¡L\ADT@H l�V evTUxJ9X?B< >aFaL\?M:=<�?M9;L:=HJ?�_pTUH=ImL\ADT@H F@9;9XTSIBAGFaH�L�F@: CDF@H=�dF@�@?]N=: Q=<XTSIBgMN=gu:=H ?MH=9X?MZ�x=CD?�N�evgm>UgMH=?BZ[?BHdL\9oN=?�N=gM_`F@AECDCDF@H=IB?

Page 58: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� v ����� ������� � � ���� ������������� ��*������ ���� �#��� ��������������������

Q=<Xgm>bAE9XAEx=CD?M9 l8q ?BIBA�<X?M>SAE?BHdL � :bL\ADCEAD9;?B<O:=H=?�Z]F@I s AEH=?�NJ? � TSTU<X?�QRTU:J<�Z[TbN=gMCDAE9X?B<^CE?�Q=<;TbIMgBN=g l�V ?B9Z]TSN u CE?B9}N=?M9�IMTUZ[QR?MH=9\FaLX?B:=<;9�9;TUHdL�Fa:=9X9;A�NJ?B9�F@:JL\T@Z�FaLX?B9 � gML\FaL\9}IBT@<X<X?M9XQ�TUH=NwFaH�L � N=?^H=TU:J>@?BCDCE?B99XQ�gBIBA � I¢F¡L\ADT@H=9B|zN=A � gM<X?MH�LX?B9�N=?�IB?BCECD?M9�N=:�Z[TSN=?}H=TUZ[ADHwF@C l¢q ?M9�Z[TSN u CE?B9�gM>@TUCD:J?BHdL � � Q=F@<;LXAD<�N=?�CD?M:=<gMLcF¡L�AEH=AELXAGF@C � 9;:=<�TbIMIB:=<;<X?MH=IB?�N�eh:=H�gm>UgMH=?BZ[?BHdL�N=?�NJgM_`F@AECDCGFaH=IB?�?ML�TUHdL�F@:=9X9;AdQRT@:=<�_pTUH=ImL\ADT@H�NJ? � �U?B<CD?i9X:JQR?M<;>SAD9;?B:=<}N=:oZ[TbN=?rH=TUZ[ADHwF@C l@� Ho? � ?ML}IM?BCE:=AnklIBAJHJ?ONJTUAEL¤Q=F@9¤IBTUHdLX<\F@AEH=N=<X?iCE?�IBT@Z]Q�TU<;LX?BZ[?BHdLN=:yQ=<XTSIBgMN=gPQR?MH=NwF@HdL^CGF�Q s F@9;?�NJ?K<X?BIMTU:J>S<X?MZ]?MHdL l£q ? � �U?BF@�U?�9;?K_`F@AELrQwF@<�:=HJ?�>@Fa<XAGFax=CD?�ADHdL\?M<XH=?Z]AE9X? � ~ �

CV � QwF@<�CD?[IBT@Z]Q�?BH=9XFaL\?M:=<�Q�TU:=<�N=gM9\F@ImL\AE>@?B<�CE?]9;:=Q�?B<;>SAE9X?B:J< A |�TU: � I � CF � Q�TU:=<CD?�<Xg¢FaIML\An>U?M<�9X:JAEL\? � C evgm>UgMH=?BZ[?BHdL�NJ?�<XgMQwF@<XFaL\AETUH lw� I s F@��:=?�gML\FaL�N=:t9;:=QR?M<;>SAD9;?B:=<�H=TUZ[ADHwF@C�?M9;LF@9X9;TbIMADg�:=H gmLcFaLyQ=:JAEL\9�NwF@H=9�CE?B��:=?BCOL\TU:J9�CD?B9�gM>UgMH=?BZ[?BHdLX9YN=: Q=<;TbIMgBN=g�9;TUHdLjF@:JLXTU<XAE9XgB9

�IB?MIBA

<X?M>SAE?BHdL � NJgB9\FaIML\An>U?M<�TU: � �@?B<iCD?K9;:=Q�?B<;>SAE9X?B:J< l£V F � �U:=<;? 7/lr{ <X?MQ=<XgM9X?MH�LX?�:JHYIMTUZ]Q�?BHJ9\FaLX?B:=<^��:=A9X:=AnL\? � C evgm>UgBHJ?BZ[?BHdL τ1

� �@?jCE?y9X:=Q�?B< >bAE9X?M:=< l�V evgm>UgBHJ?BZ[?BHdLuN=?j<XgMQwF@<XFaL\AETUH µ2H�eh?B9 L�Q�TU9;9XADxJCD?

�S:J?WNwF@H=9K:=H�gmLcFaL�QwF@<;LXADIM:=CDAE?B<ON=:�IBTUZ[Q�?BH=9XFaL\?M:=<B|RIB?W��:=A¥Q�?B<;Z]?mL�N�ehgM>SAELX?B<�NJ?W<X?M>@?BH=AE<�NwF@HJ9KCD?Z]TSN=?�H=TUZ[ADH=F@CrNwFaH=9o:=H gmLcFaL[N=: Q=<;TbIMgBN=gjADHJIBTUZ[QwFaLXADx=CE?uF¢>U?MIYCE?�9X:=Q�?B< >bAE9X?M:=< l}� QJ< u 9 µ2

|¤CD?9X:=Q�?B< >bAE9X?M:=<�?M9;L�N=?PH=TU:J>@?¢F@:YF@ImL\AE>@g l

v0 v1 v2v4

v3

Cv

Cfτ0

α 3

Comp1β 1

β 1

α 2

Etats puits

q qp0 p1

Stockvide

Stockplein

Σ Σ

α 1Σ − { , α }21 2Σ − {β , α }

S :

Cf CvCf Cv? ? ? ?

τ1Stock

pleinStock

vide

:

α 3 21Σ − { , α , µ }3 21Σ − {β , α , µ }2

µ

�������R79l|{ � � " "%$ � +,"�35" $ ��3��%+,"29�35" ���*$ ��"�� 9 �$ "%) � "� 35" 9%) ��"��0: �,9;"%) �

Page 59: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � � � ���� ���� � ��� ������� ������������ ��� ��������� ��� � x

q ?ML;L\?�F@Q=Q=<;TbI s ?�?B9 LrAEHdL\gB<;?B9;9\F@HdL\?�I¢F@<�?BCECD?iQ�?B<;Z]?mL�NJ?�N=AE9;LXADH=�U:J?B<}CfehgMLX:=N=?ON=:]Z[TSN=?^H=TUZ[ADHwF@CN=?oIM?BCDCE?oN=: Z[TSN=?oN=gB�U<XF@N=g l�V ehgMLX:=N=?[Q=<XgMCDADZ[ADH=F@AD<;?�N=:{Z]TSN=?oH=TUZ[ADH=F@C�IMTU<X<;?B9XQ�TUH=N � :JH=?�FaQbkQ=CEADIBFaL\AETUHYIMCGF@9;9XAE�S:J?�N=?WCGF[L s gMTU<XAE? ��� |�IB?��S:JA¥QR?M<XZ[?MLKN8e�F@QJQ=CDAE�S:J?B<�CE?B9�L s gBT@< u Z[?B9KNJ?�IB?MCDCD?�k¦IMA?mL^N=?�>@gB<;A � ?M<OCE?B9iQ=<;TUQ=<;ADgMLXgB9^N=?PIBT@H�LX< s CDF@x=AECDAELXg�?mLON=?PH=TUHbklx=CDTSI¢F@�@? l C F@<^IBTUHdLX<X?@|£C evAEH�LX<XTSN=:=ImL\ADT@HN=?W>aF@<;AGF@x=CE?B9KAEH�LX?B<;H=?B9M|�HJTUH �@gBH=gM<XgB?M9�QwFa<�CE?oQ=<XTSIBgMN=g@|�NwF@HJ9�CE?B9PZ]TSN u CD?B9KNJ?B9�9X:=Q�?B< >bAE9X?M:=<X9�?MLN=?M9�IMTUZ]Q�?BHJ9\FaLX?B:=<;9�9BehgBIBF@<;LX?uN=?M9�Z]TSN u CD?B9PIMCGF@9;9XAD��:=?M9 l¥q ?BIBA�<X?MH=N F@AEH=9XA}C ev:JLXADCEAD9\F¡L\ADT@H�N�e�Fa:JL\<;?B9LX<\F¢>aF@:b� 9X:=<�CDFjL s gBTU<;AD? � F@Q=QJ<XTSI s ?B9 s AEgB<XF@<XI s AE��:=?B9�T@: Z]TSN=:=CDF@AD<;?B9B|�QJ<XTUQ=<;ADgmL\guN=?�9;LcFax=ADCEAD9\Fax=AnkCEAEL\g l l l � N=A � IBADCE? l¡� HWTU:JLX<X?rIM?ML;L\?^F@Q=QJ<XTSI s ?�?B9 L¥L\< u 9¥9;QRgMIBADF@CDAE9XgB?�Z]TSN=?�H=TUZ[ADHwF@C k¦Z[TbNJ?¥N=gB�@<\F@N=gr?MLH�eh?B9 L�QwF@9�Q=<Xgm>b:J?�Q�TU:=< L\<X?OgMLX?BH=NJ:=? � CfehgMLX:=N=?^N=?M9�HJTUZ�x=<;?B:b�[Z[TbNJ?B9¤N=?i_pTUH=ImL\AETUH=H=?MZ]?MH�L�N�eh:=H9 �b9 L u Z]?]N=?]QJ<XTSN=:=IMLXADTUH l�� H � H CE?B9�Z]gMI¢F@H=AE9XZ[?B9PZ[AD9K?BH Q=CGFaIB?[N=?]Z[TSN=gBCEAD9\F¡L\ADT@H�N=?[Q=<XTSIBgMN=gB9N=A � gM<X?MH�LX9^NwF@H=9^CD?M9iN=?B:S�jZ]TSN=?B9iHJ?�9;TUHdLOQwF@9^9X: � 9XF@Z]Z[?BHdLO?m�bQ=CEADIMAEL\gM9 l

� ������� � � ��.1035 ��A���8�<�.�>�.�5���8 ��46A@ T@:=9^F¢>UTUH=9iNJg � � F@x�TU<XNJg�NwF@H=9iCE?�I s FaQ=AELX<X? ~ CE?B9rLX<\F¢>aF@:b��NJ? A F@Z[AD< qrs F � � 9X:=<�CE?�IBT@H�LX< s CE?

QwFa<�9;:=Q�?B<;>SAE9XADT@H s AEgB<XF@<XI s AE��:=?]?mL�N=AD9 L\<XAEx=:=gM? � >UTUAE<P9X?BImL\AETUH 1.1.4 |�Q=F@�U? 26 � l�V e�F@QJQ=<XTSI s ?[Q=<XTakQ�TU9XgM?�?B9 LOF@Q=Q=CEAD��:=gM? � CGF��U?B9 L\AETUHuN=?M9iZ]TSN=?B9r?MLiZ[?MLrZ�F@AEHdL\?BH=F@HdL�?BH�gm>SADN=?MH=IB?KCE?�Q=<;TUx=C u Z]?�N=?IMTUZ]Z�:JLcFaLXADTUH[?BHdLX<X?K?B:S� lw� � H�N=?K�UgM<X?M<�CfevF@CELX?B<;HwF@H=IM?�?BHdLX<X?KIB?M9iZ]TSN=?M9B|J:JH�Z]TSN=:=CE?�N=?�IMTbT@<XN=A kHwF¡L\ADT@H�FPgMLXg�ADHdLXgB�U<;g�NwFaH=9r:=HJ?�F@<;I s AELX?BImL\:=<;?�N=?�IBTUZ[Z�FaH=N=? s ADgM<\F@<;I s AD��:=?O?ML�N=AE9;L\<;ADx=:JgB? � � �U:J<X?79ln~ I � l�q ?]Z[TSN=:=CD?oQ�?B<;Z]?mL�N8e�F@9;9X:=<;?B<�CGFy<Xg¢FaIML\An>SAEL\goN=: 9;�S9;L u Z[?��UCETUxwF@C�?ML�N=?��UgM<X?M<�CE?[IMTUH � AnL?��JAE9;L\F@HdL^?BHdL\<;?�CE?B9�9;QRgMIBA � I¢FaLXADTUHJ9iN=?KZ]TSN=?�HJTUZ]AEHwF@C�?ML^IM?BCDCE?B9�NJ?KZ]TSN=?�N=gM�U<\FaN=gP?BHyH�evF@IMLXAE>aF@HdL��:�eh:=H�9X?M:=C�Z]TSN=? � CGFP_pTUAD9 lb� Hu? � ?mL¢|S?BH�Z[TbNJ?�H=T@Z]AEHwF@Cf|@CD?B9�IBT@H�LX< s CE?B:=<;9rH=T@Z]AEHwF@:b�[N=:�H=AE>@?¢F@:s Fa:JL�9;TUHdLKF@ImL\An>UgB9M|RZ]F@AE9 � CfehTbIMIB:=<;<X?MH=IB?�N�ev:JH=?�N=gm_`F@ADCECGF@H=IM?K9XAE�UHwF@CEgB?�F@:tIMTbTU<;N=ADH=FaL\?M:=<B|wIM?�N=?B< kH=AE?B<^F@ImL\An>U?B<XF[CE?PTU:YCE?B9^IBT@H�LX< s CE?B:=<;9�NJ:j_pTUHJIML\AETUH=H=?MZ]?MHdL�NJgB�U<XF@N=g�NwF@H=9^N=?M9�gmLcFaLX9�IMTUZ]Q=FaL\AEx=CD?M9� CfehgML\FaL}IBT@:=<\F@HdL�N=:oQ=<;TbIMgBN=g lbV ?^IBTSTU<;N=ADHwF¡L\?B:J<¥N=gB9XF@IMLXAE>@?B<\F�9XAEZ�:=CEL\F@H=gMZ]?MH�L¥CD?B9¤IMTUHdL\< s CD?M:=<X9}N=:_pTUHJIML\AETUH=H=?MZ]?MHdLrH=T@Z]AEHwF@C � :=9X��:�e � IB?��S:J?�CD?OIBTUZ[Q�TU9\F@HdLrN=gM_`F@AECDCDF@HdL�9;TUAEL�<XgMQwF@<;g lJ� Q=< u 9�<XgMQwF@<XF¡kLXADTUH�|dCE?B9}IBT@H�LX< s CE?B:=<;9rN=:[_pTUH=ImL\ADT@H=H=?BZ[?BHdL�H=TUZ[ADH=F@Cw9X?M<XTUHdLiFaIML\An>UgM9�NwFaH=9rN=?M9rgmLcFaLX9�IMTUZ]Q=FaL\AEx=CD?M9F¢>U?MI�CfehgML\FaL�IMTU:=<\FaH�L�N=: Q=<XTSIBgMN=g � IBTUZ[QwFaLXADx=AECDAELXgWN=?B9W<XF@IBIMTU<XNJ?BZ[?BHdL\9WN�ehgML\FaL\9 � l¥q TUZ]Z[?�N=F@H=9�P@ TU: {�x�� |wCfevF@IMLXAE>aFaLXADTUH]TU:yCGF�N=gM9\F@ImL\AE>aFaLXADTUH�?M9;L�F@9;9X:=<;gB?�QwF@<iN=?M9^>aF@<;AGF@xJCD?B9rxRTSTUCDgM?BH=HJ?B9iADHdLX?B<XHJ?B9Q=<;ADTU<;AEL\F@AD<;?B9 � gM>@gBH=?MZ]?MH�LX9�_pTU<;IBgM9 � |w9MevAEH=9XQJAD<\FaH�L^NJ:YIMTUH=IB?MQJLON=?PZ�FaIB<XT¡k F@ImL\ADT@H�N=: �^����q�����l

V FjNJgB9\FaIML\An>aFaL\AETUH N=?B9�9X:=Q�?B< >bAE9X?M:=<X9�9X?o_`F@AELPgM�dF@CD?MZ]?MHdL�?MH Z[?ML;LcF@HdL�IB?M:b��k¦IBA�NwF@HJ9�:=H gML\FaLNwFaH=9�CE?B��:=?BC�L\T@:=9�CE?B9�gM>UgMH=?BZ[?BHdLX9¥9XTUHdL}Fa:JL\TU<;AD9;gB9 l � � H�N=?�9XADZ[Q=CEA � ?M<�CD?B9�Z[TbN u CD?M9B| A F@Z[AD< qrs F � �

Q=<;TUQ�TU9X?PN=?�H�evF � TU:JLX?B<^��:�ev:JHtgML\FaLOQwF@<^Z[TbN u CD? � F@:YCEAD?M:jN8ev:=HjN=TU:Jx=CD?MZ]?MH�LON=:YH=TUZ�xJ<X?PN�ehgMLcF¡L\9NwFaH=9 �P@ T@: {�x�� � lbq ?BQ�?BHJNwF@HdLiIB?MIBA � C evAEH=IBTUHd>@gBH=AE?BHdL�N=?O<X?MH=N=<;?�CfevF@:JLXTUZ�F¡L\?iIBT@H=9XAEN=gB<;g�ADHJN=gMLX?B<XZ[AnkH=AE9;LX? lS� Hu? � ?MLB|SCETU<X9;��:=?�CE?�9;:=QR?M<;>SAD9;?B:=<�<X?MN=?M>SAD?MHdLiF@ImL\AE_ |�9;:=<�:JHugM>@gBH=?MZ]?MH�L � ADHdLX?B<XHJ? � |�ADC£N=TUAnL<;?M>U?MH=AD<�NwF@H=9�:=H gmLcFaL�IBTUZ[QwFaLXADx=CE?[Fz>@?BIuC evgmLcFaL�N=: QJ<XTSIBgBNJg l�qrs F@��:=?ugm>UgBHJ?BZ[?BHdL � AEH�LX?B<;H=? �Z u H=?tN=TUH=I�NwFaH=9�Q=CD:J9XAD?M:=<X9�gMLcF¡L\9 l1C TU:=<�CE?M>@?B<�IB?�QJ<XTUx=C u Z[?@|�CfevF@:JLX?B:=<u:bL\ADCEAD9;?tN=?M9u>@Fa<XAGFax=CD?M9IMTUZ]QJCDgBZ[?BHdL\F@AD<;?B9 � >UTUAE< � �U:=<;? 7/lE~U~ � QR?M<XZ[?ML;LcF@HdLON=?PN=A � gB<;?BH=IMAD?M<iCD?B9�LX<\F@HJ9XAELXADTUHJ9�>bAE9XgM?B9 l

Page 60: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� z ����� ������� � � ���� ������������� ��*������ ���� �#��� ��������������������

S1,h

S2,hG

G

h

S1S

2

θ θ−1

θ−1

cont

info

info

cont

info

cont

info

cont

CoordinationMacro−actionsMacro−actions

θ ’

�������879ln~ I � � �0)!�� ) �7" 35" �����! �76*+,"���:�"�� ��� ���43$� ���$ "%) � � �! "��� $ ��35"29

V evF@Q=Q=<;TbI s ?�N=? � :=9 LcF@Q s F @ TU:J<X?BCn_`FaL s 9X?�_pTSI¢FaCDAD9XF@AELO9;:=<�CD?�Z[TbN=?�H=TUZ[ADHwFaC�?mL�9;:=<�CGF[IBTUZWkQR?MH=9\FaLXADTUH � N=?PCGF�IBT@Z]Z]F@H=N=? � ?BHjI¢F@9iNJ?�NJgM_`F@AECDCGFaH=IB? l=V FWQ=<XAE9X?K?BHjIBT@Z]QJLX?KN=?PCGF�Z[TbNJA � IBFaL\AETUH9;L\<;:=IMLX:=<X?MCDCE?uN=: Q=<XTSIBgMN=g�?BH IBF@9WN=?uNJgM_`F@AECDCGFaH=IB?]H�evgmLcF@AnL�N=T@H=I�QwF@9�gmL\:=NJADgB?�?MH N=gML\F@ADCE9�?mLWQwF@<IBTUH=9;gB��:=?MH�L�QwFa9�_pTU<XZ]F@CEAD9XgM? l C Fa<�9\FuQ=<;TUQ�TU9XAnL\ADT@HYN=?�9;L\<;:=IMLX:=<X? s ADgB<XF@<XI s AD��:=?�?mLKN=gBIM?BHdL\<XF@CDAE9XgM?@|A F@Z[AD< qrs F � � >aFoN=TUH=I�xR?BF@:=IMTU:=QtQJCD:=9^CDT@ADHy?ML�<X?M9;L\?�9;LX<XADImL\?MZ]?MH�LONwFaH=9�CE?�IBF@N=<;?�N=?�CGFWL s gBTU<;AD?��� lwq ?BQ�?BH=NwFaH�LOC e�F@QJQ=CDAEI¢FaLXADTUHoN=?KIM?MLXLX?PF@Q=Q=<;TbI s ?KQRTU:J<�CGF��@?B9;LXADTUH�N=?B9^Z[TbN=?M9�N=?�_pT@H=IMLXADTUH=HJ?mkZ]?MH�LPHJgBIB?M9X9;AEL\?WC evAEHdL\<XTSN=:=ImL\AETUHtN�eh:=H IBTSTU<;N=ADHwF¡L\?B:J<B|�ADH=9;Q=AD<;g�N=?M9PLX<\F¢>aF@:b�tN=? �hV��n{ I � |8N=TUHdLKCE?B9Z]gMI¢F@H=AE9XZ[?B9�N=?uxwF@9;? � >aF@<;AGF@x=CE?B9�ADHdL\?M<XH=?M9B|�gM>UgMH=?BZ[?BHdLX9o_pT@<XIBgM9 � HJ?u<X?M9XQ�?BIMLX?BHdLoQwF@9�CD?B9 s �bQ�TakL s1u 9X?B9rN=?�C e�F@QJQ=<XTSI s ?OIBCGFa9X9XAE��:=? 8 lS� HuTU:JLX<X?OCD?B9�Z[gBI¢FaH=AD9;Z]?M9�NJ?�IBT@H=9;LX<X:=ImL\ADT@H�|�TU:�N�eh?BHJ<XADI s AD9X9;?mkZ]?MH�LB|8N=?M9�L\<XF@H=9;AEL\AETUH=9�QwF@<�NJ?B9�>aF@<XADF@x=CE?B9OADHdL\?M<XH=?M9�H�ehTUHdLKQwF@9�gmL\g�_pT@<XZ]F@CDAE9XgB9M|wI@eh?B9 L;k � k¦N=AE<X?���:=?CfevF@:JL\?M:=<KH=?WQ=<;TUQ�TU9X?oQwF@9KNJ?WZ]gMI¢F@H=AE9XZ[?�9;�S9 L\gBZ]FaLXAD��:=?oN=?WI¢FaCDIB:JC¥N=?B9PgmLcFaLX9PFaLXLX?BADHdLX9KCDTU<;9�N=?B9I s F@H=�U?MZ]?MHdL\9�NJ?�Z[TbN=?M9

�CD?P<XF � TU:JL�N=?B9�IBTUHJN=AELXADTUH=9i9;:=<OCD?B9^>aF@<XADF@x=CE?B9^F@AEH=9XA���:=?�CGFoN=gMLX?B<XZ[ADH=F¡k

L\ADT@H�N=?B9PgML\FaL\9KNJ?[<;g¢F@ImL\An>@F¡L\ADT@H�N=: Z]TSN=?�9;?W_pTUHdLKZ�FaHS:J?BCDCE?BZ[?BHdL l L�H{<;?MLXAD?BHdLPN=?WIM?B9KL\<XF¢>@Fa:b�N=?B9OQ=<XT@QRTU9;AELXADTUH=9rADHdL\gM<X?B9;9\F@HdLX?B9OQRTU:J<iCGFWIBTUHJN=:=AELX?KN=?PCfevF@CELX?B<;HwF@H=IM?�N=?B9OZ[TbN=?M9i��:=A�TUHdLOZ]TUHdLX<XgCGF�H=gMIB?B9;9XAnL\gON=?iZ]?mLXLX<X?i?BHoQ=CDF@IB?iNJ?B9}Z]gMI¢F@HJAD9XZ[?B9¤NJ?i9X:=An>bAJ9XAwCfehTUH�>@?B:JL�Z]F@H=ADQJ:=CD?M<�N=?M9�Z[TSN u CE?B9F@Q=Q=<;g s ?MH=NwF@x=CE?B9 l

� ������9> � �*>�� � ��,�+��9@3>-�3>�=8�!��>&>�(!0�'��3>3) 0�'��3� ��� 0�'���>-,�( + �!� >�+-$&'F= +&'�$-����6�,��.+&%���)����3> %<L�%3���<EB�3�#+ >B>�,#�#+ "�%3��%�$&%3>�2��$ �����9$-, =8%*6.% �8+ ��,#� �9�#>;�9��$;'�� =8, EB�2,�>-���#+/6.� �!�G=8, EGE ���26.����+/� J ���2>��#E @����<6.�3>;%#L�%��9�<EB����+&> �*> +/>$=8(��96.% ���%#L�%3���<EB����+ >5=8,���+&$��#��� @�� �*> �8+/(��F=8,#�#+&$��#��� @����3>3� �:�3> %#L�%��9�<EB����+&> B ,#$ �3� @����3>;� J �8=.(!> +&����+ �9��>3�

Page 61: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� � � ���� ���� � ��� ������� ��������������� �� ��� D��� � {

γ r41γr4

γr4 γ r41γ p41

ANf

ANv

ANf

τ r4

τ p4

αD

ANf

!

αD

ANf

!

ANv ANv

αN =0ANv

ANv

C coord:

−{ , }TcoorT

coor

γ p41

xN0 xN1

P

!

EHN,et

:

=0

=1

τ τr3{ , }.r6

on boucle.(αD A !

x x

P

D0 D1

!!

EHD,et

:

on boucle.(αD =1) .A! !

τ . ANvp3 !

τr4 . ANv

!

on boucle.(αN=1) .! !τ τr3 r4{ , }.A

Nv!

on boucle.(αN =0) .! !

NfNf=0) .!

αN =1

τ

τ

r3

p3

T

T

N

D

�������R79lE~@~ � � " "%$ � +,"�35"8$ ��3��%+,"29 35"�9%) ��"��0: �,9;"%) �79 "� 3�) ��� ��� 3$� ���$ "%) �

� ��� � � �"!�# �"!&%��O(�*�+�,-�)(�("!�. !�(�+ � 2 � !1+32 6��

q ?B< LcF@AEH=9�Q=<XTSIBgMN=gB9�QR?M:J>U?MH�L L\<;?rQ�?B< � :=?M9�CDTSI¢FaCD?BZ[?BHdL�IBT@Z]Z[?}N=?B9 A �S9;L u Z]?M9 q TUHdLXADH�:=9 � A=q �TU: �UCDT@xwF@CD?MZ]?MHdL¢|�?BH ADHdL\gM�U<\F@HdL�CD?M9�_pTUH=ImL\AETUH=9�N=?�IMTUHdL\< s CD?mklIBTUZ[Z]F@H=N=?a|�IBTUZ[Z]?oN=?M9 A �S9;L u Z[?B9� �SHwFaZ]AE�S:J?B9��O�Sx=<XAEN=?B9 � AJ� � � l A A�CDF[�U?M9;LXADTUHjN=?B9�Z]TSN=?M9ONJ?�_pTUH=ImL\AETUH=H=?MZ]?MH�LOQwFa<\F@AnL�H=FaL\:=<;?BC kCE?BZ[?BHdL�F@xRT@<XN=gM?�NwFaH=9�CE?^N=TUZ]F@ADH=?iNJ?B9 Ab� ��|�?BCECD?^H�eh?B9 LrQwFa9�?��JQJCDADIMAELX?ON=F@H=9�CD?^N=TUZ]F@ADHJ?iN=?B9 A=q�l� FaH=9�IM?�NJ?B<XHJAD?B<}IBF@9�T@H]gmL\:=N=AE?^Q=CD:JL s L�CGFKIBT@Z]Z]F@H=N=?iN=F@H=9�N=A � gB<;?BHdL\?M9�IMTUH � �U:J<\FaLXADTUH=9}N=?^_pTUH=I�kLXADTUH=HJ?BZ[?BHdL � gm>UTUCE:JL\AETUH�N�eh:=H[QRT@ADHdL¥N=?i_pTUHJIML\AETUH=H=?MZ]?MHdL � :=H[F@:JLX<X?iQ�TUADHdL¤N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL � l@ g¢F@H=Z[TUAEH=9�CD?M9^IBTUH=IM?BQJLX9�N8e�F@CnL\?M<XHwF@HJIB?K?MLON=?P9;:=AE>SA�<X?M9;LX?BHdL�QJ<XgBQ�TUH=NJgB<\FaH�LX9 l

� �YC � B � � ��.1035 ��A �/A=? 0�+ ?�A ����

V ?B9�<\F@<;?B9�LX<\F¢>aF@:b�YADHd>@?B9;LXAD9�NwF@H=9�CGFW_pTU<XZ]F@CDAE9\FaLXADTUH�NJ?�CGFo�U?M9;L\AETUHtNJ?B9�Z[TbNJ?B9ON=?B9�Q=<XTSIBgMN=gB9<;?BC u >U?MH�L�N=?M9 AJ� � lSq eh?B9 LrH=FaL\:=<;?BCECD?BZ[?BHdL¤N=F@H=9¤IB?^N=T@Z�F@AEH=?���:=?^9XT@H�L�F@x�TU<;N=gB9¤CE?B9¤Q=<;TUx=C u Z]?M9¤N=?IMTUZ]Z�:JLcFaLXADTUH�NwF@H=9�CE?B9�I s F@HJ�U?BZ[?BHdL\9�N=?}Q s Fa9X? l � F@H=9�IB?}IBT@H�LX?m�SL\? � � ��{mz�� � >UT@AD<�F@:=9;9XA � ��� "p{�x�� �FKZ[TUHdL\<Xg^��:=?OCGFK9;L\F@x=AECDAELXg � ?MH]IMTUH=9;ADN=gM<\F@HdL�CD?B9}I s FaH=�U?BZ[?BHdLX9�NwFaH=9�CE?B9}NJ�SHwF@Z[AD��:=?M9}9X:=<�I s F@��:=?<;gB�UAETUH Xi

|�NJ?YC ev?M9XQwF@IM?tN�ehgML\FaL\9]IBTUHdLXADH�: X | Xi ⊂ X � ?B9 LuN=A � IBADCE?BZ[?BHdLW>UgM<XA � F@x=CE?tF¢>U?MIt:=H9;?B:=Ci9;:=QR?M<;>SAD9;?B:=<]F@�UAE9X9XF@HdLo9X:=<oCfeh?B9;QwF@IM?YN�ehgML\FaL\9oIMTUZ]QJCD?ML X

l}V F 9 L\<XFaL\gM�UAD?yF@NJTUQJL\gM?yIBTUH=9;AD9 L\?F@CETU<X9 � F@9X9;TbIMAD?B< � I s F@IB:JH=?�N=?M9�<XgM�UADT@H=9 Xi

:=H�IMTUHdL\< s CD?B:J<OQ�TU:=<�F@9;9X:=<;?B<�:=HJ?�9 LcF@x=AECDAnL\gKCDTSI¢FaCD? l� � H N=?u�dFa<\F@HdL\AE<�CDFY9 LcF@x=AECDAnL\g[9X:=<�C ev?M9XQwFaIB?uN�ehgML\FaL\9WIMTUZ[Q=CD?mL X |�ADC}?B9 LoH=gBIM?B9;9\F@AE<X?@|�CDTU<;9�N=?uCDF

Page 62: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

v I ����� ������� � � ���� ������������� ��*������ ���� �#��� ��������������������

IBTUZ[Z�:JL\FaL\AETUHoN=:�Q=<;TbIMgBN=gON�eh:=H=?O<XgM�UADTUH Xi

�Xj

|SNJ?�9Me�F@9;9X:=<;?B<�gB�dF@CE?BZ[?BHdL�N=?OCGFPIBTUZ[Z�:JL\FaL\AETUHN=?B9O9X:=Q�?B< >SAD9X?M:=<X9OIBT@<X<X?M9XQ�TUH=NwFaH�LX9 l

� FaH=9WIB?mLo?B9XQJ<XAEL �hV��y{m{$� F�Q=<XTUQ�TU9;gu��:=?yCGFtIMTUZ]Z�:JLcFaLXADTUH N=?B9WIMTUHdL\< s CD?B:J<X9W9Beh? � ?BImL\:=?jF@:H=AE>@?¢F@:u9;:=Q�gB<XAE?B:=<�QwF@<�:=Hu9X:JQR?M<;>SAD9;?B:=<�NJ?�H=An>U?¢Fa: s F@:JL l=q ?�N=?B<;H=AD?M<�gMCGF@x�TU<X?O:=H=?�IBTUZ[Z�:JL\FaL\AETUHN=?PIBTUHdL\< s CD?M:=<^?BHj<\F@QJQRTU< LOF¢>U?BI�CGF�Nb�bH=F@Z]AE��:=?PIBTU:=<XF@HdL\?PN=:j9;�S9;L u Z[? � >UT@AD< � �U:J<X? 79ln~ 7 � l

Procédé

Controleur 1

Controleur 2

Controleur m

u

u

u

1

2

m

Superviseur

du niveau haut

Environnement

Signal de commutation

u y

^

^

^

��������79ln~ 7��� ����� � "��� ) �7" $ )5+ � �����! "�76*+,"%) �

���YC � � � � ��.�035���A �/A=?�0@+ ?�A � � � � - � � A � 5 0�+ -98�+�4 �V F]_pTU< L\?�H=TUHbklCDADHJg¢F@<;AEL\gPN=?�IB?B< LcF@AEH=9�9 �S9;L u Z]?M9KQ s �S9XAD��:=?M9P?BHdL\<XFa�GH=?�N=?B9KNJAD9XQ=F@<XAnL\gB9�N=?�_pTUHJImk

L\ADT@H=H=?BZ[?BHdL�?mL�Q�?B:JL�<;?BH=NJ<X?�N=A � IMADCE?YC evTUxbL\?BHdLXADTUH N�ev:JH Z[TSN u CE?Y�UCETUxwF@CO?MLuCGF 9 �SH�L s1u 9;? N8ev:=HIBTUHdL\< s CD?M:=<�:=HJAD��:=? � � ��{mz�� � F@9 IJI � l � F@IM? � IM?MLXLX?KH=TUH�CEADH=gBF@<XAnL\g � TU:�NJA � gB<X?MHdL\9�Q�TUADHdLX9rN=?�_pTUHJImkL\ADT@H=H=?BZ[?BHdL � |@AECJF�gML\giQJ<XTUQ�TU9Xgr:=H=?^F@Q=QJ<XTSI s ?�N=AnL\?�Z�:JCEL\A k¦Z[TbN u CD?¤��:=AbIBTUHJ9XAD9 L\? � <;?BQ=<;gB9;?BHdL\?M<�CE?B99;�S9;L u Z[?B9�H=T@HuCDAEH=g¢F@AE<X?M9 � IBT@Z]Q=CE?m�b?B9 � QwFa<�Q=CE:=9XAE?B:=<;9�Z[TSN u CE?B9}9XAEZ]Q=CE?B9 lJqrs F@IB:=H�N=?�IM?B9rZ[TSN u CE?B9?B9;L}:JH=?iN=?B9;IB<;ADQJLXADTUHWQwFa<;L\AE?BCECD?�N=:W9;�S9;L u Z[?^F@:JLXTU:=<¥N�eh:=HoQ�TUADHdL¥NJ?�_pTUH=IMLXADTUHJH=?BZ[?BHdL¤N=T@H=H=g l@� F@H=9IB?ML;L\?�F@Q=Q=<;TbI s ?a|£CfehgMLcFaQR?PN=?�9;�SHdL s1u 9X?WIMTUH=9XAE9;LX? � IBTUHJ9;L\AnL\:=?M<�:JHt?BHJ9X?BZ�x=CD? � H=A�N=?�IBTUHdLX< s CE?B:=<;9B|I s F@IB:JHtIBT@<X<X?M9XQ�TUH=NwFaH�L � :=HjZ]TSN u CE?�N=:j9;�S9;L u Z[? l

V ?B9ON=?M:b�YF@9XQ�?BImL\9 � QJ<X?BHJN=<X?�?BHYIBTUZ[QJL\?P9;TUHdL�CDFWN=gMLX?B<XZ[ADH=FaL\AETUHyN=?PCGFWIBTUZ[Z]F@H=N=?K�UCETUxwF@CE?IBTUH=9 L\<;:=AELX? � QwF@< L\AE<�N=?M9¥IBT@H�LX< s CE?B:=<;9�CETbIBF@:b��?ML¥CGF�NJgML\?M<XZ[ADHwF¡L\ADT@H�N=?rCfehADH=9 LcF@HdL�N=?rIMTUZ]Z�:JLcFaLXADTUH lq ?B<;L\F@ADHJ9�L\<\F¢>aF@:b��Z]T@H�LX<X?MH�LP��:=?oIM?BCGFuQ�?B:bL L\<;?WQ=<XAE9K?BH I s F@<;�U?WQwF@<K:JH{IMTUZ[Z�:JLcF¡L\?B:J<�?MLP:=H9X:=Q�?B< >bAE9X?M:=<KADHdL\gM�U<XgM9 � CGF[IBTUZ[Z]F@H=N=? � F@9 I I � l8� F@H=9�IB?ML;L\?WQ=<;TUQ�TU9XAnL\ADT@HtCD?�IBTUZ[Z�:JL\FaL\?M:=<�?M9;LIBTUH=9;ADN=gM<Xg�IMTUZ]Z[?[:=H ADHdL\?M<X<;:=QJL\?M:=<�N=?�IBTUZ[Z�FaH=N=?�IMTUHdL\< s CDg]QwF@<�CE?�9;:=QR?M<;>SAD9;?B:=< l}q ?uN=?M<XH=AE?B<<X?BIM:=?BAECDCE?]CE?B9�AEHJ_pTU<XZ]FaLXADTUH=9 � IBTUZ[Z]F@H=N=?a|�gmLcFaL�ADHdL\?M<XH=?]N=: Q=<XTSIBgMN=g@|�9XTU< L\AE?�N=: Q=<;TbIMgBN=g � Q�TU:=<ADH=N=AE��:=?B<}F@:oIMTUZ]Z�:JLcFaLX?B:=<��S:=F@H=NoCfevF@CELX?B<;HwF@H=IM?�N=TUAnL¤9X?^<XgBF@CDAE9X?M<¥?ML}I s T@AD9XAE<¥CD?rTU:oCD?B9¤IMTUHdL\< s CD?M:=<X9

Page 63: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� � � ���� ���� � ��� ������� ��������������� �� ��� D��� vJ~

CE?B9iQ=CE:=9OF@QJL\?M9 � �UF@<\F@HdLXAD<�CE?B9^9XQ�gBIMA � IBFaL\AETUH=9 � � �U:=<X? 79ln~Xq � l

Superviseur

Procédé

2

Com

mutateur

U(t)Y(t)

y(t)

Y(t)

Y(t)

U(t)

U(t)

U(t)1

n

2

r(t)

r(t)

r(t)

r(t) : signal de consigne

Controleur

Controleur 1

Controleur n^

^

^

�������R7/lE~Xq�� � ����1%$ � 35" ����� � ��� ��"�35" + ����*$ $ �$� 35" $ )5+ � �����! "�76*+,"%) �

E IBA�F@:=9X9;Af|SH=TU:=9i<;?MLX?BH=TUHJ9i�S:J?KCGF�IMTUZ]Z]F@H=NJ?��UCETUxwF@CE?�CDF�Q=CE:=9�9XAEZ]QJCD? � N=gMLX?B<XZ[ADHJ?B<�?M9;LiIM?BCDCE?Q�TU:=<OCGF@��:=?MCDCE?�:JH�9X?M:=C�IMTUHdL\< s CD?B:J<�?M9;LK9;gBCD?MIMLXADTUH=HJg � CDFo_pT@AD9 l L�H�QwFa<XCD?�F@CETU<X9ON=?�IMTUZ[Z�:JLcF¡L\ADT@HN=AE<X?MIML\? l¥� FaH=9�CD?�I¢F@9�T + ?BCDCE?]?M9;L[F@: IBTUHdL\<XF@AD<;?uN=gmL\?B<;Z]AEH=gB? � QwF@< L\AD<�N�eh:=H=?�IMTUZ]Q�TU9;AEL\AETUH NJ?B9IMTUHdL\< s CD?B:J<X9B|JCGFWIBTUZ[Z�:JL\FaL\AETUHu?M9;LO��:wF@CDA � gB?KN8evAEH=N=AD<;?BImL\? l

k � � � k �YZ \]R � ���=PXb�PSWJR7N T�W��S`/U,PX`V FWIBTUZ[Z�FaH=N=?K�UCETUxwF@CE?�9Beh?m�bQ=<;ADZ[?PADIBA8QwF@<i:=Hy>U?MIML\?M:=<

Uglobale(t) =∑

i∈{1,..,n} δiUi(t)|iF¢>U?MI δi = 1 T@: 0 | Ui

gML\F@HdLjCGF IBT@Z]Z]F@H=N=?t<XgB9;:=CEL\F@HdL\? N=:IMTUHdL\< s CD?B:J< i

l E C�9Me�F@�@AEL�F@ADH=9;A�N�evF@ImL\AE>@?B< � :=H�ADH=9 LcF@HdL t NJTUH=H=ga|�:=H�9;?B:=C¥IMTUHdL\< s CD?M:=<�QwFa<XZ[A�C ev?MHbk9;?BZ�x=CE?WN=?B9PIMTUHdL\< s CD?B:J<X9K9;�SHdL s gML\AE9XgM9 l�V ?WIMTUHdL\< s CD?M:=<PF@IMLXAE_�?B9 LPIB?BCE:=A¤��:=A¤IBT@<X<X?M9XQ�TUH=N F@:b��9XQ�gmkIMA � IBFaL\AETUH=9KN=?[CGF�Q s Fa9X?uFaIML\An>U? � CfehADH=9 LcF@HdL t

l�qrs F@<Xx�TUH=H=F@:=N{?ML ��+ �vq ��� I 7�� N=gBIMTUZ]Q�TU9;?BHdL�CE?Q=<;TbIMgBN=gP?MHYQ=CE:=9XAE?B:=<;9iZ]TSN u CD?B9r9XADZ[Q=CE?B9 Gi

|JLX?BCD9i��:=?PI s Fa�S:J?�Z[TbN u CD?�N=gBIM<XAELOCE?�IBTUZ[Q�TU<;LX?BZ[?BHdLN=:{9;�S9 L u Z[?uFa:JL\TU:J<�N8ev:=H Z]TSN=?WN=?o_pTUH=ImL\AETUH=H=?MZ]?MH�L�N=T@H=H=g l�� � H N=?[N=gmL\?BImL\?M<�CE?[Z[TSN=?[F@IMLXAE_NwFaH=9�CE?B��:=?MC�9;?]LX<XTU:J>@?�?MH=�dF@�Ug[CD?oQ=<;TbIMgBN=ga|�CD?B9�F@:JLX?B:=<;9�TUHdL�Q=<XT@QRTU9;g]N8e�F@N � TUADH=NJ<X?[F@: Z[TSN u CE?N=:yQ=<;TbIMgBN=gK:JHjZ[TSN=:=CD?�N=?KN=gmL\?BImL\AETUH l£q ?KZ[TbNJ:=CD?O_pTU:=<XHJAEL � I s Fa�S:J?�AEH=9;L\F@HdL^F@:yZ[TbN=:JCD?�N8e�F@I�kIMTUZ]Z[TSNwFaL\AETUHuN=?�CGFoIBT@Z]Z]F@H=N=?KCE?PZ]TSN=?�F@IMLXAE_�?ML�QwF@<^IBT@H=9XgM�S:J?BHdLKQ�?B<XZ[?ML�N=?�9XgMCD?BImL\AETUH=H=?M<OCE?<;gB�U:=CDFaL\?M:=<^F@N=gM��:wFaL l£V ?P9XI s gBZ]F[N=?PCDF � �U:=<;? 7/lE~ � N=g � H=AnL^CGFW9;LX<X:=ImL\:=<;?�Q=<;TUQ�TU9XgM? l

Page 64: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

vd7 ����� ������� � � ���� ������������� ��*������ ���� �#��� ��������������������

u

e

α

Accommodation de la commande

Mult−régulateur

Détection des modes de fonctionnement

Procédé

Σ

r G

d(k)

C

��������79lE~ � � � "�0) �� ) �7"�$ )5+ � �71$��)5+ �$ "%) ����:�"�� � �����*$ $ ��3 �$ �����

� FaH=9�IM?ML;L\?�9;L\<;:=IMLX:=<X?a|£I s F@��:=?�<;gB�U:JCGFaLX?B:=< Ci?B9 L�NJg � H=AnLON=?�_`F � TUH � 9;:=AE>S<;?�?��bQ=CDAEIBAELX?BZ[?BHdL

CGF]Nb�bH=F@Z]AE��:=?�N=:�QJ<XTSIBgBNJg Gi?MLKF@�UAD<^CETU<X9;�S:J?�IB?�N=?B<;H=AD?M<�?B9 LPF@ImL\AE_ l£� ADH=9;Af|£CD?�<XgM�U:=CGF¡L\?B:J<�IBT@< k

<X?B9;QRT@H=NwF@HdL�F@9X9;:=<X?�CD?M9iZ]?MADCDCE?B:=<;9rQ�?B< _pTU<XZ]F@H=IM?B9^?BHjxRT@:=IBCE?�_p?B<XZ[gB? � Ci, Gi � l� FaH=9 �h� ���

+ IJI � CfevF@:JLX?B:=<�Q=<XT@QRTU9;?�:=H=?�Z[gML s TbNJ?uN=?�9;�SHdL s�u 9X?jN=?M9WIBTUHdL\< s CD?M:=<X9WNJ?uIBTUZWkZ�:JLcF¡L\ADT@H�QRTU:J<OCE?B9i9 �b9 L u Z]?M9�N=T@H�LOCDFoNb�bH=F@Z]AE��:=?K?B9 L�NJg � H=AE?PQwF@<iN=?M9�gM�S:=FaL\AETUH=9^CDAEH=g¢F@AE<X?M9 l=V FIBTUZ[Z�:JL\FaL\AETUH�?BHdL\<;?�CE?B9PZ]TSN=?M9�?M9;L�F@9X9;:=<XgM?]Q=F@<�:JH 9;:=QR?M<;>SAD9;?B:=<�N=AD9;IB<;?ML���:=A}9X:=AnL�C evgm>UTUCE:JL\AETUHN=:Y9 �S9;L u Z]?�?MLON=gMIBAEN=?�F@ADH=9;A�N=:jZ]TSN=?K��:�ehADC8_`Fa:JL^Z]?mLXLX<X?P?BH � :J>S<X? � � �@:=<X? 79ln~ � � l

q1 q2

S1

S

S

2

3

Procédé + superviseur continu

Procédé + superviseur continu

Procédé + superviseur continuMode sélectionné

q x

q3

controleur de commutation discret^

�������87/lE~ � �� �*$ $ ) �$ "������� �$� �����! �76*+,"%) � 3$�,9 ���7"�

Page 65: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� � � ���� ���� � ��� ������� ��������������� �� ��� D��� vmq

q ?ML;L\?�Z[gML s TSN=?�N=?�I s TUAn�YN�eh:=H�9;?B:=C¥IMTUHdL\< s CD?M:=< � CDF[_pTUAE9�<;?B9 L\?�>aF@CGFax=CD?P?ML�? � I¢F@IM?�9XA � :=HAEH=9;L\F@HdLrN=T@H=H=g�CE?�9 �S9;L u Z]?�9X?�LX<XTU:b>U?�N=F@H=9r:JH=?�9X?M:=CD?�Q s F@9;?�N=?O_pTUH=ImL\ADT@H=H=?BZ[?BHdL lJ� F@AD9�9XA�CfehgML\FaLN=: Q=<;TbIMgBN=gj9X?yL\<;TU:J>U?j?BHdLX<X?tNJ?B:b� Q s F@9X?M9�N=?�_pTUH=ImL\AETUH=H=?MZ]?MH�LB|¤CfevF@CELX?B<;HwF@H=IM?jNJ?jIMTUZ[Z�F@HJN=?Q=<;TUQ�TU9XgM?�?M9;L^L\<;TUQyx=<X:bLcF@CE?K?MLOH=?PN=TUH=HJ?�Q=F@9^N=?PxRTUHJ9O<;gB9;:=CEL\FaL\9 l

� �YC �YC � 0 � �&4�-9>E-�8�0�+ 8 +62�8 .1A=5 -9AV F�IMTUZ[Z�:JLcF¡L\ADT@HWADH=N=AE<X?MIML\?iQ�?B:bL L\<X?^IMTUH=9XAEN=gB<;gB?�IBTUZ[Z]?i:JH=?^?m�SL\?MH=9XAETUH�N=?OCGFKQ=<;gBIMgBN=?MH�LX? l

� CDCE?PIBTUH=9;AD9 L\? � IBTUH=9;ADN=gM<X?M<�Cfeh?BH=9;?BZ�xJCD?�N=?B9�IMTUZ[Z�F@HJN=?B9�N=?�I s Fa�S:J?�IBTUHdLX< s CE?B:=<�QRTU:J<�gMCGF@x�TU<X?M<:=Ht9XAD�@HwF@C�N=?�IMTUZ[Z�F@HJN=?P�UCDTUx=F@CD? Uglobale =

i∈{1,..,n} δiUi|8F¢>U?MI 0 ≤ δi ≤ 1

lRq ?�I s TUAn�YN=? δi

IMTUZ]QJ<XAD9i?MHdL\<X? 0 ?ML 1 Q�?B<;Z]?mL�NJ?�CEAD9X9;?B<^CGFWIMTUZ]Z]F@H=NJ?��@CDTUxwFaCD?�CETU<X9^N=?�CGFWIBT@Z]Z�:bLcFaLXADTUHyN�eh:=H=?Q s F@9X?PN=?K_pTUH=ImL\AETUH=H=?MZ]?MH�L � CfevF@:JLX<X?�?mLON=TUH=IPN�ehgM>SAELX?B<^CD?M9iQ s gMH=TUZ u H=?M9�x=<;:JLcFa:b�yN=?P9\Fa:JL l

� F@HJ9 � � ����� " I 7�� |bCD?B9rF@:JLX?B:=<;9�TUHdLiADHdLX<XTSN=:=AEL�IM?�L¦�SQR?KN=?�IBTUZ[Z�:JL\FaL\AETUH�?mL�AEN=?BHdL\A � ?BHdLiNJ?B9Z[TbN u CD?M9�N=?rQ=<;TbIMgBN=gr9XADZ[Q=CE?B9�F@:JLXTU:=<�N=?rIM?B<;L\F@ADHJ9�Q�TUADHdL�N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL�Q=F@<�C evAEH�LX?B<;Z]gMN=AGF@AE<X?N�eh:=H=?[F@QJQ=<XTSI s ?WZ�:=CnL\A k¦Z[TbN u CD?PH=?M:=<XTUH=F@:b� � � �U:=<;? 79lE~fv � l�V ?M9K9;�S9;L u Z[?B9�IBTUH=9;ADN=gM<XgM9�9;TUHdLPH=TUHCEADH=gBF@AD<;?B9r?mLOH=TUHj9;LcF¡L\ADT@H=HwF@AE<X?B9 ����@�V�� @�A�� � l

SystèmeNL/NS

M

M

M

M

1

n

1

n

Fusion de

u(k)

y(k)

(ui )

u

u

1

n

v

v

1

n

�������R79ln~Xv�� � "�0) �� ) �2"�$ )5+ � ���*$ $ �$� 35" �#"%) � ������+," �!�*) � +,"29 9 �;9� �%$&"29��������� ���

V F]Z[gML s TbNJ?�:JLXADCEAD9XgM?PIBTUH=9;AD9 L\? � N=g � HJAD<O:=H�<XgM�U:=CDFaL\?M:=< CiQRT@:=<�I s F@��:=?�Z[TbN u CD?PH=?M:=<XTUH=F@C

Mi

l£V ?KZ]gMI¢F@H=AE9XZ[?KN=?PIBTUZ[Z]F@H=N=?�NJ:YQ=<;TbIMgBN=gP�UCETUxwF@CR?B9 L�T@xJL\?MHS:jQwF@<�_p:J9XADT@HjNJ?B9�F@IMLXADTUH=9iNJ?B9N=A � gM<X?MH�LX9^<XgB�@:=CGFaLX?B:=<;9i9;�SHdL s gmL\AE9XgB9 l8V ?P9XAE�UHwF@C8? � ?BIMLXAE_�N=?PIBTUZ[Z]F@H=N=? uk

?M9;LON=TUH=HJg�IMTUHJ_pTU<;Z]g�kZ[?BHdL � Cfeh?BH=9;?BZ�xJCD?�N=?M9[<;gB�U:JCGFaLX?B:=<;9W9;�SHdL s gmL\AD9;gB9 u(k) =

i∈{1,...,n} uivi|�T + CD?B9 vi

9XTUHdL[CD?M9>aF@CEADN=AnL\gB9�N=?B9OZ[TbN u CD?M9 � l.��=���� =�'���%3> �B�9��$-+-(�$ 6.�3>56.(�>�+&���F=8�*>;����+-$&� � �*> >�,#$�+&( �*>;6.�3>/6�( H %�$&����+&>KEB,.6.@3� �*>;�8+/�!� >-,�$-+-(�� $-%3����� �<6.'���$&, =8%*6.%

Page 66: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

v � ����� ������� � � ���� ������������� ��*������ ���� �#��� ��������������������

V F^N=gMLX?B<XZ[ADH=FaL\AETUHKN=?}CGFiIBT@Z]Z]F@H=N=?}�UCETUxwF@CE?¥H=gMIB?B9;9XAnL\?r:JH�9;:=AE>SAd?m�bQ=CEADIMAEL\?}N=:�IBT@Z]Q�TU<;LX?BZ[?BHdLN=:Y9 �S9;L u Z]? l

� ��� � �)(�*�� 9�#�,-�O(

� FaH=9]IM?YI s F@Q=AELX<X?a|¤H=TU:=9]F¢>UTUH=9[Q=<;gB9X?MHdL\g�:=H CGFa<X�U?�gm>U?BHdL\F@ADC^N=?yL\<XFz>aF@:S� QRTU< LcF@HdL[9X:J<[CE?B9Z]TSN=?B9WNJ?u_pTUH=IMLXADTUHJH=?BZ[?BHdLoN=?M9W9;�S9;L u Z[?B9B|}NwFaH=9WCD?uIBF@N=<;?jNJ?B9W9;�S9 L u Z[?B9[N=?�Q=<;TbNJ:=IMLXADTUH�|�N=?B99;�S9;L u Z[?B9 � gm>UgBHJ?BZ[?BHdL\9�N=AD9;IB<X?mL\9^?MLON=?M9�9 �S9;L u Z]?M9�IMTUHdL\AEHS:J9 lC TU:=<yCD?M9j9 �S9;L u Z]?M9YNJ? Q=<;TbNJ:=IMLXADTUH H=TU:J9YF¢>@TUH=9y>b:���:=? CE?�Z]TSN u CD?�N=? <Xgm_pgB<;?BH=IM? ?M9;LYCD?

������Y�]l�� ?WH=TUZ�x=<X?M:b��LX<\F¢>aF@:b�tTUHdLPI s ?B<;I s g � Z[AD?M:b�YCD?�_pT@<XZ]F@CDAE9X?B<O?BH :JLXADCEAD9\FaH�L�CD?M9KF@:JLXTakZ�FaLX?B9 � gML\FaL\9�TU:�CD?M9�<;gB9X?BF@:b�tN=? C ?ML\<;A l�� H=?�F@:JLX<X?�>@TUAD?�?m�bQ=CETU<XgM?�IBTUHJ9XAD9 L\? � gMLX?BH=N=<;?�CfehgMLX:=N=?N=?B9�Z[TSN=?B9�N=?]_pT@H=IMLXADTUH=HJ?BZ[?BHdL � N�evF@:JL\<;?B9�_pT@H=IMLXADTUH=9P��:=?uCDFjIMTUZ[Z�F@HJN=?

�?m�bQ=CETUAEL\FaL\AETUH�|�9;:=< k

>U?BAECDCDF@H=IB?a|i9X:=Q�?B< >SAD9XAETUH�|^Z]F@ADHdL\?MHwF@H=IM? l l l�q ?M9YL\<XF¢>@Fa:b� H=TU:=9jTUHdLYZ]TUHdLX<Xg CGF H=gBIM?B9;9XAELXg N�eh:=H=?F@Q=Q=<;TbI s ?]_pTU<XZ[?BCECD?oQRT@:=<�C evgmL\:=N=?�N=?B9�Z[TSN=?B9�N=?�_pTUH=ImL\AETUH=H=?MZ]?MH�L lE CE9�TUHdL�gB�dF@CE?BZ[?BHdL�Z[AD9�?BHgM>SADN=?MH=IB?���:�ev:JH�Z[TbN u CD?i:=HJAD��:=?@|d��:=?MCR��:=?O9XT@AEL}CD?�_pT@<XZ]F@CDAE9XZ[?r?ML�CGFK9 L\<X:JIML\:J<X?O:JL\AECDAD9;gB?a|U?B9 L�LX<XTUQIBTUZ[Q=CDAE��:=g lF@ TU:=9�Fz>@TUH=9�gB�dF@CE?BZ[?BHdL^IBT@H=9;L\FaL\g��S:J?�CDFoQJ<XAD9;?�?MHtIMTUZ]QbL\?PN=?�Q=CD:=9;AD?M:=<X9OQRT@ADHdL\9^N=?>b:J?�?BHdLX<\Fa�DH=?oCGF�IBTUHJ9;L\<;:=IMLXADTUH{N=?[Q=CD:J9XAD?M:=<X9PZ[TbN u CD?M9B|���:=A}H=?oQ�?B:J>@?BHdL�_pTU<;Z]?M<P:=H{LXTU:JL�IBT s gmk<X?BHdLP��:�e � IBTUHJN=AELXADTUHYN=?WZ]?mLXLX<X?�?MH�Q=CGFaIB?�N=?M9KZ]gMI¢F@HJAD9XZ[?B9�N=?�IMTUZ]Q=FaL\AEx=ADCEAEL\gKAEHdL\?B< k¦Z[TbNJ?B9B|�N=?N=gB9XF@IMLXAE>aFaL\AETUHyN=?B9^Z[TbN u CD?M9iADHwFaIML\An_p9�?MLON=?PIMT s gB<;?BH=IM?�NJ?B9OIBTUZ[Z�:JL\FaL\AETUH=9 l

� FaH=9}CGFKQwF@< L\AD? ��� TSN=?B9}N=?i_pTUHJIML\AETUH=H=?MZ]?MHdL}?ML AJ�}� F@: V���E�� HJTU:=9�Fz>@TUH=9�Z]T@H�LX<Xgi��:=?OIB?L\<\F¢>aF@AEC�N=?KL s1u 9X?�9BehADH=9;IB<;AEL^NwF@HJ9OCDF�IBTUHdLXADH�:=AELXgKN=?B9^L\<XF¢>@Fa:b�yZ[?BH=gM9OQ=F@< �H@ TU: {�x�� ?MLON=? �vqrs FJIJI � l� F@H=9�CE?�IBF@N=<X?�N=?�CDF]9 & <X?MLXg�N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL¢|�IB?M9�L\<XFz>aF@:S��TUHdL�?BH=<;ADI s AE9�CGFoL s gMTU<XAE? ��� ?BHQ=<XTUQ�TU9XF@HdL�N�eh:JL\AECDAE9X?B<^N=?M:b�tZ]TSN u CE?B9^Q�TU:=<OCGF]QJ<XAD9;?�?MH�IBT@Z]QJLX?�N8ev:=HtZ]TSN=?�N=?�N=gm_`F@ADCECGF@HJIB?

�:=H

Z]TSN u CE?�Q�TU:=<�CD?OZ[TbN=?OH=TUZ[ADH=F@Cw?MLr:=H�QRT@:=<�CE?�Z[TSN=?�NJgB�U<XF@N=g l�� H�Z]gMI¢F@H=AE9XZ[?�N8evgmLcFaLX9�ADHwFaIML\An_p9QR?M<XZ[?MLXL\F@HdLKN=?WN=gM9\F@ImL\An>U?B<PCE?�9X:JQR?M<;>SAD9;?B:=<PN=:�Z[TbNJ?�ADHwFaIML\An_ lRq ?B9PN=?B:S� F@Q=QJ<XTSI s ?B9PZ]F@H=��:=?BHdLIB?BQ�?BHJNwF@HdLiN=?�_pT@<XZ]F@CDAE9\FaLXADTUHWFa:uH=AE>@?¢F@:]N=?B9rZ]gMI¢F@H=AE9XZ[?B9�N=?�IMTUZ[Z�:JLcF¡L\ADT@H � H=TUH�NJgMLcFaADCDCEg^NwF@H=9�H@ TU: {�x�� ?MLKIMTbT@<XN=AEHwFaL\?M:=<�Q�TU:=< ��qrs F IJI � � ?MLPTUHdLKCE?��U<;TU9�AEH=IBTUHd>@gBH=AE?BHdLPN=?WH�e LX<X?�Q=<;gM>S:=?M9���:=?QRTU:J<ONJ?B:b�yZ[TSN=?B9^N=?K_pTUH=ImL\AETUH=H=?MZ]?MH�L l@ TU:=9]Fz>@TUH=9]N�e�FaADCDCE?B:=<;9�>S: ��:=?tQ�TU:=<oCE?B9[9;�S9;L u Z[?B9�IMTUHdL\AEHS:J9]H=T@H CDAEH=g¢FaAD<X?M9B|¥CDF{Z[?BAECDCE?B:=<;?

9;L\<XFaL\gM�UAD?KIMTUH=9;AD9;LX? � IMTUH=9 L\<X:JAD<X?PFa:JLcF@HdL^N=?KZ[TSN u CE?B9i��:=?PN=?KQ�TUADHdL\9 � TU:�|=Q=F@<^F@HwF@CETU�UAE?�F¢>U?MI�CE?B9AJ�}� |vNJ?KZ]TSN=?B9 � N=?O_pTUH=ImL\ADT@H=H=?BZ[?BHdLX9 lJq ?MLXLX?KF@Q=QJ<XTSI s ?�Z�:=CnL\A k¦Z[TbN u CD?�Q�?B<;Z]?mL�N=?�N=gBIMTUZ[QRTU9;?B<:=H�Z[TbN u CD?KIMTUZ]QJCD?m�b?a|���:=A�N=T@H=H=?�NJ?�Z]F@:J>aF@AE9i<XgB9;:=CEL\FaL\9M|£?BHtQJCD:=9;AD?B:J<X9OZ]TSN u CE?B9^9XAEZ]QJCD?B9M|£F¢>U?BIN=?uZ[?BADCECD?M:=<X?M9�Q�?B< _pTU<XZ]F@H=IM?B9 l¥q ?ML;L\?uN=gMZ�Fa<XI s ?uH8ev?M9;LoQwF@9�QRTU:J<�F@:JL\F@HdL�?��J?MZ]QbL\?�N=?uNJA � IB:=C kL\gB9oQ=:JAD9X��:�eh?BCECD?uHJgBIB?M9X9;AEL\?yCDF�Z]AE9X?u?MH � :J>S<;?jN8ev:=H Z[gBIBF@H=AD9;Z]?�N=?�9X:=An>SA�N=: Q=<XTSIBgMN=gjF � H N=?N=gMLX?B<XZ[ADHJ?B<iCD?M9^IBTUH=NJAEL\AETUH=9�NJ?�IMTUZ[Z�:JLcF¡L\ADT@H � ADHJ9;LcFaH�LX9i?MLOgML\FaL\9 � l

Page 67: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � ��� ��� ��� ���D��� ��� ��� ���� v �

� '=�=� � !� ��� � %��&% !� ���m� )d%

� H�<XgM9X:=Z[g@|�HJTU:=9�Q�TU:J>@TUH=9K<X?mL\?MH=AD<�F@:�L\<XFz>@?B<;9KN=?�IB?M9KN=?B:S��I s F@QJAEL\<;?B9���:=?W9;A�TUH�9XF@AEL�L\< u 9x=AE?BHW_pTU<;Z�F@CEAD9;?B<�?ML�Z]?mLXLX<X?i?BHoTS?B:J>S<;?OCDF�IBTUZ[Z]F@H=N=?a|@CGF��@?B9;LXADTUHoN=?M9}Z]TSN=?B9¤NJ?^_pT@H=IMLXADTUH=HJ?BZ[?BHdL<;?B9;LX?�:JH�Q=<XT@x=C u Z]?K?MH=IBTU<;?�H=T@HtQwF@< _`F@AELX?BZ[?BHdLOZ�F¡�DL\<;AD9;g l=� H�? � ?mL¢|wL\T@:JL\?M9�CE?B9�F@<XI s AnL\?MIML\:J<X?B9�N=?IMTUZ]Z]F@H=NJ?�Q=<XT@QRTU9;gB?M9ON=F@H=9^CD?�IBF@N=<;?�NJ?KCGF�L s gBTU<;AD?KN=?KIMTUHdL\< s CD?KQwF@<i9;:=Q�?B<;>SAE9XADT@Hj<;?BQ�TU9X?MHdL�9;:=<:=HYZ]TSN u CD?P:=H=AE�S:J?�N=:�QJ<XTSIBgBNJg�<X?MQ=<XgM9X?MH�L\F@HdLKCD?�IBT@Z]Q�TU<;LX?BZ[?BHdLO�UCDT@xwF@C�N=:�9 �S9;L u Z]? l�V FoQ=<XAE9X??MHtIBT@H=9XAEN=gB<XFaL\AETUHYCDFW�U?B9 L\ADT@HYN=?M9�Z[TbNJ?B9ON=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdLON=AD9 L\ADHJIML\9O<X?MH=NtC e�FaQ=Q=CDAEI¢F@xJADCDAnL\gON=?IM?B9OF@<XI s AEL\?MIMLX:=<X?M9OLX< u 9^N=A � IBADCE?@|S>UTUAE<X?PZ Z]?�ADZ[QRTU9;9XAEx=CD?�Q=:=AD9;��:=?

�� CE?B9YQ=<X?M9XIB<;ADQJLXADTUHJ9 � 9;QRgMIBA � I¢FaLXADTUHJ9 � AEZ]Q�TU9;gB?B9YNwF@H=9tI s F@��:=? Z[TbN=?{N=? _pT@H=IMLXADTUH=HJ?BZ[?BHdLQ�?B:b>U?BHdL LX<X?PIBTUHdLX<\F@N=AEIMLXTUAD<;?B9i?MLO?MH�LX<\Fa�DH=?B<i:JHYx=CETbIBF@�U?�NJ:Y9 �b9 L u Z]? �

� CE?KQ=<XTSIBgMN=g��UCDTUx=F@C�Q�?B:JL LX<X?�IBTUZ[Q�TU9XgPN�ehgBCEgBZ[?BHdL\9^��:=A�H=?�9XTUHdLOQwF@9^L\TU:J9O?��bQ=CDTUAnL\gM9ON=F@H=9I s F@IB:=HjN=?M9�Z[TbNJ?B9iN=?K_pTUH=ImL\AETUH=H=?MZ]?MH�L l

A ?MCDTUH�IB?�IBTUHJ9;LcF¡L¢|zH=TU:J9�F@CECDTUHJ9�Q=<XTUQ�TU9;?B<�:=H=?�?m�SL\?MH=9XAETUH�NJ?�CDFiL s gBT@<XAD?}N=?}IMTUHdL\< s CD?}QwF@<�9X:JQR?M< k>SAD9;ADTUH�QRTU:J<¤CGF�Q=<;AD9X?r?BHoIBTUZ[QJLX?iN=?iCGF��U?M9;LXADTUHWN=?M9}Z]TSN=?B9�N=?i_pTUH=IMLXADTUHJH=?BZ[?BHdL l @ T@LX<X?^F@QJQ=<XTSI s ??M9;L�:=H=?[F@Q=QJ<XTSI s ?oZ�:=CELXAnklZ]TSN u CE?@|£NwF@HJ9�CDF@��:=?BCECD?�:JH Z[TbN u CD?�9X?B<XFYFa9X9XTSIBAEg � I s F@��:=?]Z[TSN=?WN=?_pTUHJIML\AETUH=H=?MZ]?MHdL l�� AEH=9XA |�CD?B9�IBTUHdLX<\F@AEH�LX?B9�N=?]_pTUHJIML\AETUH=H=?MZ]?MHdL � 9XQ�gBIBA � I¢F¡L\ADT@H=9 � 9X?M<XTUHdLWQ=<;TUQ=<;?B9� I s F@��:=?[Z[TbN=? l�� H=9X:JAEL\?[CD?M9KZ]TSN u CD?B9KNJ: Q=<;TbIMgBN=g]F@AEH=9XA¥��:=?[CD?M9KZ]TSN u CD?B9KNJ?B9�9XQ�gBIBA � I¢F¡L\ADT@H=9IMTU<X<;?B9XQ�TUH=N=F@HdL\?B9�9X?M<XTUHdL�gMLX?BH=N=:J9�F � H N=?oIBF@<\F@ImL\gM<XAD9;?B<P:=H{Z]gMI¢F@HJAD9XZ[?�N=?oIMTUZ]Z�:JLcFaLXADTUH�Q�?B< kZ[?ML;LcF@HdL�CD?iQwFa9X9\Fa�U?�N8ev:=H]Z]TSN u CD? � CfevF@:JL\<;? l�V ehgMLcFaQR?^N=?O9;�SHdL s1u 9X?�9;?B<XF�xwFa9XgB?�9X:=<}IM?B9rNJA � gB<X?MHdL\9Z[TbN u CD?M9�gMLX?BH=NJ:=9 l

Page 68: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 69: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� �&%�)�� � )���� � "d'7%�'�� �

Page 70: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 71: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� �)��� � ������ ��������� vm{

��� %�)�� �� %�'�� �

q ?ML;L\?�NJ?B:b�bA u Z]?�QwF@< L\AD?^N=:�Z]gMZ]TUAE<X?^?B9 LiIBT@H=9;LXAEL\:JgB?�NJ?�L\<;TUAD9�I s F@QJAEL\<;?B9 lJ� CDCE?�?M9;LrIBTUH=9XF@IB<;gB?� CGFKQ=<;gB9X?MHdLcFaLXADTUH]N=?�HJT@L\<;?�IMTUHdL\<XAEx=:JLXADTUH � CfehgML\:JN=?�NJ?�CDFPIMTUZ[Z�F@HJN=?^N=?B9 AJ�}� Q�TU:=<�CGFK�U?M9;L\AETUHN=?M9^Z]TSN=?B9iNJ?P_pT@H=IMLXADTUH=HJ?BZ[?BHdLOQwF@<i:=H=?�F@QJQ=<XTSI s ?PN=?PN=gBIMTUZ[QRTU9;AELXADTUH�N=?KL¦�SQ�?�Z�:=CELXAnk¦Z[TSN u CE? l

� F@HJ9�CE?WQ=<X?MZ]AE?B<KI s FaQ=AELX<X?@|8CfevF@Q=Q=<;TbI s ?oZ�:JCEL\A k¦Z[TbN u CD?P9;?B<\FyQ=<;gB9X?MHdL\gB? l�� CECD?�IMTUH=9XAE9;LX? � <X?�kQ=<;gB9;?BHdL\?M<�:=Hy9 �b9 L u Z]?�IBTUZ[Q=CE?m�b?KQwF@<i:=Hy?MH=9X?MZ�x=CD?PN=?M9^Z]TSN u CE?B9i9;ADZ[Q=CD?M9 lwqrs F@��:=?PZ]TSN u CE?�N=:Q=<;TbIMgBN=gPIMTUZ]Z]F@H=NJgK<X?BQJ<XgB9;?BHdL\?�CD?KIMTUZ]Q�TU< L\?BZ[?BHdLi?��bAD�UgPN=:j9;�S9;L u Z[?�N=F@H=9^:=HjZ]TSN=?KN=?K_pTUH=I�kLXADTUH=HJ?BZ[?BHdL�N=T@H=H=g l=V ?KQ=F@9X9XF@�U?KN�eh:=HyZ]TSN=? � CfevF@:JL\<;?�?B9 L^N & � CfehTbIMIB:=<;<X?MH=IB?KN�eh:=H�gm>UgBHJ?BZ[?BHdL¢|N=AnLrgm>UgMH=?BZ[?BHdLON=?�IMTUZ]Z�:JLcFaLXADTUH lbV ?�Q=<XAEH=IBAEQwF@CRFz>aF@HdL\F@�U?�N=?�IB?ML;L\?KFaQ=Q=<XTSI s ?�?M9;L^N=?�Z�FaLXgB<;AGF@CEAnk9;?B<�LX< u 9�9XAEZ]QJCD?BZ[?BHdLOCD?�Z[gBI¢FaH=AD9;Z]?PN=?�9X:=An>bA l�V F[H=T@LXADTUHYN=?�9;:=AE>SA�9X?M<\FuF@x�TU<;N=gB?�?ML�_pT@<XZ]F@CDAE9XgB?Q�TU:=<iCE?B9iQ=<;TbIMgBN=gM9�9;?B:=CE9ON=F@H=9^CD?KI s FaQ=AELX<X? 3

lV ? I s F@Q=AnL\<X?�9;:=AE>aF@HdLyIMTUH=IB?M<XH=?M<\F CGF 9;�SHdL s�u 9X? N=? IBTUHdLX< s CE?B:=<;9�NwF@H=9y:=H=? Q=<;TUx=CEgBZ]FaL\AE�S:J?

N�evF@CnL\?B<;HwF@H=IM?�N=?�Z]TSN=?B9 l @ TU:=9�N=g � HJAD<XT@H=9�CD?M9�IMTUH=N=AnL\ADT@H=9�HJgBIB?M9X9XF@AD<;?B9K?ML�9X: � 9\FaH�LX?B9KQ=<;TU:J>aF@HdLC ev?��JAE9;LX?BH=IM?�N8ev:=Hj9X:JQR?M<;>SAD9;?B:=<O:=H=AE�S:J?�Q=F@<iZ]TSN=? lL�H�Z[TUHdL\<X?M<\F���:�ehADCSN=?m>bAE?BHdL}H=gMIB?B9;9\F@AE<X?�NJ?�Q=<XT@:J>U?M<¥IB?mLXL\?i:JH=ADIMAEL\g�CDT@<X9X��:=?rH=TU:=9¥IMTUH=9;ADN=gM<XTUH=9M|

IMTUZ]Z[?�NwFaH=9}CD?iI¢Fa9��@gBH=gM<\F@C |UCD?�_`F@AnL¥��:�eh:=H�9;TU:=9 k¦?BHJ9X?BZ�x=CD?^N=?^<X?M9X9;TU:=<XIM?B9�gBCDgMZ]?MHdLcF@AE<X?B9¤Q�?B:b>U?BHdL L\<X?W?MH=�dF@�@gB?B9KN=F@H=9KN=A � gM<X?BHdLX9KZ]TSN=?B9 l�� FaH=9KIB?WIBF@9KCD?M9�9XQ�gBIMA � IBFaL\AETUH=9KIBT@H � ADImL\:=?MCDCE?B9�NJ?M>S<XTUHdL L\<X?jgMLX:=N=AEgB?B9]CD?M:=<o<XgB9;TUCD:bL\ADT@H 9;?B<\F{Q=<XT@QRTU9;gB? l C F@<�FaHwF@CDT@�UAD? � CGF�IBTUZ[Z]F@H=N=?yN=?M9�Q=<;TbIMgBN=gM9B|AEC�9BevF@�UAE<\F N=?�_pTU<XZ]F@CEAD9X?M<�:=H�Z]gMI¢F@HJAD9XZ[?�N=? IBT@Z]Z�:bLcFaLXADTUH Q�TU:=<yxwF@9;IB:=CE?B<yN�eh:=H Z]TSN u CE?�N=?9;QRgMIBA � I¢FaLXADTUH � :=H�F@:bL\<X?�L\TU:bL�?BHt�dF@<\FaH�LXAD9;9\F@HdL�CE?B9OIBTUHdLX<\F@AEH�LX?B9�AEZ]Q�TU9;gB?B9ONwF@HJ9�I s F@��:=?�Z[TSN=?N=?K_pTUHJIML\AETUH=H=?MZ]?MHdL l

� H � H�|£:=HJ?�F@QJQ=CDAEI¢FaLXADTUH�9;?B<\F[N=AD9;IB:JLXgB? lRV eh?m�b?BZ[Q=CE?�<;?MLX?BH�:�|�IBTU<;<X?B9;QRT@H=N � :=Ht9 �S9;L u Z]?�Q=<;TakQ�TU9XgPQwFa<iCD?K�U<;TU:=Q�?KN=?KL\<\F¢>aF@AEC q L AJ�}� N=: P� � �Y�Oq AQl

Page 72: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 73: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

xb~

� � ����'7%�)�� �

� � � )�� � � � $ �7%�'��]$ �w !(#���

� �� > (/+��� ��9�*�+�,-�)(� I s FaIB:=H{N=?B9PZ[TbNJ?B9�N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL�IMTUH=9XAEN=gB<;gB9PQ�TU:=<�:=H 9 �b9 L u Z]?a|�IBTU<;<X?B9;QRT@H=N :=H=?

L¦�SQ�TUCDTU�@AD?PQwF@< L\ADIM:=CDA u <;?�N=?M9�<X?M9X9;TU:=<XIM?B9P:JLXADCDAE9XgM?B9O?MLKN=?M9�9XQ�gBIMA � IBFaL\AETUH=9�F@9X9;TbIMADgB?M9 l � H=?�Z[AD9;9XAETUHmi

9;?B<\FWN=g � H=AE?KNwF@H=9i:=HyZ[TbNJ?�N=?�_pTUH=ImL\AETUH=H=?MZ]?MH�L i |=CD?M��:=?BC�?MH=�dF@�@?KCGF�Z[AD9;?�?BHjF@ImL\AE>SAnL\g�N�eh:=HIM?B<;L\F@ADH�H=TUZ�xJ<X?�N=?�<X?M9X9XT@:=<XIM?B9 l � H�Z[TbN=?�N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL j

�i 6= j � <XgMQRTUHJNwF@HdL � :JH=?iF@:JLX<X?

Z[AD9;9XADT@H mjQ�?B:JLrH=gBIM?B9X9;AELX?B<�C ev?MH=�dF@�U?MZ]?MHdL � <X?B9;Q l CE?�NJgB9X?MH=�dF@�@?BZ[?BHdL � N8e�F@:bL\<X?M9�<X?M9X9;TU:=<XIM?B9 lw� ?

IM?P_`FaAEL¢|bADC�?M9;LOQ�TU9X9;ADx=CE?KN�e�Fa9X9XTSIBAE?B<i:=HJ?�IMTUH � �U:J<\FaLXADTUH�QwFa<;L\AEIB:=CEA u <X?�N=?P<;?B9X9;TU:=<;IB?B9�QwF@<iZ[TbNJ? l@ T@:=9�IMTUH=9XAEN=gB<;TUH=9[NwF@H=9]:=H QJ<X?BZ[AD?M<WL\?BZ[Q=9[CD?jZ]TSN=?yN=?jL¦�bQ�?tHJTUZ]AEHwF@C � QRT@:=<]CE?B��:=?MCOCE?

9 �b9 L u Z]?�<;?BZ[Q=CDAnL�QwF@<;_`FaAEL\?MZ]?MHdL�9XF�L � I s ? � ?mL�CE?�Z[TbNJ?�N=?�L¦�bQ�?�N=gM�U<\FaN=g � QRTU:J<X9X:JAE>S<X?�:=H=?�L � I s ??MH�N=gMQ=AEL�N�eh:=H=?ON=gM_`FaADCDCDF@H=IM? � l � F@QJQR?MCDTUH=9}��:=?�N=:]Q�TUAEH�L�N=?^>S:=?�NJ?�CDFPIMTUZ[Z�F@HJN=?@|dH=TaL\<X?^Q=<;TUQ�Tak9;AEL\AETUH[<X?BQ�TU9;?�9X:=<rCGF�9 �SH�L s1u 9;?PN=?�IBT@H�LX< s CE?B:=<;9r9;?BCDT@H�CGF�L s gBT@<XAD?�N=:uIMTUHdL\< s CD?�Q=F@<r9;:=QR?M<;>SAD9;ADTUH�?MLQ=CE:=9�Q=F@<;LXADIB:JCDA u <X?MZ]?MH�L�9X:J<¥CD?M9¥IBTUHJIB?BQbL\9¤N=?�x=F@9X?i?mL¥CD?M9�_pTU<;Z�F@CEAD9;Z]?M9�NJ?�CfevF@Q=Q=<;TbI s ?rNJ�SHwF@Z[AD��:=? l@ TU:=9OF@<X�@:=Z]?MHdL\TUH=9iCE?KI s TUA �yN=?PCfevF@Q=Q=<;TbI s ?KNJ�SHwF@Z[AD��:=?P9X?MCDTUHyCD?M9^�S:=FaL\<;?�Q�TUAEH�LX9i9X:=An>aF@HdL\9

�g�W � a _YW U�W P ��� F � H{NJ?�_`F@AD<;?�F@Q=Q=F@<\Fa�EL\<;?�?m�bQ=CEADIMAEL\?MZ]?MHdLKN=?B9K9 L\<;:=IMLX:=<X?M9�NJ?WIBTUZ[Z�FaH=N=?�9;ADZ[Q=CD?M9?mL � T@: N=AE9;LX<XADxJ:=gB?M9B|�CfevF@Q=Q=<;TbI s ?]NJ�SHwFaZ]AE�S:J?]N=?[CGF�L s gBTU<;AD?oN=: IMTUHdL\< s CD?[QwF@<�9X:=Q�?B< >SAD9XAETUHFjgMLXgu<X?mL\?BH�:=?]>bAE9 � >SAE9�N=?]CfevF@Q=Q=<;TbI s ?]9;L\FaL\AE�S:J?@|�IB?ML;L\?uNJ?B<XHJA u <;?�H=?�QR?M<XZ[?MLXL\F@HdL�Q=F@9 �C e s ?B:=<;?PF@IMLX:=?BCECD?KN=?PQ=<;TbIMgBN=?M< � :=HJ?�N=gMIBTUZ[Q�TU9XAnL\ADT@Hu9;LX<X:=ImL\:=<;?BCDCE?KN=?PCGFWIBT@Z]Z]F@H=N=? �

�&R=T �/_ WYc b�PSWJR7N a�b �hb �=PXR � b�Pf`�� N=:PQRT@ADHdL�N=?¥>S:=?}N=?B9�TU:bL\ADCE9�N=?¤Z[TbNJgBCDAE9\FaLXADTUH8|mCE?B9�F@:bL\TUZ]FaL\?M9� gmLcFaLX9�9XTUHdL�Q=CE:=9�HwFaLX:=<X?MCDCD?MZ]?MHdL�:JL\AECDAE9XgB98NwF@H=9�C e�F@QJQ=<XTSI s ?¤NJ�SHwF@Z[AD��:=? � F@CDT@<X9���:=?}CD?M9 � N CCE?�9X?M<XTUHdL�NwF¢>aF@HdLcF@�U?PNwFaH=9^CfevF@Q=Q=<;TbI s ?K9 LcFaLXAD��:=? � �

g �VW e�W T�`/c�� R=T $9_J`/c� IMTUZ[Z]?uHJTU:=9[CfevFz>@TUH=9[F@H=HJTUH=IBgyQ=<;gBIMgBN=?MZ]Z[?BHdL � >UT@AD<WI s F@QJAEL\<;? 2 � |�CD?9;:=AE>SA¥NJ?B9�Z]TSN u CE?B9K9;?B<\FyH=gMIB?B9;9\F@AE<X?[QRT@:=<K:=H=?[�U?B9 L\AETUH N=?B9�Z]TSN=?M9 l�q ?[9X:=An>SA¤<X?BQ�TU9;?[9;:=<:JH=?K_pTUH=IMLXADTUH�NJ?�QJ<XT � ?MIML\AETUHj:=H=AD��:=?MZ]?MHdL�?��bQ=CDTUAnLcF@xJCD?�9;?BCETUHYC e�FaQ=Q=<XTSI s ?KNJ�SHwFaZ]AE�S:J? �

� �Sb Um` :�9�� ��PXb9P� N�eh:=H QRTUAEHdL�NJ?o>S:=?]Q=CD:J9��@gBH=gM<\F@C |�CD?B9PAEHJ_pTU<XZ]FaLXADTUH=9�QRTU< L\gM?B9�QwF@<PCD?M9�LX<\F@IM?B9N8ev:=HjZ[TbN u CD?�<;?B9 L\?B<;TUHdL�QJCD:=9i<;ADI s ?M9O��:=?�IB?MCDCE?B9iAD9;9X:=?M9^N=?B9OgML\FaL\9 l

Page 74: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

xU7 ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

@ T@L\<;?KN=gBZ]F@<XI s ?�9Me�F@QJQ=:=AD?KgM�dF@CE?BZ[?BHdL^9X:=<^CE?B9^IBTUHJ9XADNJgB<\F¡L\ADT@H=9i9X:=An>aF@HdL\?B9�

� � HPZ[TbN=?�N=?¤_pTUH=IMLXADTUHJH=?BZ[?BHdL � �b?}CD?M9�Z[T �@?BH=9�TU:PCE?B9�<;?B9X9;TU:=<;IB?B9�H=gMIB?B9;9\F@AE<X?M9 � C ev?��JgMIB:JLXADTUHN�eh:=H=?PL � I s ?PQ=<;?B9;IB<XAnL\? �

� V ?B9O<X?B9;9XTU:J<XIB?M9�IMTUH=9 L\AELX:=?BHdLOCD?KQJ<XTSIBgBNJg�Z[TbNJgBCDAE9Xg�ADIBA�Q=F@<i:=HYF@:JL\T@Z�FaLX? � gMLcF¡L\9 � H=AE9 �� V FuIBTUZ[Z�:JL\FaL\AETUHY?MHdL\<X?�Z]TSN=?B9�ADHdL\?M<;>SAD?MH�L�9X:=AnL\? � CfehTbIMIB:=<;<X?BHJIB?�N�ehgM>@gBH=?MZ]?MHdL\9PQwF@< L\ADIM:bkCDAE?B<X9M|wF@Q=Q�?BCEgB9igm>UgBHJ?BZ[?BHdL\9�N=?PIBTUZ[Z�:JL\FaL\AETUH l

A A�H=TU:J9�IBTUHJ9XADNJgB<XT@H=9�:=H=?�L¦�bQ�TUCETU�UAD?PL\?MCDCE?���:�ehADC�?m�bAD9 L\?�LXTU: � TU:J<X9�:JH�9XTU:=9 k¦?MH=9X?MZ�x=CD?�N=?�<X?M9 k9XTU:=<;IB?M9�IMTUZ]Z�:=H=?B9�?MHdL\<X?�N=?M:b�PZ[TbN=?M9 � >@TUAD< � �@:=<X? q�ln~ � |¢ADCa9X?B<XFOHJgBIB?M9X9XF@AD<;?�N=?¤9;:=AE>S<;?�C evgm>UTUCE:JL\AETUHN=?�IB?�N=?B<;H=AD?M<�Q�TU:=<�N=gMLX?B<XZ[ADHJ?B<�IBTU<;<X?BImL\?MZ]?MH�L¥CD?B9�gML\FaL\9 � QwF@< L\AE<�N=?M9X��:=?MCD9¥:=H � <\F@IMIBTU<;N=?BZ[?BHdL �_pTUH=IMLXADTUHJH=?BCS9X?M<\F�Q�?B<;Z]AE9 l'C TU:J<���QwF@< >U?BHJAD<�HJTU:=9¥F¢>@TUH=9¥Q=<;gBIMTUH=AD9;grC ev:JLXADCEAD9\F¡L\ADT@HKN�ev:JH�Z]gMI¢F@HJAD9XZ[?N=?�9;:=AE>SA l�� FaH=9�H=TaL\<X?�Q=<XT@QRTU9;AELXADTUHyIB?�Z]gMI¢F@HJAD9XZ[?P9X?M<\FuF@9;9X:=<;g�QwF@<ON=?M9�I¢FaHwF@:b�YN�ehADHJ_pT@<XZ]FaL\AETUHADHdL\?M<XI¢FaCDgB9K?MHdL\<X?oCE?B9�Z[TbN u CD?M9�N=?M9�QJ<XTSIBgBNJgB9P?BH=�UF@�UgB9KN=F@H=9KI s F@IM:=H{N=?B9PZ[TbN=?M9�IBT@H=9XAEN=gB<;gB9 l�V ?< s CE?KN=?PIB?B9OI¢FaHwF@:b�yIMTUH=9;AD9;LX?B<XF � ?BHJ<X?B�@AD9;LX<X?M<^LXTU:JLX?B9^CD?M9O9;gB��:=?MH=IB?M9�N�ehgM>@gBH=?MZ]?MH�LX9��UgMH=gB<;gB9^QwF@<CD?KQ=<;TbIMgBN=gKN=?MQ=:=AE9iCfehADH=9 LcF@HdLiN=?K9;TUHjF@IMLXAE>aFaLXADTUH � :J9X��:�e � C evAEH=9;L\F@HdLiT + :=Hygm>UgBHJ?BZ[?BHdL�Q�?B<;Z]AE9�N=?IBTUZ[Z�:JL\FaL\AETUH�9Beh?B9 L�Q=<;TbNJ:=AEL l

������������������

mode j

mode i

engagement de nouvelles ressources

ressource n’éxistant plus dans le mode j

ressources communes engagées dansles mode i et mode j

�������Qq�ln~�� � "2929 �*) � �2"29 ���*$ $ ) �#"29���)�" $ ��35"29 ��"� �

V F�Z[AD9;?�?BH � :J>S<;?WN=:�9X:=An>SA�Q�?B<XZ[?ML�N=?�N=gmL\?M<XZ[ADH=?M<�CfehgML\FaL�NJ?�<\F@IMIBTU<;N=?BZ[?BHdLB|�I@eh?B9 L;k � k¦N=AE<X?CfehgMLcF¡L^N=:YHJTU:J>U?BF@:tZ[TSN=?PF@N=gM�S:=FaL�F¢>@?BI�CfehgMLcF¡L � QwFa<;L\AE<�N=:=��:=?MC�CfehgM>UgMH=?BZ[?BHdL�N=?�IBTUZ[Z�:JL\FaL\AETUHFt?B: CEAD?M: l�� � H N�e�FaQ=Q=<Xg s ?BHJN=?B<�CDFjQ�TU< L\gB?]N=?�HJT@L\<;?]Q=<;TUQ�TU9XAnL\ADT@H�|�H=TU:=9�IBTUHJ9XADNJgB<XT@H=9�NwFaH=9�:=HQ=<X?MZ]AE?B<�LX?BZ[Q=9¥CD?rI¢F@9¥CEADZ[AELXg � NJ?B:b��Z]TSN=?B9�N=?�_pTUH=ImL\ADT@H=H=?BZ[?BHdL lUV F��UgBHJgB<\FaCDAD9XFaL\AETUH � Q=CD:=9;AD?M:=<X9Z]TSN=?B9W9;?B<XF QJ<XgB9;?BHdL\gM?Y:JCEL\gM<XAE?B:=<;?BZ[?BHdL l¥q ?MLXLX?y�UgBH=gM<\F@CEAD9XFaL\AETUH H=?�9;?yCDADZ[AELX?B<XFjQwFa9W9X?B:JCD?BZ[?BHdL� CfevF@:=�UZ[?BHdLcF¡L\ADT@H N=: H=T@Z�x=<X?tN=?�Z[TbN=?M9uZ]F@AD9oL\AE?BH=N=<XF gB�UF@CD?MZ]?MH�LuIBTUZ[QJL\?YN=?B9�NJA � gB<X?MHdL\?B9IBTUZ�xJADHwF@AE9XTUHJ9iQRTU9;9XAEx=CD?M9iN=?PIBTUZ[Z�:JL\FaL\AETUHu?BHdLX<X?�Z]TSN=?B9 l

Page 75: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� x,q

� F@Q=Q�?BCDT@H=9P?BH � H ��:=?]HJTU:=9�F¢>UTUH=9�F@N=TUQbL\goCGF�9;LX<X:=ImL\:=<;?]Z�:=CELXAnk¦Z[TSN u CE?���:=A}Q�?B<XZ[?ML�N=?[<X?�kQ=<;gB9;?BHdL\?M<O:JH�9;�S9;L u Z[?@|wN=AnLiIBTUZ[Q=CE?m�b?�N=:u_`F@AnL�N=?M9 n Z]TSN=?M9�N=?�_pTUH=ImL\AETUH=H=?MZ]?MH�L�QRTU9;9XAEx=CD?M9B|JQ=F@<:=H]?BH=9;?BZ�xJCD?ON=?�Z[TSN u CE?B9}Q=CD:J9�9;ADZ[Q=CD?M9¤Z�F@AE9}I¢F@<XF@IMLXgB<XAE9\F@HdL�I s F@IM:=HuCDFPL¦�SQ�TUCDTU�@AD?i?ML�CD?^IMTUZ]Q�TU< kLX?BZ[?BHdLOFaLXLX?BH=NJ:YN=:j9;�S9 L u Z[?�?BH=�dFa�Ug � ��:=A�Q�?B:JL�F¢>UTUAE<igM>@TUCD:=g � NwF@H=9^IB?M9�NJA � gB<X?MHdL\9^Z]TSN=?M9 l

V ?tN=gm>U?MCDTUQ=Q�?BZ[?BHdL�NJ?tIB?YI s F@Q=AnL\<;?t9X?j_p?B<XF N=?tCDF _`F � TUH 9;:=AE>aF@HdLX?�N=F@H=9uCDF{9;?BIMLXADTUH q�l 7 |

C e�F@QJQ=<XTSI s ?OZ�:=CELXAnklZ]TSN u CE?�9X?M<\F�N=g � H=AE?�F@:uIBF@9rCEADZ[AELXg � N=?B:S�uZ[TbNJ?B9 lSV ?B9rQ=<XAEH=IBAEQwF@:b�[<;gB9X:JCELcF¡L\9N=?rIB?ML;L\?�9;?BImL\ADT@HW9X?B<;TUHdL}?m�bQ�TU9XgM9¤NwF@H=9¥CE?B9¥QJ<XTUQ�TU9XAnL\AETUH=9 q�lrq ?ML q�l|v LX<\F@AnLcF@HdL¥NJ?�CGF�NJgML\?M<XZ[ADHwF¡L\ADT@HN=?M9�gmLcFaLX9}N=?^<\F@IMIBTU<;N=?BZ[?BHdL lbq ?OI¢F@9}CEADZ[AEL\g�9X?M<\FPADCDCE:=9;LX<Xg�Q=F@<}:=H]?��b?BZ[Q=CD? � 9;?BImL\ADT@H q�l�79l � � l�� F@H=9CDF{9;?BIMLXADTUH q�l|q CD?M9]<;gB9;:=CEL\FaL\9oL s gMTU<XAE��:=?B9]N=?tCDF{9;?BIMLXADTUH q�l 7 9X?M<XTUHdL��@gBH=gM<\F@CEAD9XgM9]?mL�gM�dF@CE?BZ[?BHdLAECDCD:J9;L\<;gB9 l

� � � � 8:# �"! �"!�9�� . � ��!�#$�"!&%'�O( *�+�, �O(�(�!�. !�(/+

@ T@:=9�IMTUH=9;ADN=gM<XTUH=9}��:�eh:=Hu9 �b9 L u Z]?OH=?OQR?M:JL L\<;?�?MH=�dF@�@gO��:=?ONwF@HJ9�:=H[Z[TbN=?^N=?i_pTUHJIML\AETUH=H=?�kZ[?BHdL � CGFW_pTUAE9 l£� :=<XF@HdL�IM?ML�?MH=�dF@�@?BZ[?BHdL�CDF[9 L\<X:JIML\:J<X?�?mL�CDF[L � I s ?�NJ:t9;�S9 L u Z[?�<;?B9;LX?BHdL � �UgB?M9 lq eh?B9 L � C evTSIBIM:=<X<;?BH=IM?WN�eh:=H gm>UgMH=?BZ[?BHdL�IBTUHJN=:=AD9XF@HdL � CGF�Z[TbNJA � IBFaL\AETUHtN=?oCDF�9;LX<X:=ImL\:=<;? � ?BH=�UF¡k�U?MZ]?MHdL�T + N=gM9X?MH=�dF@�U?MZ]?MHdL�N=?o<;?B9X9;TU:=<;IB?B9 � TU:{N=?oCGFuL � I s ?[�S:8evAEC¤9X?B<XFj?MHd>bAE9\F@�@g]N�eh?BHJ�dF@�U?M<�CE?H=T@:J>U?BF@:Y9 �S9;L u Z]?�NwF@HJ9O:JHYZ[TbNJ?�N=A � gB<;?BHdL l � HyZ]TSN=?K<XgM9X:=CnL\?PN=TUHJI�NJ?�C e�FaIML\An>aFaL\AETUH�N�eh:=HjZ]T¡kN u CD?]N=: 9;�S9;L u Z[?yF@:=��:=?MCr9X?M<XTUHdL[F@9;9XTSIBAEgB?B9�N=?B9�9;QRgMIBA � I¢FaLXADTUHJ9�<X?MCD?M>aF@HdL�N=?uCGFjH=TU:J>@?BCECD?�L � I s ?FaL;L\?MH=N=:=? l

� F@HJ9�IM?ML;L\?¤9X?MIMLXADTUH�|BH=TU:=9�F@CECDTUHJ9�H=TU:=9�AEHdL\gB<;?B9;9X?B< � CDF�Q=<XTUxJCDgBZ]FaLXAD��:=?�NJ:�Z[TSN u CE?¥N=:PQ=<XTSIBgMN=g<;?BQ=<;gB9X?MHdL\grAEIBAUQ=F@<�:=H�Fa:JL\TUZ]FaLX? � gmLcFaLX9 l V e�FaIML\An>aFaL\AETUHKN�eh:=H�Z[TbNJ?¤N=?¤_pTUH=IMLXADTUHJH=?BZ[?BHdL�_`F@AEL�9X:=AnL\?� CfevF@Q=Q=F@<XAnL\ADT@H�N�ev:JHYgm>UgBHJ?BZ[?BHdL�N=AnL^N�eh?m�bIB?MQJL\AETUH lRq ?ML�gM>@gBH=?MZ]?MH�L�QR?M<XZ[?MLON=?�IBTUZ[Z�:JLX?B<iN�eh:=HZ[TbNJ? � :=HWF@:JLX<X?�N=TUH=I�N�ev:JH�Z]TSN u CD?}N=:�Q=<;TbIMgBN=g � :=HWFa:JL\<;?rZ[TbN u CD? l V ?�Q=<XT@x=C u Z]?�Z�F � ?B:=<�CDTU<;9N=?�IBTUZ[Z�:JL\FaL\AETUH�?BHdL\<;?�CD?M9�N=A � gM<X?BHdLX9�Z[TbN u CD?M9�N=?M9¥Q=<XTSIBgMN=gB9�IBTUH=9;AD9 L\? � ADN=?MH�LXA � ?M<�C evgmLcFaL�IBTU<;<X?MIMLN=?�N=gBQwFa<;L � <;?B9;Q l CfehgML\FaLWN=?�<;?MLXTU:=< � N=: Z]TSN u CE?�H=T@:J>U?MCDCD?MZ]?MHdLoF@IMLXAE>@g � <;?B9XQ l <X?MH=TU:J>@?BCDCE?BZ[?BHdLF@ImL\An>Ug � l¥q ?mLWgML\FaL�NJAEL�N=?uN=gMQwF@<;L � IBF@<�AEC�HJ?uIBTU<;<X?M9XQ�TUH=N=<XFtQwF@9�_pT@<XIBgMZ]?MHdL � C evgmLcFaL�ADH=AnL\ADF@C¥N=:Q=<;TbIMgBN=g � NJTUAEL L\<X?oIMTUZ]Q=FaL\AEx=CD? � F¢>U?MI]C evgmLcFaL � QwF@< L\AD<KNJ:=��:=?BC�CfehgM>@gBH=?MZ]?MH�L�N�eh?m�bIB?MQJL\AETUH 9Mev?M9;LQ=<;TbNJ:=AEL lB@ TU:J9�FaxRTU<;N=?B<;TUH=9}IB?OQ=<;TUx=C u Z]?i?MH]HJ?�IMTUH=9XAEN=gB<XF@HdL�NwF@H=9�:=H[Q=<X?MZ]AE?B<¥L\?MZ]QJ9���:=?ON=?M:b�Z[TbNJ?B9iN=?K_pTUH=ImL\AETUH=H=?MZ]?MH�L � H=TUZ[ADHwFaC8?MLON=gM�U<\FaN=g � l

C ����� B � < ��+68 -98�0�+ � ��.�<=? 8 � 8�+�>�8 .1A �V ?�Q=<;ADH=IMADQ�?�N=?�IMTUZ[Z�:JLcF¡L\ADT@H�<X?mL\?MHS:yH=gMIB?M9X9XAnL\?KCDF�Z]AE9X?�?BH�Q=CDF@IB?�NJ?�N=?B:S��I¢FaHwF@:b�uN�evAEHJ_pTU< k

Z]FaL\AETUH � � �U:=<;? q�l�7 � l�qrs F@��:=?oI¢F@H=F@C�_pTU:J<XH=AnL�CfehADHb_pTU<XZ]FaL\AETUHjH=gBIM?B9X9XF@AD<;? � CGFuN=gmL\?M<XZ[ADHwFaLXADTUHYN=?C evgmLcFaLiNJ?�NJgBQwF@< LONwF@H=9^CD?KZ[TSN u CE?KF@IMLXAE>@g l

��� �/� %8+ � +q

6�' EB,.6.�i

�3>�+ 6.( +2=�, EB�9� +&( @���� � L��= '�� %8+ � +q′

6.' EB, 6��j

>�( � J �3�9>-�<E @9� ��6.�3>B$&�3>&>-,�'�$ =8�*>=8, E�E '����*>;����+-$&� � �*> 6.��'.=�EB, 6��3>;,���+ �!�0EB4#E � � = +&( L ( +-% 6����9>;� �*> 6.��'�= %8+ � + >5=8,��2>�(!6.%�$&%3>3�

Page 76: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

x � ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

Modèle 1

canald’information 1,2

canald’information 2,1

Modèle 2

������� q�l�7�� � "�0) �� ) �2"�$ )5+ � $ ��3��%+," 3 �$� 98+," � �*9�35"�35"%)D" $ ��35"29�35".- ��� �� "�����!�#"%$&"��!

A T@AEL i :JH�ADH=NJADIB?PN=?�Z]TSN=?PN=?�_pTUH=IMLXADTUHJH=?BZ[?BHdL¢|�F@CETU<X9^Q�TU:=< i ∈ {1,2} |£H=T@:=9�NJg � H=AE9X9;TUH=9�CE?Z]TSN u CE?OF@:JL\T@Z�FaLX? Gi = (Qi, Σi, δi, qi,0, Qi,m) ��:=A�N=gMIB<XAnLrCE?^Z]TSN=?ON=?O_pT@H=IMLXADTUH=HJ?BZ[?BHdL i |SFz>@?BI �

�Qi �

?MH=9X?MZ�x=CE? � H=A�N�ehgMLcF¡L\9^NwF@H=9^CE?KZ]TSN=? i�

�Σi �

I¢F@<XF@IMLXgB<;AD9X?PC ev?MH=9X?MZ�x=CD?KNJ?B9^gM>@gBH=?MZ]?MH�LX9B|�N=AELOFa:=9X9;A�FaCDQ s FaxR?mL ��

δi : Qi × Σi −→ Qi?B9;L�CGF�_pTUH=ImL\ADT@H QwF@< L\AE?BCDCE?�N=?yL\<\FaH=9XAnL\ADT@H l C TU:J<]L\T@:JL q ∈ Qi

?ML

σ ∈ Σi|8TUH�H=TaL\?WQwF@< δi(q, σ)!

� <;?B9;Q l δi(q, σ)¬! � 9;A δi(q, σ) ?��bAD9;LX? � <;?B9XQ l H�eh?m�bAD9 L\?WQwF@9 � lq ?ML;L\?P_pTUH=IMLXADTUHyQ�?B:JL LX<X?PgMLX?BH=NJ:=?�NJ?�CDFW_`F � TUHj9X:=An>aF@HdL\? δi : Qi × Σ∗

i −→ Qi|=L\?BCECD?���:=?

∀s ∈ Σ∗i?ML σ ∈ Σi

| δi(q, sσ) = δi(δi(q, s), σ) ?mL ∀q ∈ Qi| δ(q, ε) = q

��

qi,0 �gmLcFaLOAEH=AELXAGF@C�N=:jZ]TSN=? i

��

Qi,m �?BHJ9X?BZ�x=CD?PN=?M9OgmLcFaLX9 � HwF@:b��N=:YZ[TSN=? i | Qi,m ⊆ Qi

lV ?�Z[TSN=? 1 9X?M<\F]LXTU: � TU:=<;9�IMTUH=9XAEN=gB<;g�IBT@Z]Z[?PCD?�QJ<X?BZ[AD?M<�Z[TSN=?�9;gBCE?BIMLXADTUHJH=g@|RF@ADHJ9XA G1

9;?B<\FCD?K9X?M:=C�Z]TSN u CD?�N=:jQ=<;TbIMgBN=gPADHJAEL\ADF@CD?MZ]?MHdL�F@ImL\An>Ug l

V evF@IMLXAE>aFaL\AETUH � NJgB9\FaIML\An>aFaL\AETUHP?B9;L}IMTUH=9;gBIB:bL\AE>@? � CfehTbIMIB:=<;<X?BHJIB?iN�eh:=HWgM>@gBH=?MZ]?MHdL�NJ?iIBTUZ[Z�:JL\F¡kL\ADT@H ldV FKN=gB9XF@IMLXAE>aFaL\AETUHWN�eh:=H[Z]TSN u CE?�9XAE�UH=A � ?i9\FKZ[AD9X? � ?MH]9;ADCD?MH=IB? �

�N=F@H=9}IB?mL�gmLcFaL}Q=F@<;LXADIB:JCDAD?M<

CD?�Z[TbN u CD?ON=gM9\F@ImL\AE>@gK?B9 L^QwF@9X9;AE_ � C evgMIBTU:JLX?�N=?M9igM>@gBH=?MZ]?MH�LX9^�S:JA�N=g � CD?BHdL l=� ?KIM?�_`F@AELB|bHJTU:=9�Q=<;TakQRTU9;TUH=9iN�ehADHdLXgB�U<;?B<iF@:�Z[TSN u CE?�N�ehTU<XAE�UADHJ?�:=H�gmLcFaL^AEHwF@IMLXAE_�IMTU<X<;?B9;QRTUHJNwF@HdLOF@:u_`F@AnL���:=?KCD?�Z]TSN u CE?H=?�Q�?B:JL�Q=CD:=9 � gmLcF@HdL�NJgB9\FaIML\An>Ug � LX<X?�<;gBIB?MQJL\An_�F@:b�YgM>@gBH=?MZ]?MHdL\9KQ=<;gB9X?MHdL\gB9 l�@ TU:J9�F@:=�@Z]?MH�LXTUH=9F@ADH=9;ARI s F@��:=?KZ]TSN u CD? Gi

NJ?�IB?mL�gML\FaLiQwFa<;L\AEIB:=CEAD?M< qi,in|JFaQ=QR?MCDg�gMLcF¡L�ADH=F@IMLXAE_ |�ADH=9;Q=AD<;g�N=:�IBTUH=IM?BQJL

N�evgmLcFaLrQ=:=AnL\9�Q=<XTUQ�TU9;g�QwF@< �P@ TU: {mx�� ?ML�NJ?�CfehgML\FaL�H=TUHu9;AD�UHJA � IBFaL\An_8Q=<;TUQ�TU9XgOQwF@< �v� FaH IJI � lbq TUZ]Z[?:=H 9;?B:=C}Z[TbNJ?�N=?W_pTUH=ImL\ADT@H=H=?BZ[?BHdLP?M9;L�<X?MLX?BH�: � CDFu_pTUAD9M|8CD?WZ[TSN u CE?�gMLX?BH=N=: Gi,et

F@IMLXAE>@g � :=HADH=9 LcF@HdL�N=TUH=H=g�?B9 LrCE?�9;?B:=C�Z]TSN u CD?iH=?�9X?^L\<XT@:J>aF@HdLrQwFa9�NwFaH=9r9;TUH�gmLcFaL�ADHwFaIML\An_ l � gBIBAEQ=<XTS��:=?BZ[?BHdLCfehgMLcF¡L^N=?KL\TU:=9^CE?B9iZ[TbN u CD?M9iH=TUHYF@IMLXAE>UgM9^?B9;LOCE?B:=<iQ=<;TUQ=<;?�gmLcFaLOAEHwF@IMLXAE_ l@ TU:=9�N=g � HJAD9X9;TUH=9 Σ′ IBT@Z]Z[?^Cfeh?BH=9;?BZ�x=CE?�NJ?B9rgm>UgMH=?BZ[?BHdL\9iNJ?�IMTUZ]Z�:JLcFaLXADTUHoQ�?B<;Z]?mLXLcFaH�L�N=?

L\<\FaH=9XAnL\?B<rN=:yZ]TSN u CE? G1F@:�Z[TbN u CD? G2

?ML : ���2" :�"��79 �,l=� FaH=9iCD?�I¢F@9i9;ADZ[Q=CD?�N=?�N=?M:b�yZ[TbN=?M9�N=?_pTUH=IMLXADTUHJH=?BZ[?BHdL¢|zC e�FaCDQ s FaxR?mL Σ′ 9X?B<XFOIMTUH=9 L\AELX:=g}N=?B9�N=?M:b��gM>@gBH=?MZ]?MHdL\9 α1,2

?ML α2,1

l¢V ehgM>@gBH=?MZ]?MHdLα1,2

� <;?B9XQ l α2,1 � Q�?B<;Z]?mLPN=?oN=gB9XF@IMLXAE>@?B<PCD?�Z[TSN u CE? G1

� <X?B9;Q l G2 � ?MLPN�evF@IMLXAE>@?B<PCD?�Z[TSN u CE? G2

Page 77: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� x �

� <X?B9;Q l G1 � l� "%$ �$�#!�)�" ( ��+ � � � '%"� ���+ ��'���+

Σ"29� �9 ��� � 351�"�� "� ���,9�9 �*) 9� ��+ � � � '%"� �9&'

Σ = Σ1∪Σ′∪Σ2

� ��:�"��Σ1

��+ � � � '%"� #3�)$ ��35"

1�Σ′ "�� 9;"%$ '�+," 35"29 1%:�1��#"%$&"��! �9 35" ���*$ $ ) �$ "����� "� Σ2

��+ � � � '%"� �3�)&$ ��35"2

� � � �*) "�7"+ "�� 9;"%$ '�+,"&35"29 1%:�1��#"%$&"��! �9 35" ���*$ $ ) �$ "�����"29� 83$�,9 � ��� �! 35" + ��+ � � � '%"� 35"29 35"%)D" $ ��3��%+,"295'Σ′ ∩ Σi = ∅

+ �!�*) �i ∈ {1,2} - �

� "%$ �$�#!�)�" /� �*$ $&" �!�*) � +,"29 ��+ � � � '%"� �9 35"�$ ��35"29���+ "�� 9;"%$ '�+,"�35"29 1%:�1��#"%$&"��! 9 35" ���*$ $ ) ��$ �����

Σ′ ��"%) �� "�7" 9 ��� � 351 "�� 1%:�1��#"%$&"��! �9 �����! "�26*+ � '�+,"29 "� � � �����! "�76*+ � '�+,"29��

A A¤CDFu<X?BZ]F@<;�S:J? ~ F�Q�?B:{N�evAEHdL\gB< L�?BH L\?M<XZ[?oN=?oIBTUZ[Z�FaH=N=?@|RCGF�9X?MIBTUHJN=?]?MH <;?M>aF@H=I s ?]?M9;LZ]F � ?B:J<X? l=� CECD?Kgm>UTS�S:J?�HwF¡L\:=<;?BCDCE?BZ[?BHdLiCE?B9iH=T@LXADTUHJ9iN=?PIBTUHdL\< s CGFax=ADCEAEL\gON=?PCGF��@?B9;LXADTUHyN=?M9�Z[TSN=?B9 lq ?mLXL\?P��:=?M9;L\AETUHYF@xRT@<XN=gM?�N=F@H=9 ��� F@x {mv$� 9X?B<XF[<;?BQ=<;AD9;?�Fa:YI s FaQ=AELX<X? 4

lV e�F � TU:JL�N8ev:=H gmLcFaL�ADHwF@ImL\An_ � Cfeh?BHJ9X?BZ�x=CD?uNJ?B9�gmLcFaLX9�N=? Gi

H=gMIB?B9;9XAnL\?�N=TUHJIuN�evF � TU:JLX?B<�C ev?MHbk9;?BZ�x=CE?¥N=?M9�gm>UgMH=?BZ[?BHdL\9�N=?}IBT@Z]Z�:bLcFaLXADTUH � C e�FaCDQ s FaxR?mL�N=?¤C e�F@:bL\TUZ]FaL\?a|BF � HPN=?}QRTU:b>UTUAE<�ADHdL\gM�U<X?M<F@:�Z[TSN u CE?�gMLX?BH=N=:{CD?M9�L\<XF@H=9XAnL\AETUH=9�?MHdL\<X?oIM?ML�gML\FaLPADHwFaIML\An_}?MLPCE?B9PF@:JLX<X?M9 l @ TU:=9PQRT@:J>UTUHJ9PF@CDTU<;9N=g � H=AE<iCD?KZ[TbN u CD?�gmL\?MH=N=:tIMTUZ[Z]?�9;:=AEL � � "�q1C�@ I ~ � � �

Gi,et = (Qi,et, Σi,et, δi,et, qi,0,et, Qi,m,et)Fz>@?BI

�Qi,et = Qi ∪ {qi,in}

��

Σi,et = Σi ∪ Σ′ �

�qi,0,et =

{

qi,09XA i = 1

qi,in9XA i = 2

�Qi,m,et = Qi,m

�� V ?�QJCD:=9�NJgBCDAEI¢FaL�?B9 LKCGF�NJg � H=AnL\AETUH�N=?WCDF]_pTUH=ImL\ADT@H�N=?�LX<\F@H=9;AELXADTUH�gmL\?MH=N=:=? δi,et

l�V ?M9�N=?M:b�QJ<X?BZ[AD?M<X9PI¢Fa9�9;TUHdL�gm>bAEN=?BHdLX9B|�CD?WL\<;TUAD9;A u Z[?WH=gMIB?B9;9XAnL\?B<XFYN=?M9�N=gm>U?MCDTUQ=Q�?BZ[?BHdLX9�:=CnL\gB<;AD?M:=<X9 l� HjIBTUHJ9XADNJgB<\FaH�L i 6= j |wHJTU:=9OF¢>UTUH=9 �~,l

∀q ∈ Qi?mL ∀σ ∈ Σi

|J9XA δi(q, σ) ?��JAE9;LX?�FaCDTU<;9 δi,et(q, σ) := δi(q, σ)�

7/l∀q ∈ Qi

� Q=F@<;LXAD<¥N=:J�S:J?BCwCfehgM>@gBH=?MZ]?MHdL}N=?iIBTUZ[Z�:JL\FaL\AETUH αi,jQR?M:JL LX<X?i�UgMH=gB<;g^F@CDTU<;9

δi,et(q, αi,j) := qi,in

l�q ?PI¢F@9^IBT@<X<X?M9XQ�TUH=N � CDF�IBTUZ[Z�:JL\FaL\AETUHuN=AE<X?MIML\? �q9l 9XA q = qi,in

|£CD?�9X?M:=C�gm>UgBHJ?BZ[?BHdLKQ�TU9X9;ADx=CE?�?M9;L αj,i

l A A i = 2� ?ML�N=TUH=I j = 1 � IB?�I¢F@9

IBTU<;<X?B9;QRT@H=N � CfevF@IMLXAE>aFaLXADTUH N=: Z[TbN u CD? G29X:=AnL\? � C evgm>UgMH=?BZ[?BHdLoN=?uIMTUZ[Z�:JLcF¡L\ADT@H

α1,2

�δ2,et(q2,in, α1,2) � l A A i = 1

� ?mL�N=TUHJI j = 2 � AEC¤9BevF@�UAEL�N=?[CGFj<Xg¢FaIML\An>aFaL\AETUH N=:Z]TSN u CE? G1

9X:=AnL\? � C evgm>UgMH=?BZ[?BHdL^N=?KIMTUZ]Z�:JLcFaLXADTUH α2,1

�δ1,et(q1,in, α2,1) � l=� F@H=9iCD?M9

N=?B:b�tI¢Fa9B|8CDF]N=gmL\?M<XZ[ADHwFaLXADTUHjN=?�CfehgMLcF¡L�FaL;L\?MADHdL�NwFaH=9�:=H�NJ?B9�Z[TbN u CD?M9�CETU<X9ON=?�IM?ML;L\?IBTUZ[Z�:JL\FaL\AETUHuADHd>@?B<X9;?�HJgBIB?M9X9;AEL\?�N=?M9�AEHJ_pTU<XZ]FaLXADTUH=9�CDAEgB?B9 � C e�F@:bL\<X?KZ[TSN u CE? l

Page 78: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

x,v ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

C ��� � � � 0 � �&4�-9>E-98 0�+ 2�4 � 032��=?�AG1

>�4 � 032��=?�AG2

q TUZ[Z[?YH=T@:=9�C e�F¢>UT@H=9�N=g � � N=AnL¢|}CD?jZ]TSN=?jADH=AnL\ADF@Cr?M9;L�CE?YZ[TbNJ? 1l�� ADH=9;A�C evgmLcFaL]ADHJAEL\ADF@C�N=?

G1,et?B9 L q1,0

|�F@CETU<X9P��:=?uIM?BCE:=A}N=? G2,et?M9;L q2,in

l � F@HdL��S:8ev:=H gm>UgMH=?BZ[?BHdLWN=?]N=gM_`FaADCDCDF@H=IM?WH�e�FQwF@9�CDAD?M: � α1,2

NwFaH=9PIB?[I¢F@9 � |�CD?WZ[TbN u CD? G1,et<X?M9;LX?�F@ImL\An_ |�I@eh?B9 L;k � k¦N=AE<X?oNwF@H=9P:=H gML\FaL q ∈ G1

|F@CDTU<;9]��:=?tCD?jZ]TSN u CE? G2,et

<X?M9;L\?YNwF@H=9�CfehgMLcF¡L q2,in

l ������������� C evgm>UgBHJ?BZ[?BHdLuN=?tIBTUZ[Z�:JL\FaL\AETUHα1,2

QR?M:JLO9X:=< >U?MH=AD<^NwF@HJ9iQ=CD:=9;AD?M:=<X9^gML\FaL\9iNJ:YZ[TbN u CD? G1

l=V T@<X9X��:=?�IB?mL^gM>@gBH=?MZ]?MH�L�9X:=< >SAD?BHdLB|wCD?Z]TSN u CE? G1,et

QwF@9;9X?oN=TUHJI@|�QwFa<�N=g � H=AELXADTUH�|RNwF@H=9KC evgmLcFaL q1,in

l C F@<KIBTUHdLX<X?WCGF]N=gMLX?B<XZ[ADH=FaL\AETUH�N=?CfehgMLcF¡L�FaIML\An>Ug[NwF@H=9�CD?oZ[TbN u CD? G2,et

N=gBQ�?BHJN N=?[CGFy9X:=IMIB?B9;9XAETUH N=?M9�gm>UgBHJ?BZ[?BHdL\9 � L\<\FaIB? � F¢�dFaH�L?B:tCEAD?M:YF¢>aF@HdLOCfehgM>@gBH=?MZ]?MH�L α1,2

l£� Ht? � ?MLB|wNwF@H=9OCD?KIBF@9OT + ADC�?m�bAE9;L\?PN=?M9�<;?B9;9XTU:=<;IB?M9�IBT@Z]Z�:JH=?B9F@:b��NJA � gB<X?MHdL\9KZ[TbN u CD?M9 Gi,et

IBT@H=9XAEN=gB<;gB9B|�CE?�I s F@HJ�U?BZ[?BHdLPN=?WZ[TbNJ?�H=?WN=T@AELKQwFa9�?BHdL\<XFa�GHJ?B<KN=?I s F@H=�U?MZ]?MHdLiN�ehgMLcF¡L � ��:=A�H=?�9X?B<XF@AELrN & � F@:=IB:JHugM>@gBH=?MZ]?MH�L � � N=?M9�<X?M9X9;TU:=<XIM?B9iIMTUZ]Z�:=H=?B9 lDC TU:=<N=gMLX?B<XZ[ADHJ?B<oCfehgML\FaL]F@IMLXAE>UgyNwFaH=9 G2

FaQ=< u 9]C evgm>UgBHJ?BZ[?BHdL α1,2|}ADC�_`F@:JL[N=TUH=Ij9X:JAE>S<X?jCfeh?BH=9;?BZ�xJCD?

N=?B9PgM>@gBH=?MZ]?MHdL\9�Fz�UF@HdLP?B: CDAE?B:�N=F@H=9KCD?�Z]TSN u CE? G1N=?BQ=:JAD9KCfehADHJ9;LcFaH�L�ADH=AnL\ADF@C � :=9X��:�e � CfehADH=9 LcF@HdL

T + C evgm>UgBHJ?BZ[?BHdL�N=?jIBTUZ[Z�:JL\FaL\AETUH α1,29Beh?B9 L�Q=<XTSN=:=AnL l C F@<�FaHwF@CDT@�UAD?yF¢>U?MI�CD?M9�FaQ=Q=<XTSI s ?M9�N=?

���8s T z�x�� � �8s T {d7 � ?ML �h��V�{m{$� |UH=TU:=9�:JLXADCDAE9XTUHJ9�:=H[I¢F@H=F@CwN�ehADHJ_pTU<;Z�F¡L\ADT@H π1,2Z]FaLXgB<XADF@CDAE9\F@HdL�CD?i9;:=AE>SA

N=?B9�gM>UgMH=?BZ[?BHdLX9¤N=? G1,etQRT@:=<�NJgML\?M<XZ[ADH=?M<�CfehgMLcF¡L�FaIML\An>Ug�NwF@H=9 G2

l@q ?mLXLX?r9;LX<X:=ImL\:=<;?r?M9;L�<\F@Q=Q�?BCEgB?9X:=<OCGF � �@:=<X? q�l|q�l

Modèle 1 Modèle 2

s

d’information 1,2canal

ππ

1,21,2

(s)

�������7q�lrq��� �$����+ 3� � �/- ���0$ �$ "�����π1,2

"��! "�2" +,"29 $ ��3��%+,"29 35"29 ��� � �21435129G1,et

"� G2,et

� TU<;Z]?MCDCD?MZ]?MHdL¢|BCE?�IBF@HwF@C�N�ehADHb_pTU<XZ]FaL\AETUH π1,2?M9;L¥:JH=?�_pTUHJIML\AETUH�N=?rQ=<;T � ?BImL\AETUH laq ?ML;L\?�_pT@H=IMLXADTUH

N=?PQ=<XT � ?MIMLXADTUHj?B9 L�NJg � H=AE?PQwF@<�j ��� NVW PSWJR7N � �YZ ��� � R�� `/U,PSWJR7N ��PX`/NVT ��` �

� ��� π1,2 : Σ∗

1 −→ Σ∗2

"%+�+," !�)�"∀σ ∈ Σ1

"� ∀s ∈ Σ∗

1 :

π1,2(ε) = ε

π1,2(sσ) =

{

π1,2(s)σ9��

σ ∈ Σ1 ∩ Σ2

π1,2(s)9��

σ ∈ Σ1 \ Σ2

q ?mLXL\?WHJTU:J>U?MCDCE?�N=g � H=AELXADTUH�NJ?�Q=<XT � ?BIMLXADTUH�HJ?WIBTUHdL\<XF@ADHdLKQ=F@9�CD?M9KF@CEQ s F@x�?MLX9 Σ1?ML Σ2

|RI@eh?B9;LQRTU:J<X��:=TUA^H=TU:J9]C e�F@QJQR?MCDTUH=9oQ=<;T � ?BImL\AETUH gmL\?MH=N=:=? lr� FaH=9�CE?jIBF@9[QwF@<;LXADIM:=CDAE?B<�T +

Σ2 ⊆ Σ1|¤?BCECD?

Page 79: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� xmx

IMTU<X<;?B9XQ�TUH=N � CGF�Q=<;T � ?BImL\AETUHuHwFaLX:=<X?MCDCE?�IMCGF@9;9XAD��:=?MZ]?MHdLi:JL\AECDAE9XgB?ONwF@HJ9�CGFPL s gMTU<XAE?�N=?�IMTUHdL\< s CD?�Q=F@<9;:=QR?M<;>SAD9;ADTUH �hV��nzmz$�#�hV ADH { � �#� � �O� ��IJI � � >UT@AD<iQwF@�@? 7 z � l

V F]Q=<;T � ?BImL\AETUH π1,2Q�?B<;Z]?mL�N�ehTUx=9;?B< >U?B<�:=H=AD��:=?MZ]?MHdL�CfehTSIBIB:J<X<X?MH=IB?�N=?B9�gM>UgMH=?BZ[?BHdLX9PF@Q=QwF@< k

LX?BHwF@HdL � CfehADHdLX?B<X9;?BImL\ADT@H Σ1 ∩ Σ2?mL�NJTUH=I�NJ?�H=?]9X:=An>b<;?]��:=?]CD?M9�<X?M9X9;TU:=<XIM?B9�IMTUZ[Z�:=H=?M9�?MH�LX<X?

CE?B9iZ[TbN u CD?M9 G1?ML G2

l�q ?�9;TUHdL�C � CD?B9^9;?B:=CE?B9OADHJ_pTU<;Z�F¡L\ADT@H=9 � IBT@H=HwFa�EL\<X?PCETU<X9iN=:jQwF@9;9\F@�@?�N�eh:=HZ[TbNJ? � :=H Fa:JL\<;? l�V F�QJ<XTUQ�TU9XAnL\AETUHt9;:=AE>aF@HdL\?�_pTU<XZ]F@CDAE9X?PCGF[N=gMLX?B<;Z]AEHwFaL\AETUHtNJ?�CfehgML\FaL�N=?�N=gBQwFa<;LN=? G2

|wIB?P��:=A�IMTU<X<;?B9XQ�TUH=N � CGF�N=gmL\?B<;Z]AEHwFaLXADTUH�N=? δ2,et(q2,in, α1,2)gM>UTS��:=gB?�Q=CE:=9 s F@:JL l

� �SR7aKR7cfW PSWJR7N � �YZ� ���

suiv(s)+ "�� 9;"%$ '�+," 35"29 1%:�1��#"%$&"��! �9 !�) � 9%) ��:�"��! �+ � 9;1!�)�"�� �2"�3� 1%:�1��#"%$&"��! �9

s�

∀s ∈ L(G1)� "%+ !�)�"

α1,2 ∈ suiv(s)��+ 1� �$ 35" 351 � �$�� �3�)!$ ��3��%+,"

G2

"29� �3 ���!�#1 ���*$ $&" 9%) � 'δ2,et(q2,in, α1,2) = δ2(q2,0, π1,2(s)) �

j ��� R7NVcIP �Sb�PSWJRQNA TUAnL s ∈ L(G1)

:=H=?�9XgM��:=?BH=IM?�N�ehgM>@gBH=?MZ]?MH�LX9��UgMH=gB<;gB9�Q=F@< G1

� QwF@< L\AE<iN=?�9;TUHtgmLcFaLOAEH=AELXAGF@C?mL�LX?BCDCE?P�S:J? α1,2 ∈ suiv(s)

l�V Fo9XgB��:=?MH=IB? s = σ1σ2σ3σ4 . . . σn?B9 L�N=T@H=I�:JH=?�9;gB��:=?BHJIB?�N�ehgM>@gmk

H=?MZ]?MHdL\9r�@gBH=gM<XgB9�9X:=<�CfevF@CDQ s F@x�?ML Σ1

l L�<B| Σ1IBT@Z]Z[?^CD?OZ]TUHdLX<X?OCGF � �U:=<;? q�l � 9;?�N=gMIBTUZ[Q�TU9X?O?BH

N=?M:b�y?MH=9X?MZ�x=CD?M9�NJAD9 � T@ADHdL\9�

Σ1 = (Σ1 \ Σ2) � ∪(Σ1 ∩ Σ2)

\ 2Σ 1 Σ Σ Σ 12Σ Σ 2

Σ Σ1 2

1\

�������Qq�l � � � �$�� "� �����(35"8+ ��+ � � � '%"� Σ1

A :JAE>aF@HdL^IB?mLXL\?PQwFa<;L\AnL\AETUH�N=?B:S�yI¢F@9^9;TUHdL�Q�TU9X9;ADx=CE?B9�

\]b c�Z �π1,2(s) = ε

q ?MCGFjADZ[Q=CDAE�S:J?[��:=? ∀ σ ∈ s, σ 6∈ Σ1 ∩ Σ2

l�� FaH=9�IM?uI¢F@9�F@:=IM:=H=?u<;?B9X9;TU:=<;IB?�IBT@Z]Z�:JH=?H8e�FjgM>UT@CD:=g l�� :JL\<;?BZ[?BHdL�N=AnL�FaQ=< u 9�CGFj9XgM�S:J?BH=IM?�N�evgm>UgMH=?BZ[?BHdL\9 s |�L\TU:bL\?B9�CD?M9�<;?B9X9;TU:=<;IB?B9IMTUZ[Z�:=H=?M9�N=?M9�Z[TbN u CD?M9 G1

?ML G29;?�LX<XTU:b>U?BHdL¤N=F@H=9�CD?B:J<�gmLcFaL�ADH=AnL\ADF@C lm� AEH=9XA |zCfehTbIMIB:=<;<X?BHJIB?

NJ?�CfehgM>@gBH=?MZ]?MHdLiN=?�IMTUZ[Z�:JLcF¡L\ADT@H α1,2IBT@H=N=:=AnLrC e�F@:bL\TUZ]FaL\? G2,et

NJ?BQ=:=AE9rC evgmLcFaL q2,in>U?M<X9

C evgmLcFaL�ADH=AnL\ADF@C�N=:WZ]TSN u CD? G2

ldq ?mL�gMLcF¡L¤?B9 L}CD?�Q=<;TbNJ:=AEL�I¢F@< L\gB9;AD?MH[NJ?�L\TU:=9¤CE?B9¥gmLcFaLX9¤ADH=AnL\ADF@:b��.�

Σ1 \ Σ2 = {σ ∈ Σ1 | σ 6∈ Σ2}

Page 80: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

x,z ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

N=?PI s F@��:=?�<X?M9X9XT@:=<XIM?�IBT@H=9;LXAEL\:=F@HdL^CD?KZ[TbN u CD? G2

lw� T@H=I

δ2,et(q2,in, α1,2) = δ2(q2,0, π1,2(s)) = δ2(q2,0, ε) = q2,0

\ b1c k �π1,2(s) 6= ε

q ?BCDFuADZ[Q=CDAE�S:J?���:�ehADC�?m�bAD9 L\? k gM>@gBH=?MZ]?MHdL\9 σiLX?BCE9���:=? i ∈ {1, . . . ,n} ?ML σi ∈ Σ1 ∩ Σ2

l� ehT +

π1,2(s) = siF¢>U?BI si

CGF]9;gB��:=?MH=IB?WTU<;N=TUH=HJgB?�N=?M9�gM>@gBH=?MZ]?MHdL\9 σi

l�� AEH=9XA�H=TU:=9�H=TU:=9L\<;TU:J>UT@H=9oNwF@H=9oCGFY9XAELX:wFaLXADTUH T + F@: Z[TUAEH=9�:=H=?yN=?M9W<X?M9X9XT@:=<XIM?B9�IMTUZ[Z�:=H=?M9 i F�I s F@H=�UgN�ehgMLcF¡L l C F@<KIBTUHJ9XgB��:=?MHdL�C evgmLcFaLPF¡LXL\?MADHdLKNwFaH=9KCD?�Z[TSN u CE? G2

HJ?WN=?M>S<\F�QwFa9 L\<;?W9XTUH gmLcFaLADH=AnL\ADF@C l E C�9X?M<\FoN=gMLX?B<;Z]AEH=gKQwF@<

δ2,et(q2,in, α2,1) = δ2(q2,0, π1,2(s)) = δ2(q2,0, si).

p� " "%$ � +,"� ��� 9�� 351�� ��� 9 + "#" "%$ � +," � �$�� � "%+ "#"� "�#�$� 35"8+ � ) ��) �7" � � �1�

q

σ12

σ3

n

q

qq

σ

σ2

σ1

σm

G Gα

α

σ

q1

q

q

q

2

3

n

q

q2

mq

1’

1, 2,

1, 2

1, 2

α 1, 2

et et

α 1, 21,0

2,in

1,in

2,0

������� q�l � ��� " "%$ � +," 3� ��� � + ��� �$ "�����

" $ ��3��%+,"G1

� 3�$&"� ���*$ $&" 1� �$ � �!� �"��+.+ 1� ��$ q1,0

��% � �$�� � � 3�)�!�)�"%+n1%:�1��#"%$&"��! 9

σ1

�σ2

� �.�.� �σn

9 ���! �!�;929�� '�+,"29�� " $ ��3��%+,"G2

� 3�$&"� ���*$ $&" 1� ��$ � �!� "�"��+ + 1� ��$ q2,0

+G2,et

� 3�$&"� ���*$ $&" 1� �$ � �!� "�"��+

q2,in - �� ) � �!�;9 ��� 9G!�)�" �!�*) � +," $ ��3��%+,"

G1

+ � ���%) ���7"�� �2"�35" + 1%:�1��#"%$&"��! σ1

$ ���#" :�"��29 ) �!1� ��$ q1

%� �$�� "� � 3�)�!�)�"%+ + � ���%) ���7"�� �2"�35" + 1%:�1��#"%$&"��! 35" ���*$ $ ) �$ "�����

α1,2

��"%) #9;" ��� ��3�) � �7"�� � ��� � ���%) ���2"�� �2"���9;"%+ ��� � �� �7"�351*) �!� "������� ����� 3�) � :�"��79�+ 1� ��$ � ��� �� "� -

q1,in

� � ��9%) � �!�;9 �$�! K!�)�"σ1 6∈ Σ1∩Σ2

Page 81: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� x,{

��+ ���79π1,2(σ1) = ε

� ���$� 9��2" � �*9�� + � ���%) ���7"�� �2" 35"σ1

� ���"��� " ��)!�%) �#" �7"2929 �*) � �2" 3�) $ ��3��%+,"G2

�� " �2"�- �$� *��+ 1� ��$ 35" 351 � �$�� 3�) $ ��3��%+,"G2

9;"�� � + 1� ��$ � �!� "�"��+q2,0

� ) �,96!�) ��+ � �� � �*9 "%)3� 1%:$�*+ ) ����� 35" �2"2929 �*) � �2"29 ���*$ $ ) �#"29 %

G1

"� G2

� � � �7"%:��$� ����"�� 9�� ��� 9%) � �!�;9;" !�)�"σ2

"29� ���*$ $ ) ����)�"&35"%)�"���+ � � � '%"� 9

Σ1

"� Σ2

+σ2 ∈ Σ1 ∩Σ2 - � ��+ ���79�+ � �7"2929 �*) � �2" ���*$ $ ) �#" %

G1

"� G2

!�) � �51�� ���7"σ2

� 1%:$�*+ )�1�� � ��+ 1%:�1��#"%$&"��! 35" ���*$ $ ) ��$ �����α1,2

9;" ��� ��3�) � ����� �29 + � ���%) ���7"�� �2" 35"

σ2

� ��+ ���79 + 1� ��$ 35" 351 � �$�� 3�) $ ��3��%+,"G2

9;"��#� 351� "��0$ � �#1 3� ����� �29δ2(q2,0, π1,2(σ2))��:�"��

π1,2(σ2) = σ2

�y

A :=<�IB?ML¥?m�b?BZ[Q=CD?a|aHJTU:=9¥Q�TU:J>@TUH=9¥IMTUH=9;L\FaL\?M<¥��:=?iCfevF@N � T@H=IMLXADTUH�N�eh:=HWgML\FaL¤ADH=F@IMLXAE_=:JH=AD��:=?�N=F@H=9CE?KZ]TSN u CE? G2,et

IBTUHJN=:=AELOZ]F@C s ?B:=<;?B:=9;?BZ[?BHdL � :=HYAEH=N=gmL\?B<;Z]AEH=AD9;Z]?���:�evAEC�9BevF@�UAnLiZ�FaADHdL\?MHwF@HdL^N=?CE?M>U?M< l£� Hj? � ?ML¢| � QwF@< L\AE<�N�eh:=HtgmLcFaL^AEHwF@IMLXAE_ q2,in

|wAEC�?m�bAD9 L\?a|wQRTU:J<OCE?KZ Z]?Kgm>UgMH=?BZ[?BHdL�N=?�IMTUZWkZ�:bLcFaLXADTUH α1,2

Q=CD:=9;AD?M:=<X9�gMLcF¡L\9rN8e�F@<;<XAn>UgB?�9X?MCDTUHuC e s AD9;LXTU<XAE��:=?�?MH=<X?M�UAD9 L\<;g�F¢>aF@HdL�CGF�IBTUZ[Z�:JL\FaL\AETUH lC TU:=<�CD?m>U?B<�IM?ML�ADH=N=gmL\?M<XZ[ADH=AE9XZ[?@|mH=TU:=9�N=g � H=AD9;9XTUH=9�:=H�?BH=9;?BZ�xJCD?}N�ehgM>UgMH=?BZ[?BHdLX9¥QR?M<XZ[?ML;LcF@HdL¢|zQ=F@<CDF@xR?MCDCEAD9\F¡L\ADT@H�|aNJ?�N=AD9 L\AEH=�U:=?M<�NwFaH=9�CD?�Z]TSN u CD? G2,et

CD?M9rN=A � gM<X?BHdLX?B9�TSIBIM:=<X<;?BH=IM?B9iN=?�CfehgM>UgMH=?BZ[?BHdLN=?PIMTUZ]Z�:JLcFaLXADTUH α1,2 �

� �SR7aKR7cfW PSWJR7N � � k� ) � 35"�+,"%:�"���+ � � 351� "��0$ � �!�,9%$&" 35"29 $ ��3��%+,"29�� � �*) 9 �*929 � ������� 9 %�+ 1%:�1��#"%$&"��! 35" ���*$ $ ) ��$ �����α1,2

) � "�� 9;"%$ '�+," 351*) �!� � �$�K'α1,2 = α1,2,k si δ2(q2,0, π1,2(s)) = q2,k �

V FtQ=<;TUQRT@9XAELXADTUH q�ln~ 9BevF@Q=QJCDAD��:=?]9X?M:=CD?MZ]?MH�L � :=H=?]9X?B:JCD?u9;gB��:=?BHJIB?yN�ehgM>UgMH=?BZ[?BHdLX9 l�E C�H�ev?M9;LQwFa9���:=?B9 L\AETUH N�evF@Q=Q=CEAD��:=?M<�IM?MLXLX?�Q=<;TUQ�TU9XAnL\ADT@H � Cfeh?BH=9;?BZ�x=CE?]NJ?B9�9;gB��:=?BHJIB?B9WQ�TU9;9XADxJCD?B9�Q=:=AE9X��:=?IM?ML�?MH=9X?MZ�x=CE?�?B9 L�ADH � H=A lG@ TU:=9�Q=<;TUQ�TU9XTUHJ9�F@CETU<X9�:=H=?�NJgBZ]F@<XI s ?�9XAEZ]Q=CE?���:=A�Q�?B<XZ[?MLrN=?�IBF@CDIM:=CD?M<LXTU:JL\?M9PCD?B9K9;gB��:=?MH=IB?M9�QwF@< LcF@HdL�N=?BQJ:=AD9PCfehgML\FaLPADHJAEL\ADF@C�N=: QJ<XTSIBgBNJg[?mL�Z]?MHwF@HdL � C ev?MH=9X?MZ�x=CE?[NJ?B9gmLcFaLX9KT + CfehgM>UgMH=?BZ[?BHdL�N=?WIBT@Z]Z�:bLcFaLXADTUH α1,2

QR?M:JLP9X?oQ=<;TbN=:JAD<X? l < � IM? � CDFuIBTUHJHwF@AD9;9\F@HJIB?oN=?IM?�CDF@H=�dFa�U? K H=TU:=9^N=gmL\?B<;Z]AEH=?B<;TUH=9^CfehgML\FaLiN=?P<XF@IBIMTU<XN=?MZ]?MHdL�?MHYCE:=A�F@QJQ=CDAE�S:=F@HdLiCGF�_pTUH=ImL\AETUH�N=?Q=<;T � ?BImL\AETUH π1,2(K)

l� �SR7aKR7cfW PSWJR7N � � �� ���

Q = {ql, . . . ,qn}+ "�� 9;"%$ '�+," 35"29 1� �$ �9 3�) $ ��3��%+,"

G1

% � �$�� "� � 35"296!�)�"%+ 9�+ 1%:�1��#"%$&"��! 35"���*$ $ ) �$ "�����

α1,2

"29� �!�;929�� '�+,"��( � � �*) �

q ∈ Q- �$� �7"

+ � - � 1� "��0$ � �#"��!+," + �$��� � �5" Kq

�����! "����$�! �*) "29 +,"29 9;1!�)�"�� �2"29 �����$�! ����*$ $&" 1� ��$ 3� ����� �$� �#" + 1� �$ � �!� �"��+ 3�) $ ��3��%+,"

G1

"� ���*$ $&" 1� ��$ ) ����+q

�+ ' - � ��+ �%) +,"��

π1,2(Kq)�

+#� - � 1� "��0$ � �#"�� + "�� 9;"%$ '�+,"835"29 1� �$ �9 35" 351 � �$�� �3�) $ ��3��%+," G2

"�� ��� � + � !�) �$�! 'δ2,et(q2,in, α1,2) = δ2(q2,0, π1,2(Kq)) �

Page 82: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

z I ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

C ��� � C � 0 � �&4�-9>E-98 0�+ 2�4 � 032��=?�AG2

>�4 � 032��=?�AG1

� Q=< u 9�F¢>UTUAE<�9;:=AE>SA}CfehgM>@TUCD:bL\ADT@H N=: IBTUZ[Q�TU<;LX?BZ[?BHdL�NJ: Z]TSN u CD? G1?ML�N=gMLX?B<XZ[ADHJg[C evgmLcFaL�N=?

N=gBQwFa<;L^N=:yZ[TbN u CD? G2|=HJTU:=9^F@CECDTUH=9�Z�FaADHdL\?MHwF@HdL�IMTUH=9XAEN=gB<;?B<^CGF�IBTUZ[Z�:JL\FaL\AETUH�AEH�>@?B<;9X?@|wIaev?M9;L k � k

N=AD<;?¤gMLcFax=CDAE<8CD?¤IBF@9�T + CfehgM>@gBH=?MZ]?MH�L�N=?}IMTUZ]Z�:JLcFaLXADTUH α2,1Q�?B:JL�9;?�QJ<XTSN=:=AD<;?¤NwF@H=9 G2

l � F@Q=Q�?BCETUH=9�S:J?@|rIMTUZ[Z]?yL\TU:bL�gm>UgBHJ?BZ[?BHdLyN=?tIMTUZ[Z�:JLcF¡L\ADT@H�|¥IB?mL�gM>@gBH=?MZ]?MHdL�ADHwFaIML\An>U?j:=H Z[TbN u CD?jQ�TU:=<?BH F@IMLXAE>@?B<�:=H F@:bL\<X? � ADIMArAEHwF@IMLXAE>@?B< G2

?MLW<;g¢F@ImL\An>U?B< G1 � l¤q TUZ[Z]?�NwF@H=9�CE?uI¢Fa9WQ=<XgMIBgBNJ?BHdL[CD?Q=<XTUxJC u Z[?�IMTUH=9;AD9;LX? � N=gmL\?M<XZ[ADH=?M<�CfehgML\FaL � QwF@<;LXAD<�N=:=��:=?BCrCD?�Z[TSN u CE? G1

9X?M<\F�<XgBF@IMLXAE>@g l @ TU:=99\F¢>UTUHJ9tZ]F@ADHdL\?MHwF@HdL¢|iQJ:=AD9;�S:8evAECK?m�bAD9 L\? N=?B9j<X?M9X9;TU:=<XIM?B9�IMTUZ[Z�:=H=?M9B|i��:=?{IB?MLYgML\FaLjN=?M>S<XF LX<X?IBTUZ[QwFaLXADx=CE?KF¢>U?BI�CfehgML\FaL^N=:yZ[TbN u CD? G2

T + C evgm>UgMH=?BZ[?BHdL�N=?PIBTUZ[Z�:JL\FaL\AETUH α2,19Mev?M9;L�Q=<XTSN=:=AnL l

C F@<WF@HwFaCDTU�UAE? � IM?���:=AiF�gMLXg�Q=<XgM9X?MH�LXgyQ=<XgMIBgBNJ?BZ[Z]?MH�LB|¥H=TU:J9WN=g � HJAD9X9;TUH=9W:=H IBF@HwF@C�N�evAEHbk_pTU<XZ]FaL\AETUH π2,1

� � �U:=<X? q9lrv � QRTU:J<�9X:=An>b<;?�CfehgM>@TUCD:JLXADTUH N=: IBTUZ[QRT@<;L\?MZ]?MHdL�N=: Z]TSN u CD? G2?ML

N=gMLX?B<XZ[ADHJ?B<iCfehgML\FaL^N=?P<X?mL\TU:J<�FaN=gB��:wFaLONwFaH=9^CD?KZ[TbN u CD? G1

l

Modèle 1

G G

Modèle 2

canal d’informationΠ

sΠ(s)

2,1

2,1

1 2

�������Qq�l|v��� �$����+ 3� � �/- ���0$ �$ �����π2,1

� TU:JLX?M_pTUAE9B|8CDF�IBT@H=9XAEN=gB<XFaL\AETUH�N=?WC evgm>UTUCE:JL\AETUHtN=?WC ev?MH=9X?MZ�x=CE?�N=?B9K<;?B9;9XTU:=<;IB?M9�IMTUZ[Z�:=H=?M9�ADZWkQRTU9;?rN=?�IBT@H=HwFa�EL\<X?}L\T@:JL\?�Cfe s AD9 L\TUAE<X?¥Q=F@9X9;gB?�N=?MQ=:=AE9�CDFOQ=<;?BZ[A u <X?}9XgMCD?BImL\AETUH�N=?�Z[TbN=? l @ TU:J9�N=?m>UTUH=9N=TUH=IuNJgML\?M<XZ[ADH=?M<�CDFj_pTUHJIML\AETUH NJ?]L\<XF@H=9;AEL\AETUH gmL\?MH=N=:=? δ1,et(q1,in, α2,1)

?MH H=TU:=9�xwF@9XF@HdLW9X:=<�CGFL\<\FaIB? s N=: Z]TSN u CE? G1

Q=<XgMIBgMNwF@HdL�CfehgM>UgMH=?BZ[?BHdL�N=?�IMTUZ[Z�:JLcF¡L\ADT@H α1,2 � ?mLP9X:=<KCDF]L\<XF@IB? s′ N=:Z]TSN u CE? G2

|J��:=A89X:=AnL�CfehgM>@gBH=?MZ]?MHdL α1,2?ML�Q=<XgMI u NJ?KCfehgM>UgMH=?BZ[?BHdL α2,1

l=V F�Q=<;TUQ�TU9XAnL\ADT@H�9X:JAE>aF@HdL\?_pTU:=<XHJAEL�CE?�IBF@N=<;?�_pTU<XZ[?BC�Q�TU:=<�CGF�N=gmL\?M<XZ[ADHwFaLXADTUHjN=?�IM?ML�gMLcF¡LKN=?�<;?MLXTU:=< � gMLcF¡L � QwFa<;L\AE<�NJ:=��:=?BCCD?KZ[TbN u CD? G1

9X?B<XF]<;g¢F@ImL\AE>@g � l� �SR aKR7cfWJPXWYR7N � ���� ���

suiv(s)+ �7"29 � �

suiv(s′) - + "�� 9;"%$ '�+," 35"29 1%:�1��#"%$&"��! �9,!�) � 9%) ��:�"��! + � 9;1!�)�"�� �2" 3� 1%:�1��#"�$&"��! 9

s+ �7"29 � �

s′ - �

∀s ∈ L(G1) "%+ !�)�"

α1,2 ∈ suiv(s)��"�

∀s′ ∈ L(G2,δ2(q2,0,π1,2(s)))8 "%+ !�)�"

α2,1 ∈ suiv(s′)�

+ 1� �$ 35" �7"� �*) ��3�) $ ��3��%+,"G1

"29� 3 ���!�#1 � �$�5'δ1,et(q1,in, α2,1) = δ1(q1,0, π1,2(s)π2,1(s

′)) �

:�� � ���*> +�( � '.+&( ��� ( =�(�6.��=8,#�9>�(!6.%3$-�3$5� J �3�9>��#E @����α1,2,k

=3��$���,�'9> = ���3$$= ��,#�9> �?%<L ����'��3$5� J %#L�,���'.+&( ,#� 6.' EB,.6.@����G1

) EB,.6.@����<6����2>;� �*0#'9��� ���3>;%#L�%��9�<EB����+&> 6�� =8, EGE '.+&��+-(�,�� � J (���+-�3$ L (��������3��+;�2��>3�� �

L(G2,δ2(q2,0,π1,2(s))) = {u ∈ (Σ2)∗ | δ2(δ2(q2,0, π1,2(s)), u)!}

Page 83: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� zJ~

j ��� R7NVcIP �Sb�PSWJRQNA :=An>aF@HdLr��:=? π1,2(s)

?ML π2,1(s′) 9XTUAE?BHdL�gM�dF@:b� � ε TU:]QwF@9B|�?mL�N=TUHJI�9;?BCDT@H�CfehgM>@TUCD:bL\ADT@H[T@:�H=TUH

N=?M9^<X?B9;9XTU:J<XIB?M9�IMTUZ]Z�:=H=?B9M|w��:wFaL\<;?PI¢F@9^9XT@H�L � gMLX:=N=AE?B< l\]b c�Z �

π1,2(s) = ε ?mL π2,1(s′) = ε

� :=IB:JH=?oN=?B9�<X?M9X9XT@:=<XIM?B9�IMTUZ[Z�:=H=?M9K?BHdL\<;? G1?mL G2

H�evFygm>UTUCE:=g@|�IM?]��:=A¤AEZ]QJCDAD��:=?���:=?�

∀σ ∈ s | σ ∈ Σ1?ML σ 6∈ Σ2

F@CETU<X9 δ2(q2,0, π1,2(s)) = δ2(q2,0, ε) = q2,0

lV ?KZ[TbN u CD? G2

F@N=Z[?ML^NJTUH=IPIBTUZ[Z[?�gML\FaL^N=?PN=gBQ=F@<;LOF@QJ< u 9^C evTSIBIM:=<X<;?BH=IM?�NJ?KCfehgM>UgMH=?BZ[?BHdLNJ?�IMTUZ[Z�:JLcF¡L\ADT@H α1,2

9XT@HYQ=<;TUQ=<;?KgMLcF¡L�AEH=AELXAGF@C q2,0

l� ?�Z Z[?KQ�TU:=<iCfehgML\FaL^N=?P<X?mL\TU:J<iQ=:=AD9;��:=? δ1(q1,0, π1,2(s)π2,1(s

′)) = δ1(q1,0, ε) = q1,0

l� ADH=9;Af|bCD?KZ[TbN u CD? G1

F@N=Z[?ML^IBT@Z]Z[?KgML\FaL^N=?P<X?mL\TU:=<�

δ1,et(q1,in, α2,1) = δ1(q1,0,π1,2(s)π2,1(s′)) = δ1(q1,0, ε) = q1,0

\]b c k �π1,2(s) = ε ?mL π2,1(s

′) 6= ε� F@H=9iCD?KZ[TSN=? 1 F@:JIB:=H=?P<;?B9X9;TU:=<;IB?�H�e�FWgm>UTUCE:=g@|=?MHY<;?M>aF@H=I s ?�N=F@H=9^CD?�Z[TSN=? 2 |wFa:jZ[TUAEH=9:JH=?P<X?B9;9XTU:J<XIB?�IBT@Z]Z�:JH=?K?BHdL\<;? G1

?ML G2FogM>@TUCD:=g l

π1,2(s) = ε ADZ[Q=CDAE��:=?���:=? δ2(q2,0, π1,2(s)) = δ2(q2,0, ε) = q2,0

lq ?MQR?MH=NwF@HdL�9XA π2,1(s

′) 6= ε |wADC�?��JAE9;LX? σ′ ∈ s′ L\?BC���:=? σ′ ∈ Σ1 ∩ Σ2

l£� ?�IM?K_`F@AELB|=CfehgML\FaL^N=?<;?MLXTU:=<rN=F@H=9rCE?�Z[TbN u CD? G1

9X?M<\F�gm>U?BHdLX:=?BCECD?BZ[?BHdLiNJA � gB<X?MHdL�N=?�C evgmLcFaL�ADHJAEL\ADF@C q1,0

l=q ?mLigML\FaLNJ?r<X?mL\TU:J<�?B9 L¤N=gmL\?B<;Z]AEH=grQ=F@<�C ev?MH=9X?MZ�x=CD?�N=?B9�gM>UgMH=?BZ[?BHdLX9¤IBTUZ[Z�:=H=9�F@:b��N=?B:S�WF@CEQ s F@x�?MLX9

Σ1?ML Σ2

F@Q=QwFa<;L\?MHwF@HdL � s′l=� AEH=9XA |=TUHyQR?M:JLOgBIM<XAD<;?

δ1,et(q1,in, α2,1) = δ1(q1,0,π1,2(s)π2,1(s′)) = δ1(q1,0, π2,1(s

′))

\]b c � �π1,2(s) 6= ε ?mL π2,1(s

′) = ε� F@H=9jCD? Z]TSN=? 1 F@: Z]TUAEH=9�:=H=?{<X?M9X9;TU:=<XIM? IMTUZ]Z�:=H=?{F gm>UTUCE:=g l�C Fa<jIMTUHdL\<;? F@:=IM:=H=?<;?B9;9XTU:=<;IB?�IBTUZ[Z�:=HJ?K?BHdL\<;? G1

?ML G2H�evF[gm>UTUCE:=gPNwF@H=9^CE?KZ]TSN=? 2

lπ1,2(s) 6= ε AEH=N=AD��:=?K��:�ehADC�?��bAD9;LX? σ ∈ s LX?BC���:=? σ ∈ Σ1 ∩ Σ2

l E C�?MHt<XgM9X:=CnL\?P��:�evF@:tZ[TUADHJ9:JH=?�<X?M9X9;TU:=<XIM?iIBTUZ[Z�:=HJ?�F�I s FaH=�Ug�N�ehgML\FaL¤?mL¤IB? � :J9;L\?�Fz>aF@HdL�CfehTbIMIB:=<;<X?BHJIB?�N=?rCfehgM>UgMH=?BZ[?BHdLNJ?�IBTUZ[Z�:JL\FaL\AETUH α1,2

lb� ADHJ9XAf|SCfehgML\FaL�NJ?�N=gBQ=F@<;LiNJ:�Z]TSN u CE? G2H�eh?B9;L^QJCD:=9r_pT@<XIBgMZ]?MHdL q2,0

Z]F@AE9�:=HjgMLcF¡L^N=TUH=H=gPQwFa< δ2(q2,0, π1,2(s))l

� H[Q=<X?MHwF@HdL�?BH[IBTUHJ9XADNJgB<\F¡L\ADT@H[��:=? π2,1(s′) = ε |dIB?MCGFKADZ[Q=CEAD��:=?r��:=?^C evgmLcFaL}N=?^<;?ML\T@:=<}NwF@H=9

CE?uZ[TbN u CD? G1?B9 L[N=gMLX?B<XZ[ADHJgu9X:=AnL\? � CfehTSIBIB:J<X<X?MH=IB?�N8ev:=H gM>@gBH=?MZ]?MHdL]NJ?jIMTUZ[Z�:JLcF¡L\ADT@H

α2,1QwF@<

δ1,et(q1,in, α2,1) = δ1(q1,0,π1,2(s)π2,1(s′)) = δ1(q1,0, π1,2(s))

\]b c � �π1,2(s) 6= ε ?mL π2,1(s

′) 6= ε� :yZ]TUAEH=9i:=H=?P<;?B9X9;TU:=<;IB?�IBTUZ[Z�:=H=?PFogM>@TUCD:Jg�N=F@H=9^CD?M9iN=?B:b�jZ[TSN=?B9 1 ?mL 2

l

Page 84: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

zd7 ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

� HtF@NJTUQJLcFaH�LOCE?KZ Z]?K<XF@AD9;TUH=H=?MZ]?MH�L^��:=?PQ=<;gBIMgBN=?MZ]Z[?BHdL¢|£AEC�?B9 L�gm>SADN=?MH�LO��:=?�

δ1,et(q1,in, α2,1) = δ1(q1,0, π1,2(s)π2,1(s′))

q TUZ[Z[?�Q�TU:=<�CDFuIBTUZ[Z�:JL\FaL\AETUHtN=: Z[TbN u CD? G1F@:�Z[TSN u CE? G2

|8CD?�Z]TSN u CE? G1,et?B9 LPADH=NJgmk

L\?B<;Z]AEH=AD9 L\? l C T@:=<KCD?m>U?B<KIM?MLPAEH=N=gMLX?B<;Z]AEH=AD9;Z]?a|RAEC�_`F@:bLPgB�dF@CE?BZ[?BHdL�CDF@x�?BCDCEAD9;?B<OCD?B9Kgm>UgMH=?BZ[?BHdL\9�N=?IBTUZ[Z�:JL\FaL\AETUH α1,2

lGA :=AE>aF@HdL�CD?^Z Z[?OQJ<XADHJIBADQ�?i��:=?ONwF@H=9�CGFKQ=<;TUQRT@9XAELXADTUH q�l�7 |dH=T@:=9�QJ<XTUQ�TU9XT@H=9�

� �SR aKR7cfWJPXWYR7N � � �� ) � 35"�+,"%:�"�� + � � 351� "��0$ � �!�,9%$&"�35"29 $ ��3��%+,"29�� � �*) 9 �*929 � ������� 9 %�+ 1%:�1��#"%$&"��! 35" ���*$ $ ) ��$ �����α2,1

) � "�� 9;"%$ '�+," 351*) �!� � �$�K'α2,1 = α2,1,k si δ1(q1,0, π1,2(s)π2,1(s

′)) = q1,k �

q TUZ[Z[?rQ�TU:=<¥CDF�Q=<XTUQ�TU9;AEL\AETUH q9lE~ |aH=TU:=9¤gmL\?MH=N=TUH=9}CDF�Q=<XT@QRTU9;AELXADTUH�Q=<XgMIBgBNJ?BHdL\?�F@:b��CGF@H=�UF@�U?B9 lC TU:=<KI s F@��:=?WgML\FaLKN=?�NJgBQwF@< L q NJ:{Z[TSN u CE? G2

|8H=T@:=9�I¢FaCDIB:JCDTUH=9�Cfeh?BH=9;?BZ�xJCD?�N=?M9KCGF@HJ�dF@�U?M9���:=AQwF@<;LX?BHdL¤N=? q ?mL¥��:=AbZ u H=?BHdL � :=H�gML\FaL¥T + CfehgM>@gBH=?MZ]?MH�L¥N=?rIMTUZ]Z�:JLcFaLXADTUH α2,1

QR?M:JL¥9;?�Q=<;TbN=:JAD<X? l� �SR aKR7cfWJPXWYR7N � � �

( ��� 1� "��%$ � �#"��Q = {qk, . . . ,qn}

+ "�� 9;"%$ '�+," 35"29 1� �$ �9(35" 351 � �$�� 35"G2

+#�2"29 1� �$ �9(35"351 � �$�� ���! �1� 1 351� "��0$ � �#129��$��� �2" % + � ��� ���!�;9�� "����� � � � - �

/ ��� 1� "��%$ � �#"��Q′ = {ql, . . . ,qm}

+ "�� 9;"%$ '�+," 35"29 1� ��$ 9 ���(+ 1%:�1��#"%$&"��! �35" ���*$ $ ) ��$ "�����α2,1

��"%) .9;" ��� ��3�) � �7"��� �� �*) �

q ∈ Q- �$� �7"

+ � - � �*) �q′ ∈ Q′ - �$� �2"

��� � 1� "��0$ � �#"�� + "�� 9;"%$ '�+," 35"29 + �$��� � �5"29Kq′

� �$�� ��$�! 35"q"� �$&"����$�! �%

q′�

� ��� � ��+ �%)5+,"��π2,1(Kq′)

�� � ��� � ��+ �%)5+,"��8+ 1� �$ 35" �7"� �*) ��3�)!$ ��3��%+,"

G2

"�� ��� � + � !�) �$�! 'δ2,et(q2,in,αj,i) = δ2(q2,0,π2,1(Kq′)) �

C ��� ��� � < ��+68 -�8�0�+;5Q0 � ��? � -9AG2�AGi,et

V ?B9PQ=<;TUQ�TU9XAnL\ADT@H=9�Q=<;g¢F@CDF@x=CE?BZ[?BHdLKgML\F@x=CEAD?B9KQ�?B<;Z]?mLXLX?BHdLPN=?oIBTUZ[Q=CEgML\?M<�CGFuIMTUH=9 L\<X:JIML\AETUH N=?B9Z]TSN u CE?B9�gMLX?BH=N=:J9¥QRT@:=<�I s Fa�S:J?�Z]TSN=?}N=?r_pT@H=IMLXADTUH=HJ?BZ[?BHdL i

l@� F@H=9�IM?r��:=Ab9X:=AnL¢| H=TU:=9�N=g � H=AD9;9XTUH=9_pTU<XZ[?BCECD?BZ[?BHdLiCE?B9iZ[TbN u CD?M9igMLX?BH=N=:J9 � Gi,et � Q�TU:=<iI s F@��:=?�Z]TSN=?�NJ?P_pT@H=IMLXADTUH=HJ?BZ[?BHdL i �

Gi,et = (Qi,et, Σi,et, δi,et, qi,0,et, Qi,m,et)T +�

�Qi,et = Qi ∪ {qi,in}

Page 85: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� zmq

�Σi,et = Σi ∪ Σ′ �

�qi,0,et =

{

qi,09XA i = 1

qi,in9XA i = 2

�Qi,m,et = Qi,m

�� CDF�_pTUH=ImL\ADT@H�gML\?MH=N=:=?�N=?�CGF�LX<\F@H=9;AELXADTUH δi,et

?B9 L�NJTUH=H=gM?�IMTUZ[Z]?K9;:=AEL�

~,l∀q ∈ Qi

?mL ∀σ ∈ Σi9XA δi(q, σ) ?m�bAD9 L\?a|RFaCDTU<;9 �

δi,et(q, σ) := δi(q, σ)7/l

∀q ∈ Qi

� QwF@< L\AE<�N=:=��:=?MCiCfehgM>UgMH=?BZ[?BHdL[N=?�IMTUZ]Z�:JLcFaLXADTUH αi,jQR?M:JL LX<X?��UgMH=gB<;g

δi,et(q, σ) := qi,inq9l�A :=AELX? � CfehTbIMIB:=<;<X?MH=IB?WN=?WC evgm>UgMH=?BZ[?BHdLPN=?WIMTUZ]Z�:JLcFaLXADTUH α1,2N=?MQ=:=AD9K:JH�gMLcF¡L q N=:

G1|=C evgmLcFaL^NJ?�NJgBQwF@< LON=:YZ[TSN u CE? G2

?B9 L�

δ2,et(q2,in, α1,2) = δ2(q2,0, π1,2(Kq))T +

Kq?B9 L�CE?iCGF@HJ�dF@�U?�IMTUHdL\?MHwF@HdL}L\TU:JLX?B9}CD?M9}9XgB��:=?MH=IB?M9�F¢�dFaH�L�IMTUZ]Z[?igML\FaL}N�ehTU<XAE�UADHJ?

CfehgMLcF¡L^ADH=AnL\AGFaCRN=:yZ[TbN u CD? G1?ML^IBT@Z]Z[?KgML\FaL � HwF@C q

lqrs F@��:=?�TbIMIB:=<;<X?BHJIB?�N=?PCfehgM>UgMH=?BZ[?BHdL α1,2

9X?M<\FoCGF@x�?BCECDAE9XgB?�9X:=An>aF@HdL^CGF�< u �UCD?�

α1,2 = α1,2,k9;A δ2(q2,0, π1,2(Kq)) = q2,k

� l CfehgMLcF¡L�NJ?�<;?ML\T@:=<�NJ:tZ[TbN u CD? G1|£9X:=AnL\? � C evTSIBIM:=<X<;?BH=IM?�NJ?�C evgm>UgBHJ?BZ[?BHdL�N=?�IBT@Z]Z�:Sk

LcFaLXADTUH α2,1NJ?BQ=:=AE9 q′ N=:jZ]TSN u CD? G2

|w?B9 L�

δ1,et(q1,in, α2,1) = δ1(q1,0, π2,1(Kq′))T +

Kq′?M9;L}CD?�CGF@HJ�dF@�U?�IBTUHdLX?BHwF@HdL¥LXTU:JLX?B9¤CD?M9�9;gB��:=?BHJIB?B9�F¢�dF@HdL¤IMTUZ[Z]?�gMLcF¡L¥N�ehTU<XAE�UADHJ?

:=HYgmLcFaL^NJ?�N=gMQwF@< L^N=:YZ[TSN u CE? G2?MLOIMTUZ]Z[?KgML\FaL � HwFaC q′

lqrs F@��:=?�TbIMIB:=<;<X?BHJIB?�N=?PCfehgM>UgMH=?BZ[?BHdL α2,1

9X?M<\FoCGF@x�?BCECDAE9XgB?�9X:=An>aF@HdL^CGF�< u �UCD?�

α2,1 = α2,1,k9;A δ1,et(q1,0, π2,1(Kq′)) = q1,k

C ����� � � � A � ��?�A&2 HY>�� ��?�8 5Q>E-�8�0�+C T@:=<rAECDCD:J9;L\<;?B<}CfevF@Q=QJ<XTSI s ?�Z�:JCEL\A k¦Z[TbN u CD?�Q=<XT@QRTU9;gB? � I¢F@9�CDAEZ]AnL\g � NJ?B:b��Z]TSN=?M9rN=?O_pTUH=IMLXADTUHSk

H=?MZ]?MHdL � |¤HJTU:=9oIBTUHJ9XADNJgB<XT@H=9o:=H 9 �S9;L u Z]?yZ]F@H�:J_`F@ImL\:=<;AD?B<WIMTUZ[QRTU9;g�N=?yN=?B:S� Z�F@I s ADH=?M9WADN=?MHbkLXAD��:=?B9 M1

?ML M2|bN�eh:=H=?KZ]F@I s ADHJ?�<X?MN=TUH=N=F@HdL\? M3

?ML�N�ev:JH�9;L\TSI � AEHdL\?B<;Z]gMN=AGFaAD<X? S |JIMTUHJ_pTU<;Z]g�kZ[?BHdL � CGF � �U:J<X? q�lrx9l

V ?B9�N=?B:b�tZ]F@I s ADHJ?B9 M1?ML M2

_pTUH=ImL\AETUH=H=?MH�L�N=?�_`F � TUHtADH=N=gMQR?MH=NwF@HdLX?@|�Q=:=AD9;?BHdL�NJ?B9�Q=A u IM?B9x=<;:JL\?M9r?MH�F@Z[TUHdL�?mL�<;? � ?ML;L\?MH�LrN=?B9�Q=A u IB?M9r:=9;ADH=gM?B9�?MHuF¢>aF@C lSV F�Z]F@I s AEH=? M3

?B9 L�?BH]<X?MN=TUH=NwFaH=IB?F¢>U?MI�CDF�Z�FaI s ADH=? M1

lV F�Z]F@I s ADHJ? M1

QJ:=AD9;?�N=?M9�Q=A u IB?M9�x=<X:bL\?B9rN�ev:JHu9;LXTbI � F@Z[TUHdL�N=?�I¢F@QwFaIBAELXg�9;:=Q=Q�TU9XgM?�ADH � H=AD? lq ?mLXL\?]F@ImL\ADT@H{?M9;L�Z[TbN=gMCDAE9XgB?WQ=F@<PCfehgM>UgMH=?BZ[?BHdL�IBTUHdLX< s CDF@x=CD? d1

l�� Q=< u 9�LX<\F@AnL\?MZ]?MH�LPQ=F@<PCGF�Q=<X?�kZ[A u <X?¤Z]F@I s ADHJ?@| CGFiQ=A u IB?�?B9 L¥?MH=9X:=AnL\?�N=gBQ�TU9;gB?rN=F@H=9�CD?}9;LXTbI � ADHdLX?B<XZ[gBNJAGF@AE<X? S

laq ?BIMAb?M9;L�Z]TSN=gBCEAD9;gQwFa<�CfehgM>@gBH=?MZ]?MHdLPADH=IMTUHdL\< s CGF@x=CE? f1

l8V TU<;9X��:=?WCDF�Z�FaI s ADH=? M1?B9 LK?BH Z]F@<XI s ?a|8C evTSIBIM:=<X<;?BH=IM?�N=?

Page 86: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

z � ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

�����

�����

MMachine

Machined3

1d

Machine Mf2d

f

f

M3

1

2S

2

3

1

perturbation

������� q�lrx�� � �;9� �%$&"8$ �$��)0- � �� ) ��� "�� %� "�����,9 $ � ��� � �#"29�"� �9� � ��� � �! "��%$&143$�"�$� �7"

CfehgM>UgMH=?BZ[?BHdL p1IBTUHJN=:=AEL�CGFyZ�FaI s ADH=?[NwF@HJ9�:=H gmLcFaL�N=?�Q=F@H=H=? l¥V FYQ=A u IM?�?BH IBTU:=<;9�N=?[L\<\FaAEL\?�k

Z]?MH�Lr?B9 LiF@CETU<X9}9X:JQ=QRT@9XgB?�QR?M<XN=:=? l=V F�<;gBQwFa<\FaLXADTUH[N=?�CDF�Z]F@I s AEH=?ON=gM_`F@AECDCDF@HdL\? M1?M9;L�Z[TSN=gBCEAD9XgM?

QwF@<OCfehgM>UgMH=?BZ[?BHdL�IBTUHdL\< s CGFax=CD? r1

l£V F[N=?B:b�bA u Z[?�Z]F@I s AEH=? M2IMTUZ]Z[?BHJIB?�9XTUHj_pTUH=IMLXADTUHJH=?BZ[?BHdL

� gM>@gBH=?MZ]?MHdL�IMTUHdL\< s CGF@xJCD? d2 � QwF@<�CE?�<X?mL\<\FaAEL�N8ev:=HJ?WQ=A u IB?�N=: 9 L\TSI � Sl�V FuQ=A u IB?�L\<\FaAEL\gM?�QwFa<�CGF

9X?BIMTUH=N=?yZ]F@I s AEH=?u9X?M<\F�N=gMQRT@9XgB? � gM>UgMH=?BZ[?BHdL[ADHJIBTUHdL\< s CGFax=CD? f2 � NwF@H=9W:=H 9 L\TSI � F¢>aF@CrNJTUHdLWCGFI¢F@QwFaIBAELXg�?B9 LP9X:=QJQRTU9;gB?ogB�UF@CD?MZ]?MH�L�ADH � HJAD? lRV FuZ�FaI s ADH=? M3

?B9;LP<;?BN=T@H=NwF@HdL\?oF¢>@?BIoCGF�Z]F@I s AEH=?

M1

l� � H N=?j<XgMN=:=AE<X?jH=T@L\<;?ygML\:JN=? � N=?B:S� Z[TSN=?B9[N=?y_pTUH=IMLXADTUHJH=?BZ[?BHdL¢|¤HJTU:=9[H=?tIMTUH=9XAEN=gB<;TUH=9

QwF@9oCD?M9�QwF@H=HJ?B9oN=?B9oZ]F@I s AEH=?B9 2 ?mL 3l}q ?MIBAiH=T@:=9WQR?M<XZ[?MLoN=?�IMTUH=9;ADN=gM<X?B<W:JH Z[TSN=?uH=TUZ[ADH=F@C

NwF@H=9�CD?B��:=?MC�CE?B9�Z�F@I s ADH=?M9 1 ?ML 2 Q=<;TbN=:JAD9X?MHdL�?ML�:=H�Z[TSN=?�NJgB�U<XF@N=g�N=F@H=9�CE?B��:=?MC�CDF]Z]F@I s AEH=? 3<X?BZ[Q=CDF@IB?�CGF[Z�F@I s ADH=? 1 ��:=A�?B9 LK?BH�Q=F@H=H=? l�V F]Z]F@I s AEH=? M2

?M9;L�N=TUH=I�CDF[<;?B9;9XTU:=<;IB?WIMTUZ]Z�:=H=?N=?B9ON=?B:S�jZ]TSN=?B9 lE H=AnL\ADF@CD?MZ]?MH�LB|=CD?PIm�bIMCD? M1 → M2 → M1 . . . LX<\F@AnL\?PH=TU<;Z�F@CE?BZ[?BHdLOCD?M9�Q=A u IM?B9�xJ<X:JLX?B9 l8q eh?B9;L

CfehTUx � ?BImL\An_}QRTU:J<�CD?M��:=?BC�CD?�9 �S9;L u Z]?oF]gML\g�IBTUH � : � Z[TbNJ?�H=TUZ[ADH=F@C � l£V F]IBTUZ[Z�:JL\FaL\AETUHYNJ:�Z]TSN=?H=TUZ[ADHwF@CU>@?B<;9¤CD?�Z]TSN=?�N=gB�U<XF@N=g � <X?M9XQ l N=:�Z[TSN=?�NJgB�U<XF@N=g�>@?B<;9¥CD?�Z]TSN=?�H=TUZ[ADHwFaC � ?B9 L¤?BHJ�U?BH=NJ<XgB?QwF@<�CfehTbIMIB:=<;<X?MH=IB?�N=?}CfehgM>@gBH=?MZ]?MH�L�N=?�IBTUZ[Z�:JL\FaL\AETUH p1

� <;?B9XQ l r1 � l¡V ?}Z]TSN=?¤N=gM�U<\F@NJg�IMTU<X<;?B9;QRTUHJNF@CDTU<;9 � :=HY9;?BIMTUH=NtIm�SIBCD? M3 → M2 → M3 . . .

V ?B9yZ[TbN u CD?M9jF@:JL\T@Z�FaLX?B9 G1| G2

?mL G3<;?B9;QR?MIML\An>U?MZ]?MH�LYN=?M9YZ]F@I s AEH=?B9 M1, M2

?mL M3

9XTUHdL[N=TUH=HJgB9WNwF@HJ9[CDF � �U:J<X? q�l|z�l¤V ?B9 �1u I s ?M9]?MH Q�TUAEH�LXADCECDgB9�<X?MQ=<XgM9X?MH�LX?BHdL]CD?B9Wgm>UgMH=?BZ[?BHdL\9[N=?IBTUZ[Z�:JL\FaL\AETUH�?BHdL\<;?PCD?B9^Z[TbNJ?B9iH=TUZ[ADH=F@C8?mL�NJgB�U<XF@N=g l

V evF@CDQ s F@xR?mL��UCDTUx=F@C Σ = {d1, d2, d3, f1, f2, f3, p1, r1}?B9 L�9;IBAEH=N=g[?BH LX<XTUAE9�F@CDQ s F@xR?mL\9

�C e�F@C k

Q s F@x�?ML�N=:tZ[TSN=?PH=TUZ[ADHwF@C Σn = {d1, d2, f1, f2}|wCfevF@CEQ s F@x�?ML^N=:YZ]TSN=?PN=gM�U<\F@NJg Σd = {d2, d3,

f2, f3}?mL^CfevF@CDQ s F@x�?MLiN=?M9�gm>UgMH=?BZ[?BHdL\9�N=?PIBTUZ[Z�:JL\FaL\AETUH Σ′ = {p1, r1}

l

� � k � � � Z � R�T�` N�R � WYN�b _V ?tZ[TSN u CE?jHJTUZ]AEHwF@C Gn

N=: Q=<;TbIMgBN=ga|�<;?BQ=<;gB9X?MHdL\g�NwF@HJ9�CGF � �U:=<;? q�l|{ |}?B9 LuTUxbL\?BH�: ?MH 9X?xwF@9\FaH�LO9;:=<^CD?B9iZ[TSN u CE?B9iF@:bL\TUZ]FaL\?M9iN=?KCGF � �U:=<X? q�l|z ?MLO9;:=<iCGF�N=g � H=AnL\ADT@H�N=?PCfevF@CDQ s F@xR?mL Σn

N=:

Page 87: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� z �

Modèles G i

d

p1

f i

r1f1

Modèle G 1

1di

A

M

A1

1 1P

i

Mi

(i = 2, 3)

������� q�l|z � � ��3��%+,"29���) �*$ �$ "29 35"298$ � ��� � �#"29M1

�M2

"� M3

Z[TbNJ?�H=TUZ[ADHwFaC l

qn,0 qn,1

qn,3

f1

f2 f2

d2d2

d

f1

qn,2

d1

1

�������Qq9lr{�� � ��3��%+,"Gn

3�) $ ��35" � �*$ � ����+

V ?B9ogM>@gBH=?MZ]?MHdL\9�NJ?jIMTUZ[Z�:JLcF¡L\ADT@H H=? � �U:=<;?BHdL[QwF@9oNwF@H=9oIM?jZ[TSN u CE? l¤� H ? � ?ML¢|¤IM?B9[gM>@gmkH=?MZ]?MHdL\9KH=?W9;?B<XT@H�LPQJ<XAD9�?BH IBTUHJ9XADNJgB<\F¡L\ADT@H��S:J?WQRTU:J<�CD?�Q=F@9X9XF@�U?WN�eh:=H Z]TSN=? � :JH Fa:JL\<;? l C F@<s �SQRTaL s1u 9X?@|¤C evTSIBIM:=<X<;?BH=IM?uN=?�C evgm>UgBHJ?BZ[?BHdLoN=?�QwF@HJH=?�N=?uCDFtZ�FaI s ADH=? M1

QR?M:JLW9X?�QJ<XTSN=:=AD<;? �

QwFa<;L\AE<rN=?M9^gMLcF¡L\9 qn,1?mL qn,3

T + CDF�Z�FaI s ADH=? M1?M9;LO?BH�_pTUHJIML\AETUH=H=?MZ]?MHdL^H=TU<XZ]F@C � � �U:J<X? q�ln~ I � l

� >aF@HdL]NJ?jQ�TU:=<;9X:=An>S<X?yH=TU:=9o9;:=Q=Q�TU9XTUHJ9]N=gM9XTU<;Z�FaAD9���:=?jCfehgM>@gBH=?MZ]?MH�L]N=?y<XgMQwF@<XFaL\AETUH H=?yQR?M:JL9;?WQ=<XTSN=:=AE<X?���:�e � QwF@< L\AD<�N=?B9PgmLcFaLX9 qd,1

?ML qd,2|�I@eh?B9 L;k � k¦N=AE<X?�CETU<X9;�S:J?�CGF�Z]F@I s AEH=? M3

F � HJA¥N=?Q=<;TbNJ:=AD<;? l

� � k � � � k �&R=T�` T � � �Sb T �A :=AnL\? � C evgm>UgBHJ?BZ[?BHdLON=?PIBTUZ[Z�:JL\FaL\AETUH p1

|JCD? � H=TU:b>U?¢Fa: � 9;�S9 L u Z[?PIBTUHJ9XADNJgB<XgP?M9;L^CD?KIMTUZWkQ�TU9XgjN=?M9�Z[TbN u CD?M9]Fa:JL\TUZ]FaLX?B9[N=?YCDF{Z]F@I s AEH=? M2

?mL�N=?YCGF Z�FaI s ADH=? M3

� � �U:J<X? q�lE~@~ � l�q ?

Page 88: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

zmv ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

d

f

qn,0 q

qn,3qn,2

n,1

qd222f

d1

1

f1

d1

p1

p1

f 2 n,in

�������Qq�ln~ I � � ��3��%+," 1� "�� 3�)Gn,et

"%$ �!���#�$� �2" 3�) $ ��35" � �*$ � ����+

9;�S9;L u Z[?�IMTU<X<;?B9;QRTUHJN � CDF�QwF@<;LXAD?�N=:y9;�S9;L u Z[?��@CDTUxwFaC8:JLXADCDAE9XgONwF@H=9^CE?�Z]TSN=?�NJ?�_pTUH=IMLXADTUHJH=?BZ[?BHdLN=gB�U<XF@N=g l

q q

q

f

f2 f2

d2d

d

f

q

dd,0 d,1

d,3d,2

2

3

3

3

3

�������7q�ln~U~�� � ��3��%+,"Gd

3�) $ ��35"�351$�$�#� 351

V TU<;9X��:�ehADC�9Me�F@�@AD<\F�N8e�F@9;9X:=<;?B<[CGF�IMTUZ]Z�:JLcFaLXADTUH N=: Z[TSN=?uH=TUZ[ADH=F@C�>@?B<X9oCE?�Z]TSN=?�N=gM�U<\F@NJg@|CfehgMLcF¡LYAEH=AELXAGF@C qd,0

H=?{Q�TU:=<X<XF Q=F@9jLXTU: � TU:J<X9 L\<;? :bL\ADCEAD9;g�I¢F@<jCDTU<;9X��:=?{CGF QwF@H=HJ? 9;:=<;>SAD?MHdL¢|OCD?Q=<XTSIBgMN=g�N=: Z[TSN=?YHJTUZ]AEHwF@C^F gm>UTUCE:=gt?mLuC evgmLcFaL]ADH=AnL\ADF@C�N=: QJ<XTSIBgBNJg�N=gB�@<\F@N=gYH=?tIMTU<X<;?B9;QRTUHJNQ=CD:=9 � CfehgML\FaL � QwF@<;LXAD<�NJ:=��:=?BC�CGFWQwFaH=H=?P9Beh?B9 L�Q=<;TbNJ:=AELX? l C TU:=<ON=gMLX?B<XZ[ADHJ?B<iCfehgML\FaL^N=?PN=gMQwF@<;LON=:Z]TSN u CE?KN=gB�@<\F@N=ga|wH=TU:=9^:JLXADCEAD9XT@H=9�CGF�_pT@H=IMLXADTUHyN=?PQ=<;T � ?BImL\ADT@H

πn,d : Σ∗n −→ Σ∗

dLX?BCDCE?���:=? ∀σ ∈ Σn

?mL ∀s ∈ Σ∗n :

πn,d(ε) = ε

πn,d(sσ) =

{

πn,d(s)σ9XA σ ∈ Σn ∩ Σd

πn,d(s)9XA σ ∈ Σn \ Σd

� F@QJQR?MCDTUH=9[��:=?�CE?B9�gmLcFaLX9�N=?YN=gBQ=F@<;L�N=: Z[TbN u CD?yN=gM�U<\F@NJgt9XT@H�L�?BH <;?BCDFaL\AETUH F¢>@?BI�CE?B9]LX<\F@IM?B9�UgBH=gM<XgM?B9PNwF@H=9KCE?�Z[TbN u CD?�H=TUZ[ADHwF@C�?ML�Z]?MHwF@HdL � N=?B9KgmLcFaLX9KT + CfehgM>@gBH=?MZ]?MHdL�NJ?WIBTUZ[Z�:JL\FaL\AETUH

p1Q�?B:JL�9X?�Q=<XTSN=:=AE<X? lw� F@H=9�IB?�IBTUHdLX?m�SL\?�H=TU:=9�F@CDCETUH=9iN=gmL\?M<XZ[ADH=?M<B|w9X:JAE>aF@HdL�CDFWQ=<XTUQ�TU9;AEL\AETUH q�l|q |

Page 89: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� z�x

C ev?MH=9X?MZ�x=CD?rN=?^IB?B9¤LX<\F@IM?B9}��:=A=Z u H=?MH�L}>@?B<X9}CE?B9¤gML\FaL\9 qn,1?ML qn,3

lBC TU:=<¤? � ?MIML\:J?B<}IB?^I¢FaCDIB:JCf|@HJTU:=9F@QJQ=CDAE�S:JTUH=9iCGF�< u �UCE?KN�e � <XNJ?BH � >UT@AD< � HJH=?m�b? � Q�TU:=<iQ=CE:=9^N=?PQ=<XgMIBAE9XADT@H=9 � l

� � k � � � � \]R � ���=PXb�PSWJR7N N�R � W N�b _→

T � � �Sb T �q F@CEIB:=CETUH=9WNwF@HJ9[:JH Q=<;?BZ[AD?M<�L\?BZ[Q=9oCfeh?BHJ9X?BZ�x=CD?�N=?M9[LX<\F@IM?B9[��:=AiZ u H=?BHdLo>U?M<X9[CfehgML\FaL qn,1

|Iaev?M9;L;k � k¦NJAD<X?�CD?�CDF@H=�dFa�U? Kn,1 = {s ∈ L(Gn) | δn(qn,0, s) = qn,1}

l=� e�F@QJ< u 9iCE?�Z[TbN u CD?�F@:JL\T@Z�FaLX?N=?PCDF � �U:=<;? q9lr{ H=TU:J9�FaxRTU:bL\AD9;9XTUHJ9�Fa:j9 �S9;L u Z]?�N�ehgB��:wFaLXADTUHJ9O9;:=AE>aF@HdL

qn,0 = d1 qn,1 + d2 qn,2 (1)

qn,1 = f1 qn,0 + d2 qn,3 + ε (2)

qn,2 = d1 qn,3 + f2 qn,0 (3)

qn,3 = f1 qn,2 + f2 qn,1 (4)

(4) + (3) + (2) ⇒ qn,3 = f1(d1qn,3 + f2qn,0) + f2(f1qn,0 + d2qn,3 + ε)

= (f1d1 + f2d2)qn,3 + (f1f2 + f2f1)qn,0 + f2

q ?mLXL\?PgM�S:=FaL\AETUHy?B9;L�gB��:=An>aF@CD?MH�LX? ��

qn,3 = A qn,3 + B T +A = (f1d1 + f2d2)

?ML B = (f1f2 + f2f1)qn,0 + f2

� evF@Q=< u 9KCGF]< u �@CD?�N�e � <;N=?BH8|�Q=:=AE9X��:=? ε 6∈ A |8?MCDCD?�F@N=Z[?MLK:JH=?�?MLP:JH=?�9X?M:=CD?W9;TUCD:bL\ADT@H � A∗Bl

� Hj<X?BZ[Q=CDF � F@HdL A | B QwF@<iCD?M:=<X9^?��JQJ<X?B9;9XAETUH=9B|£H=T@:=9iL\<XT@:J>UTUHJ9�

qn,3 = (f2d2 + f1d1)∗[(f2f1 + f1f2)qn,0 + f2] (5)

(5) + (2) ⇒ qn,1 = f1qn,0 + d2(f2d2 + f1d1)∗(f2f1 + f1f2)qn,0

+ d2(f2d2 + f1d1)∗f2 + ε

⇒ qn,1 = [d2(f2d2 + f1d1)∗(f2f1 + f1f2) + f1]qn,0

+ d2(f2d2 + f1d1)∗f2 + ε (6)

(5) + (3) ⇒ qn,2 = d1(f2d2 + f1d1)∗(f2f1 + f1f2)qn,0

+ d1(f2d2 + f1d1)∗f2 + f2qn,0

⇒ qn,2 = [d1(f2d2 + f1d1)∗(f2f1 + f1f2) + f2]qn,0

+ d1(f2d2 + f1d1)∗f2 (7)

(1) + (6) + (7) ⇒ qn,0 = d1[d2(f2d2 + f1d1)∗(f2f1 + f1f2) + f1]qn,0

+ d1d2(f2d2 + f1d1)∗f2 + d1

+ d2[d1(f2d2 + f1d1)∗(f2f1 + f1f2) + f2]qn,0

+ d2d1(f2d2 + f1d1)∗f2

⇒ qn,0 = [(d1d2 + d2d1)(f2d2 + f1d1)∗(f2f1 + f1f2) + d1f1 + d2f2]qn,0

+ (d1d2 + d2d1)(f2d2 + f1d1)∗f2 + d1

Page 90: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

zmz ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

q ?mLXL\?PgM�S:=FaL\AETUHjF@N=Z[?ML^Cfeh:=H=AE��:=?P9XTUCE:JL\AETUH�

qn,0 = [(d1d2+d2d1)(f2d2+f1d1)∗(f2f1+f1f2)+d1f1+d2f2]

∗[(d1d2+d2d1)(f2d2+f1d1)∗f2+d1]

q ?mLXL\?�?m�bQ=<X?M9X9;ADTUH <;?BQ=<;gB9X?MHdL\?�Cfeh?BHJ9X?BZ�x=CD?[N=?B9�L\<\FaIB?B9��UgBH=gM<XgM?B9�NwFaH=9�CD?[Z[TbN u CD? GnF¢�dFaH�L

IBTUZ[Z]?oTU<;AD�UAEH=?�C evgmLcFaL qn,0?mL�IMTUZ[Z]?WgmLcFaL � HwFaC qn,1

l E C}9Me�F@�@AELPN=TUHJI]N=: CGF@HJ�dF@�U? Kn,1

l�V evF@QbkQ=CDAEI¢FaLXADTUHjN=?�CDF[_pTUHJIML\AETUHtNJ?�Q=<;T � ?BImL\ADT@H πn,d

9;:=< Kn,1NJTUH=H=?

� πn,d(Kn,1) = (d2f2)∗ l A ?MCDTUHYCGF

Q=<XTUQ�TU9;AEL\AETUH q�l|q |=C evgmLcFaL^N=?PN=gMQwF@< L�N=F@H=9^CD?KZ[TbN u CD?�N=gB�U<XF@N=gP9X?M<\FoN=TUH=IPN=T@H=H=gPQwF@<�

δd(qd,0, πn,d(Kn,1)) = δd(qd,0, (d2f2)∗) = qd,0

� ADH=9;A�TUHy<X?mL\<XT@:J>U?P? � ?BImL\An>U?BZ[?BHdLOCfehgML\FaL^ADHJAEL\ADF@C£N=? G2Q=:JAD9X��:=? ∀s ∈ (d2f2)

∗ |=CE?KZ]TSN u CE?�N=?CGFW<X?M9X9XT@:=<XIM?�IMTUZ]Z�:=H=? M2

9X?KL\<;TU:J>U?PNwFaH=9^9XTUHjgML\FaLOADH=AnL\AGFaC q2,0

l

� FaH=9^CD?KI¢Fa9OT + C evgm>UgMH=?BZ[?BHdL�N=?PQwF@H=H=?P9;?�QJ<XTSN=:=AEL^N=F@H=9^CfehgML\FaL qn,3|wCfeh?BHJ9X?BZ�x=CD?KN=?M9OLX<\F@IM?B9

�UgBH=gM<XgM?B9�N=F@H=9[CD?yZ]TSN u CD? GnN=?BQ=:JAD9oCfehgML\FaL[ADH=AnL\AGFaC�>@?B<X9]CfehgML\FaL qn,3

Q�?B:JL LX<X?yI¢FaCDIB:JCDgyN=?yCGFZ Z]?�_`F � TUHj�S:J?�QJ<XgBIMgBN=?MZ]Z[?BHdL l @ TU:=9OF@x�TU:JLXAD9X9;TUH=9^F@:j9;�S9 L u Z[?PN�ehgB��:wFaLXADTUH=9

qn,0 = d1 qn,1 + d2 qn,2

qn,1 = f1 qn,0 + d2 qn,3

qn,2 = d1 qn,3 + f2 qn,0

qn,3 = f1 qn,2 + f2 qn,1 + ε

V FW<XgM9XTUCE:JL\AETUH�N=?PIB?P9;�S9 L u Z[?�N=TUH=H=?PCDFo9;TUCD:bL\ADT@H�

Kn,3 = [(d1d2 +d2d1)(f2d2 +f1d1)∗(f2f1 +f1f2)+d1f1 +d2f2]

∗[(d1d2 +d2d1)(f2d2 +f1d1)∗]

L�< πn,d(Kn,3) = (d2f2)∗d2

|�CfehgML\FaL�N=?ON=gBQwFa<;L�N=:�Z[TbN u CD?^N=gM�U<\FaN=g GdQ�TU:=<}IB?�H=TU:J>@?¢F@:�I¢F@9

?B9;L�N=TUHJI�

δd,et(qd,in, p1) = δd(qd,0, πn,d(Kn,3)) = δd(qd,0, (d2f2)∗d2) = qd,2

V F � �@:=<X? q9lE~ 7 <X?BQJ<XgB9;?BHdL\?PIM?B9iN=?M:b��gmLcFaLX9�N=?KN=gMQwF@<;L�QRTU9;9XAEx=CD?M9r?BH�Z[TSN=?�N=gM�U<\FaN=g lFA :=AE>aF@HdLCD?B9i< u �UCE?B9�gMH=TUH=IMgB?M9OQJ<XgBIMgBN=?MZ]Z[?BHdLB|wCfehgM>UgMH=?BZ[?BHdL p1

� <X?B9;Q l r1 � FogmL\gK<;?BZ[Q=CGF@IMg�QwFa<�CD?M9igM>UgMH=?mkZ]?MH�LX9 p1,i

� <X?M9XQ l r1,i � 9XA�?mL�9;?B:=CE?BZ[?BHdLO9XA δd,et(qd,in, p1) = qd,i

� <X?B9;Q l δn,et(qn,in, r1) = qn,i � l

� � k � � � � \ R � ���=PXb�PSWJR7N T � � � b1T%�→

N�R � WYN�b _� FaADHdL\?MHwF@HdLr��:=?�H=TU:=9rF¢>UTUH=9�gML\F@x=CDAwCE?�Z[gBIBF@H=AE9XZ[?ONJ?�I s FaH=�U?BZ[?BHdLrN=:�Z[TbNJ?OHJTUZ]AEHwF@C=>@?B<X9

CD?^Z]TSN=?iN=gM�U<\FaN=g@|d?mL�IM?�9;:=AELX? � C evTSIBIM:=<X<;?BH=IM?�NJ?OC evgm>UgMH=?BZ[?BHdL�N=?�IMTUZ[Z�:JLcF¡L\ADT@H p1|UH=T@:=9rFaCDCDT@H=9

_`F@AD<;?KN=?PZ Z]?K��:wF@HdL � CfehTbIMIB:=<;<X?MH=IB?PN=?PCfehgM>@gBH=?MZ]?MHdL�N=?P<;gBQwF@<XFaL\AETUH r1

l

Page 91: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5��� � � � ���� ��� ��� � � ���� ��� �#��� �����������������#�/� zm{

q q

q

f

f2 f2

d2d

d

f

q

dd,0 d,1

d,3d,2

2

3

3

3

3

q

p

p

r

r

1,0

1,2

1,0

1,2

d,in

������� q�ln~ 7�� � ��3��%+," 1� "�� 3�)Gd,et

3�)!$ ��35"�351$�$�#� 351

V F�_pTUH=IMLXADTUHyN=?PQ=<;T � ?BImL\AETUH πd,n

� I¢F@H=F@C�N�ehADHJ_pT@<XZ]FaL\AETUH � ?M9;LON=g � H=AD?PQwFa< �πd,n : Σ∗

d −→ Σ∗n

L\?BCECD?���:=? ∀σ ∈ Σd?ML ∀s ∈ Σ∗

d :

πd,n(ε) = ε

πd,n(sσ) =

{

πd,n(s)σ 9;A σ ∈ Σd ∩ Σn

πd,n(s) 9;A σ ∈ Σd \ Σn

� ?BZ]F@<X��:=TUHJ9¥��:=?�IB?mLXLX?�H=TU:J>@?BCECD?rIMTUZ[Z�:JLcF¡L\ADT@H�Q=<;gB9;?BHdL\?^:=H=?rN=A � IB:JCEL\g�QwF@<�<\F@Q=Q�TU< L¤F@:�IBF@9Q=<;gBIMgBN=?MZ]Z[?BHdLiL\<XF@AELXg lJ� Hy? � ?mL¢|wCD?�Z]TSN u CE?�N=gM�U<\FaN=g�F@N=Z[?MLiN=?M:b�ygmLcFaLX9iN=?KN=gBQ=F@<;L qd,0

?ML qd,2|

IMTUHdL\<\FaAD<X?MZ]?MHdLPF@:�Z[TbN u CD?�H=TUZ[ADHwF@C���:=A¥H�eh?BH F@N=Z[?ML��S:8ev:=H l�� � H N=?WNJg � H=AE<KCfehgML\FaL�N=?W<;?MLXTU:=<NwFaH=9�CE?PZ]TSN=?PH=TUZ[ADHwFaCf|JAEC�_`F@:JLON=g � H=AD<^L\T@:JL\?M9�CE?B9^L\<\FaIB?B9�F¢�dF@HdL�QRTU:J<OT@<XAD�@ADH=?K:=HYN=?B9�gML\FaL\9ON=?N=gMQwF@< L qd,0

?mL qd,2?MLiF@xRT@:JL\AE9X9\FaH�LrNwF@H=9r:=H�gML\FaL � Q=F@<;LXAD<rNJ:=��:=?BCRCfehTbIMIB:=<;<X?BHJIB?�N=?�CfehgM>UgMH=?BZ[?BHdL

N=?P<;gBQwF@<XFaL\AETUHy?B9 L�Q�TU9X9;ADx=CE? l£� ?�IB?K_`F@AnL¢|=NJ?B:b�jIBF@9�NJ? � �@:=<X?P9XT@H�L�Q�TU9X9;ADx=CE?B9 l£� F@H=9O:=HYQJ<X?BZ[AD?M<LX?BZ[Q=9�H=TU:J9KN=g � HJAD9X9;TUH=9PCfeh?BHJ9X?BZ�x=CD?�NJ?B9�L\<XF@IB?M9KN�ehTU<XAE�UADH=?�CfehgML\FaL�N=?WNJgBQwF@< L qd,0

|8?MH=9X:JAEL\?WHJTU:=9LX<\F@AnL\?B<;TUH=9�CE?KI¢F@9ON=?M9^LX<\F@IM?B9OF¢�dF@HdL�QRT@:=<iTU<XAE�UADHJ?�CfehgML\FaL qd,2

l

� � k � � � � \]b c�Z��E_�����PXb�P T�`yT%� a�b �XP `/cOPqd,0

� H 9X?Y<Xgm_pgB<\FaH�L � C e�Fa:JL\TUZ]FaLX?jNJ?YCDF � �@:=<X? q�lE~@~ � QwF@�U? zmv � |¤CE?B9[gML\FaL\9 � QwF@< L\AE<[NJ?B9X��:=?MCD9C evTSIBIM:=<X<;?BH=IM?�N=?uC evgm>UgMH=?BZ[?BHdLoN=?]<XgBQ=F@<\FaLXADTUH ?B9 LWQRT@9X9XAEx=CD?]9XTUHdL qd,0

?ML qd,2

l�� � H N=?�IBF@CDIM:=CD?M<C ev?MH=9X?MZ�x=CD?�N=?M9�L\<XF@IB?M9���:=ASZ u H=?BHdL�9XTUAnL�>@?B<;9 qd,0

9;TUAEL�>U?M<X9 qd,2|aAECd9X: � LB|aIMTUZ]Z[?}Q=<XgMIBgMN=?BZ[Z]?MHdL¢|

N=?P<;gB9XT@:=N=<X?PCE?B9^N=?B:S�y9;�S9;L u Z[?B9�N�evgM��:wFaL\AETUH=9^9X:JAE>aF@HdL\9�

� ~ � � � ?MI s ?B<;I s ?�NJ?B9iL\<XF@IB?M9�N=? qd,0>U?M<X9 qd,0 �

qd,0 = d3 qd,1 + d2 qd,2 + ε

qd,1 = f3 qd,0 + d2 qd,3

qd,2 = d3 qd,3 + f2 qd,0

qd,3 = f3 qd,2 + f2 qd,1

Page 92: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

{ I ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

�f7 ��� � ?MI s ?B<;I s ?�NJ?B9iL\<XF@IB?M9�N=? qd,0>U?M<X9 qd,2 �

qd,0 = d3 qd,1 + d2 qd,2

qd,1 = f3 qd,0 + d2 qd,3

qd,2 = d3 qd,3 + f2 qd,0 + ε

qd,3 = f3 qd,2 + f2 qd,1

V ?B9^N=?M:b�j9;�S9 L u Z[?B9ON�ehgB��:wFaLXADTUHJ9OT@H�LO<;?B9XQ�?BImL\An>U?BZ[?BHdL�CD?M9i9XTUCE:JL\AETUH=9�9;:=AE>aF@HdL\?M9�

(1) ⇒ Kd,0 = [(d3d2 + d2d3)(f2d2 + f3d3)∗(f2f3 + f3f2) + d3f3 + d2f2]

(2) ⇒ Kd,2 = [(d3d2 + d2d3)(f2d2 + f3d3)∗(f2f3 + f3f2) + d3f3 + d2f2]

.[(d3d2 + d2d3)(f3d3 + f2d2)∗f3 + d2]

C F@<OF@Q=QJCDADIBFaL\AETUHuN=?PCDFW_pT@H=IMLXADTUH�N=?PQ=<;T � ?BImL\AETUH � IM?B9^N=?B:S�jCGF@H=�UF@�U?B9M|=H=TU:J9OT@xJL\?MH=TUH=9�

πd,n(Kd,0) = (d2f2)∗

πd,n(Kd,2) = (d2f2)∗d2

� ADHJ9XAf|a?ML�9X?MCDTUHoCDF�Q=<XT@QRTU9;AELXADTUH q�l|v � Q=F@�U? zd7 � |UCD?M9¤gML\FaL\9¤N=?^<;?ML\T@:=<¤<X?MCGFaLXAE_p9 � I s FaIB:=H=?ON=?M9}LX<\F@IM?B9Kd,0

?mL Kd,29;TUHdLO<X?B9;QR?MIMLXAE>U?MZ]?MHdL qn,0

?ML qn,2

l

� � k � � � � \ b1c k � _�����PXb�P�T�` T �/a�b �XP `9cIPqd,2

C F@<�F@H=F@CDTU�@AD?^F@:uQJ<X?BZ[AD?M<�IBF@9B|bH=TU:=9�I¢F@CEIB:=CETUH=9�Cfeh?BH=9;?BZ�xJCD?ON=?B9rLX<\F@IM?B9���:=A�Z u H=?MH�L�9XTUAnL�>@?B<X9qd,0

9;TUAEL�>@?B<;9 qd,2|£F¢>@?BI�CD?B9i9 �S9;L u Z]?M9�N8evgM�S:=FaL\AETUH=9^ADN=?MHdL\AD��:=?M9 l

� ~ � � � ?BI s ?M<XI s ?�N=?B9iL\<XF@IB?M9^N=? qd,2>@?B<X9 qd,0 �

qd,0 = d3 qd,1 + d2 qd,2 + ε

qd,1 = f3 qd,0 + d2 qd,3

qd,2 = d3 qd,3 + f2 qd,0

qd,3 = f3 qd,2 + f2 qd,1

�f7 ��� � ?MI s ?B<;I s ?�NJ?B9iL\<XF@IB?M9�N=? qd,2>U?M<X9 qd,2 �

qd,0 = d3 qd,1 + d2 qd,2

qd,1 = f3 qd,0 + d2 qd,3

qd,2 = d3 qd,3 + f2 qd,0 + ε

qd,3 = f3 qd,2 + f2 qd,1

V ?B9^9;TUCD:JLXADTUHJ9�9XTUHdL�

(1) ⇒ Kd,0 = [(f3d3 + f2d2)∗(d3f2 + f2d3)(f3d3 + d2f2)

∗(f3d2 + d2f3)]∗

.[(d3f3 + f2d2)∗[(d3f2 + f2d3)(f3d3 + d2f2)

∗f3 + f2]]∗

(2) ⇒ Kd,2 = [(d3f3 + f2d2)∗(d3f2 + f2d3)(f3d3 + d2f2)

∗(f3d2 + d2f3)]∗

.[(d3f3 + f2d2)∗]

Page 93: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5���5� � � �������� ���N�*������ {J~

V e�FaQ=Q=CDAEI¢FaLXADTUH�N=?PCGF�_pTUH=ImL\AETUHyN=?PQ=<XT � ?MIMLXADTUHyN=TUHJH=?�

πd,n(Kd,0) = (d2f2)∗

πd,n(Kd,2) = (d2f2)∗d2

� H � H�|�?ML�L\T@: � TU:=<;9�9;?BCDT@H CGFyQ=<;TUQRT@9XAELXADTUH q�l|v |�CE?B9�gMLcF¡L\9�N=?�<;?ML\T@:=<�<;?BCDFaL\An_p9 � I s F@IM:=H=?uNJ?B9LX<\F@IM?B9 Kd,0

?ML Kd,29XTUHdL�<X?M9XQ�?BIMLXAE>@?BZ[?BHdL qn,0

?ML qn,2

lV ?PZ]TSN u CE?�gMLX?BH=NJ:tN=:jZ]TSN=?�HJTUZ]AEHwF@CR?B9;LON=T@H=IPN=TUH=H=g�QwF@<iCDF � �U:=<;? q�lE~fq�l

d

f

qn,0 q

qn,3qn,2

n,1

qd222f

d1

1

f1

p

p

f 2

r

d1

r

1,0

1,2

1,0

1,2

n,in

������� q�lE~fq � � ��3��%+," 1� "�� 3�)Gn,et

3�) $ ��35" � �*$ � ����+

� ��� � 8:#�����(�� � 8 ���n. � ��!�#

C �YC � B *m+@-9.�032�4657-98�0@+q ?ML;L\?i�UgMH=gB<XF@CDAE9\FaLXADTUH�IBTUH=9;AD9 L\? � N=g � H=AD< n Z]TSN=?B9�N=?�_pTUH=ImL\ADT@H=H=?BZ[?BHdL}FaADH=9;AJ��:=?iCD?M9 m IMTUZWk

Z�:bLcFaLXADTUH=9�Q�TU9X9;ADx=CE?B9 l�� F@H=9�:=H Q=<X?MZ]AE?B<�L\?BZ[Q=9M|�H=TU:J9WF@x�TU<XN=?M<XTUHJ9�CfevF@Q=Q=<;TbI s ?�Z�:=CnL\A k¦Z[TbN u CD?�UgMH=gB<XF@CDAE9XgM?@|UQ=:JAD9B|dN=F@H=9�:=H]9;?BIMTUH=N]LX?BZ[Q=9B|dCDF�_pTU<XZ]F@CDAE9\FaLXADTUH�N=?B9�Z[gBI¢FaH=AD9;Z]?M9¤N=?�IMTUZ[Z�:JLcF¡L\ADT@H9;?B<\FYQ=<XgM9X?BHdLXgB? l}V Ft�@?B9;LXADTUH N=?B9�Z]TSN=?B9�IBTUHJ9XAD9 L\? � F@9X9;:=<X?M<�CD?M9 m QwF@<;IBTU:=<;9�F@:bL\TU<;AD9XgM9�QwFa<XZ[ACE?B9 n Z[TbN=?M9K<X?mL\?BH�:=9�QwF@<KCE?WIBTUHJIB?BQbL\?B:J< l�q ?B9PQwF@<;IBTU:J<X9PQR?M:J>U?MHdL�<;gB9X:JCEL\?M<PN�ev:JH P�����Y� TU:N=?�LXTU:JLOF@:bL\<X?KT@:JL\AEC l @ TU:=9^<XF@Q=Q�?BCDT@H=9���:=?PH=TU9�LX<\F¢>aF@:b�yIMTUH=IB?M<XH=?MHdL�:=HJAD��:=?BZ[?BHdL^CDF��U?B9 L\ADT@H�?MLH=T@HjCDFWN=g � HJAEL\AETUH�N=?PIB?M9�Z[TSN=?B9 l

C �YC ��� � � ��.1035 ��A �&4�? -98 � 032��=?�A :�<=+�<�.�>�? 8��/<=A� � H�N=?OQ=<X?MH=N=<;?�?BH]IBTUHJ9XADNJgB<\F¡L\ADT@H]Q=CE:=9XAE?B:=<;9�Z[TSN=?B9}N=?^_pTUH=ImL\ADT@H=H=?BZ[?BHdLB|SHJTU:=9�F@N=TUQJLX?B<;TUH=9

CE?B9¥H=TaLcFaLXADTUH=9�9X:=An>@FaH�LX?B9 l�V eh?BHJ9X?BZ�x=CD?iN=?M9}Z]TSN=?B9¤NJ?�_pTUH=IMLXADTUHJH=?BZ[?BHdL¤?M9;L�H=T@LXg I = {1,2, . . . ,n}T +

n ∈ N?mL n ≥ 2

� l�C F@<PIBTUHd>U?MHdL\ADT@H H=TU:=9P9;:=Q=Q�TU9XTUHJ9���:=?[CD?oZ]TSN=?oF@ImL\An_rAEH=AELXAGF@CE?BZ[?BHdL�?M9;L.��� ( �3� �3�#+&���96�' ) � � =��#> ,�

n = 1�*> +B��,#>&>�( @���� E ��(!> � J � �9�#>B6�J (���+-%3$-4�+ ��,�'�$B��,�+-$&� ������$&, = �9�?��'�(!>&0#'�J (��=8,#$-$&�3>-�2,#�96 � � J ������$&, = ��� =����#>->-(!0#'9��) =8�3��+-$ ����(�>-%���,�' ��,��:)�0#'9( ��� =8,#�9>-(�6.@3$-� 0�' J '�� >��3'�� EB,.6.���

Page 94: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

{d7 ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

CD?uZ[TbNJ? 1l¥� I s F@��:=?yZ]TSN=?uNJ?u_pTUH=IMLXADTUHJH=?BZ[?BHdL i ?M9;L[F@9;9XTSIBADg�:JH Z[TSN u CE?uF@:JLXTUZ]FaL\? Gi =

(Qi, Σi, δi, qi,0, Qi,m)lΣ ?B9 LWCfeh:=H=AETUH{N=?�L\T@:=9�CD?M9�F@CEQ s F@x�?MLX9�N=?M9WF@:JLXTUZ]FaL\?M9�gBCEgBZ[?BHdLcFaAD<X?M9�N=?

Z]TSN u CE?B9 GiFa:=�UZ[?BHdL\g N=? Cfeh?BHJ9X?BZ�x=CD? Σ′ N=?B9jgM>@gBH=?MZ]?MHdL\9�N=? IMTUZ]Z�:JLcFaLXADTUH8|r9\FaI s F@HdLt��:=?

Σ′ ∩ Σi = ∅ Z]F@AE9���:=? Σi ∩ ΣjQR?M:JL L\<;?PH=TUHy>bAEN=? � IMTUZ]Q�TU9XF@HdL\9iIBT@Z]Z�:JH=9i?BHdL\<;?�Z[TSN=?B9 � l

V eh?BH=9;?BZ�x=CE? Σ′ NJ?B9jgM>UgMH=?BZ[?BHdLX9tN=? IBT@Z]Z�:bLcFaLXADTUH ?M9;LjN=g � H=AKQwF@< ⋃n

i,j,i6=j{αi,j}T +

αi,j

<X?BQJ<XgB9;?BHdL\?�CfehgM>@gBH=?MZ]?MH�L�F@9;9X:=<XF@HdL�CDFWIBTUZ[Z�:JL\FaL\AETUHuN=:jZ]TSN=? i >U?M<X9OCD?�Z[TSN=? jl

q ?M9¤H=TUZ�x=<;?B:b��gM>@gBH=?MZ]?MH�LX9�NJ?iIBTUZ[Z�:JL\FaL\AETUH�9;AD�UH=A � ?BHdL¤��:=?^Q=CE:=9XAE?B:=<;9¥IBT@Z]Z�:bLcFaLXADTUH=9�9XTUHdLQRTU9;9XAEx=CD?M9

�QwF@9;9\F@�@?[NJ:{Z[TSN=? 1 F@:�Z[TSN=? 2 |�Q=F@9X9XF@�U?WN=: Z[TbN=? 1 F@:�Z]TSN=? i |�N=: Z[TbN=? 2 F@:

Z]TSN=? k |@?ML\I l � TU:JL\?M9}IB?B9}IMTUZ]Z�:JLcFaLXADTUHJ9�ADHJN=:=AD9;?BHdL}:=H=?igmLcF@Q�?iN=?^Z[gBZ[TU<XAE9\FaLXADTUH�N=?iL\<XF@IB?M9¤Q=CD:=9ADZ[QRTU9XF@HdL\? l C <;?BH=TUHJ9KCD?�I¢F@9�T + NwF@HJ9�:=H�Z[TbNJ? i ADC�?m�bAD9 L\?�:JH=?�IBT@Z]Z�:bLcFaLXADTUH�>U?M<X9KCE?�Z[TbNJ? j |Q=:=AD9 � QwF@< L\AD<KNJ?[IM?BCE:=AnklIBA¥:=HJ?]IMTUZ]Z�:JLcFaLXADTUH�>@?B<;9�CE?[Z[TSN=? k

l�� FaH=9�IM?]IBF@9B|�AEC¥?B9 L�HJgBIB?M9X9XF@AD<;?N=?PZ]gMZ]TU<;AD9;?B<rC e s AD9;LXTU<XAE��:=?�N=:yQ=<;TbIMgBN=g Gi

NwF@H=9iCE?�Z[TbN=? i |£F¢>aF@HdL^CGF�Q=<;?BZ[A u <X?�IMTUZ]Z�:JLcFaLXADTUH8|Q=:=AD9yIM?BCD:JAKN=:�QJ<XTSIBgBNJg Gj

NwFaH=9yCD? Z]TSN=? j |^F¢>aF@HdLjCGF 9X?MIBTUH=NJ? IMTUZ]Z�:JLcFaLXADTUH l � TU:JLX?B9jIB?B9Z]gMZ]TU<;AD9XFaL\AETUH=9[N=?B9 s AE9;LXTU<XAE�S:J?B9u9;TUHdL�H=gBIM?B9;9\F@AE<X?B9 � CDF N=gMLX?B<;Z]AEHwFaL\AETUH NJ?B9�gML\FaL\9�N=?�N=gBQ=F@<;LNwF@H=9�I s F@IB:JH�N=?B9�Z]TSN=?B9O>U?M<X9�CE?B��:=?MC�F@x�TU:JLXAELO:=H=?�IBTUZ[Z�:JL\FaL\AETUH l�q TUZ[Z[?�Q�TU:=<OCfevF@Q=QJ<XTSI s ? �2 Z[TSN=?B9M|=IB?M9OZ[gBZ[TU<;AD9\F¡L\ADT@H=9r9;TUHdL�<;g¢F@CEAD9;gB?B9iQ=F@<iN=?B9OI¢FaHwF@:b�yN8evAEHJ_pTU<XZ]FaLXADTUH]H=T@L\gM9 πi,j

� � �@:=<X?q�lE~ � � Q�TU:=<P:=H I¢F@HwFaC�Q=F@<;L\F@HdL�NJ: Z]TSN=? i >U?B<;9�CE?]Z[TbNJ? j

� CD?o9X?MH=9�NJ: I¢F@H=F@C}IBTU<;<X?M9XQ�TUH=N Fa:9X?BHJ9�N=?PCDFoIMTUZ[Z�:JLcF¡L\ADT@H � � l

Modèle Modèle Modèle

π π

π

π

π

1,2

1 Modèle 2

1,

i,1 n,i

ni

i,ni

�������Qq�ln~ � � � ��� �$���5"29 3� � �/- ���0$ �$ ����� 9 �#1��2"2929 �$� �2"29 % + �A�5"29� "����� 35"29 $ ��35"29

V ?�Z[TbN u CD?]gML\?MH=N=: N=: Q=<XTSIBgMN=g�QRT@:=<WI s F@IM:=H NJ?B9oZ]TSN=?M9�N=?�_pTUH=ImL\ADT@H=H=?BZ[?BHdL i ∈ I ?B9;LN=TUH=H=g�QwF@<iCE?KZ]TSN u CD?KF@:bL\TUZ]FaL\? Gi,et

_pT@<XZ[?BCDCE?BZ[?BHdL�NJg � H=A �)"�q1C @ I � � QwF@<�

Gi,et = (Qi,et, Σi,et, δi,et, qi,0,et, Qi,m,et)F¢>@?BI

�Qi,et = Qi ∪ {qi,in}

��

Σi,et = Σi ∪ Σ′i|�T +

Σ′i?B9 L�C ev?MH=9X?MZ�x=CD?oN=?M9�gm>UgBHJ?BZ[?BHdL\9�Q�?B<;Z]?mLXL\F@HdL�N=?[��:=AEL;L\?M<�T@: N=?

�� � � �2�3'.+56.,#�F= �?� L�,#( $ 6.�3'.= =3���9��'.=1).'�� 6����9>5= �2��0�'��<>��3�9>3).����+-$&�<6.��'.= E ,.6.�*>/6.,#����%3>3�

Page 95: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5���5� � � �������� ���N�*������ {mq

<;?M>@?BH=AE<�Fa:jZ[TSN=? i�

�qi,0,et =

{

qi,09XA i = 1

qi,in9XA i 6= 1�

Qi,m,et = Qi,m

l� V F�_pTUH=ImL\AETUH�gMLX?BH=N=:J?�N=?PCDFWLX<\F@HJ9XAELXADTUH δi,et

?M9;L�N=g � HJAD?KIBT@Z]Z[?K9X:=AnL�

~,l∀q ∈ Qi

?mL ∀σ ∈ Σi9XA δi(q, σ) ?m�bAD9 L\?�F@CDT@<X9 δi,et(q, σ) := δi(q, σ)

�7/l

∀q ∈ Qi

� Q=F@<;LXAD<¥N=:J�S:J?BCwCfehgM>@gBH=?MZ]?MHdL}N=?iIBTUZ[Z�:JL\FaL\AETUH αi,jQR?M:JL LX<X?i�UgMH=gB<;g^F@CDTU<;9

δi,et(q, σ) := qi,in

��

δj,et(qj,in, αi,j)|£F¢>U?MI � i,j ∈ I2 ?mL i 6= j � 9X?M<\FoN=g � HJAD?P:=CELXgB<;AD?B:J<X?BZ[?BHdL l

C �YC �YC ��0�. � >�? 8��/>E-�8�0�+ 2�4 � <=5 >�+�8���� AG2�AG5 0 � �&4�-9>E-�8�0�+� >@FaH�L}NJ?iN=gMLX?B<XZ[ADHJ?B<¤Cfeh?BHJ9X?BZ�x=CD?�NJ?B9}gML\FaL\9¤N=?i<XF@IBIMTU<XNJ?BZ[?BHdL}N�eh:=H=?^IBTUZ[Z�:JL\FaL\AETUH�NJTUH=H=gM?@|

H=T@:=9KQ=<XgMIBAE9XTUH=9P��:=?[QRT@:=<�:=H{Z]TSN=?�NJTUH=H=goQ=CE:=9XAE?B:=<;9KgM>UgMH=?BZ[?BHdLX9�N=?oIBT@Z]Z�:bLcFaLXADTUH�Q�?B:b>U?BHdL L\<X?�IBTUH=9;ADN=gM<XgM9 l£� ?KQ=CE:=9B| � QwF@< L\AD<�N�eh:=HyZ]TSN=? i :=H�gM>@gBH=?MZ]?MH�LON=?KIMTUZ[Z�:JLcF¡L\ADT@H�Q�?B:JLiZ[?BHJ?B<>@?B<X9y:=H Fa:JL\<;?�Z]TSN=? k T +

i ?ML k H=?�9XT@H�LyCEADgM9�QwF@<uF@:=IB:JH=? <X?BCDFaL\AETUH N8evTU<;N=<X?�Q=F@<;LXADIB:JCDA u <X? l� H N�e�Fa:JL\<;?yLX?B<;Z]?M9B|¤CGF�H�:=Z[gB<;T@LcFaLXADTUH NJ?B9[Z]TSN=?B9oH=?y<;?BQ=<;gB9X?MHdL\?�Fax=9XTUCE:=Z[?BHdLoQwF@9o:=H TU<XNJ<X?N�evF@ImL\AE>aFaLXADTUH N=?B9�Z[TSN=?B9 lr� AEH=9XA�CfehTbIMIB:=<;<X?BHJIB?�N�eh:=H gM>@gBH=?MZ]?MHdLtN=?tIBTUZ[Z�:JL\FaL\AETUH αi,k

� Fz>@?BIi 6= k � � QwF@<;LXAD<�N�ev:JHYZ[TbN u CD? Gi

Q�?B:JL^Z[?BHJ?B<�>U?M<X9O:=HyZ]TSN u CD? Gk

l=� HJ9X:=AnL\?KCfehTSIBIB:J<X<X?MH=IB?PN�eh:=Hgm>UgBHJ?BZ[?BHdLWN=?]IBTUZ[Z�:JL\FaL\AETUH αk,j

Q�?B:bL�IMTUH=N=:=AE<X?o>U?M<X9�:=H Z]TSN u CE? GjT +

j QR?M:JL�Fa:=9X9;Arx=AE?BH L\<X?�ADHJ_pgM<XAD?M:=<���:=?W9;:=QRgM<XAE?B:=< � k

� F¢>U?BIogM�dF@CD?MZ]?MHdL j 6= k � l�q ?WZ[gBI¢FaH=AD9;Z]?�N=?WIBTUZ[Z�:JL\FaL\AETUH?M9;LOADCECD:=9 L\<Xg�QwF@<iCGF � �U:=<X? q�ln~ � l

α1,i

Gi

α i,k

G1 G GGj2 k Gl

αl,n

nG

αk,j

α j,l

�������7q�ln~ � �� �*$ $ ) ��$ "����� "��! �7" +,"29 $ ��3��%+,"29835"29 ��� � �21435129

@ T@:=9�F¢>UT@H=9�>S: 9;:=<�C ev?��J?MZ]QJCD? � N=?M:b� Z[TSN=?B9�N=?]_pT@H=IMLXADTUH=HJ?BZ[?BHdL���:=?]QRT@:=<�NJgML\?M<XZ[ADH=?M<CE?B9KgML\FaL\9KNJ?WN=gBQwFa<;L�N�eh:=H Z]TSN u CE?@|RADC�?M9;L�H=gMIB?B9;9\F@AE<X?oN=?WIBF@CDIM:=CD?M<�CD?M9KgM>UT@CD:JLXADTUH=9KQ�TU9;9XADxJCD?B9KNJ?B9<;?B9X9;TU:=<;IB?B9WIMTUZ[Z�:=H=?M9�NwF@H=9�CD?�Z[TSN u CE?uF@ImL\AE_�Q=<XgMIBgBNJ?BZ[Z]?MH�L l}q ?uIBF@CDIM:=C�HJgBIB?M9X9;AEL\?�CE:=AnklZ Z]?N=?�IBTUH=H=Fa�DLX<X?�Fa:=9X9;A�CD?M9�gML\FaL\9�NJ?�N=gBQ=F@<;L^N=?�IB?�Z[TbNJ?�Q=<;gBIBgMN=?BHdL l£� Hy<;?BZ[TUHdLcF@HdLiFaADH=9;A8N=?�Z[TSN=?� Z[TSN=?]AEC}N=?M>SAD?MHdLWIBCDF@AD<���:=?uCGFjN=gMLX?B<;Z]AEHwFaL\AETUH{N=?B9�gmLcFaLX9�N=?uNJgBQwF@< L�N�eh:=H Z[TbNJ?�QwF@< L\AEIB:=CEAD?B<AEZ]Q=CEAD��:=?YN=? <X?BZ[TUHdL\?M<�9X:=IMIB?M9X9XAn>U?MZ]?MH�L � :=9X��:�evF@: I¢F@CEIB:=CKN=?M9ygM>UT@CD:JLXADTUH=9�Q�TU9;9XADxJCD?B9 � QwF@< L\AE<N=:jZ[TbN=?P9;gBCD?MIMLXADTUH=HJg�AEH=AELXAGF@CE?BZ[?BHdL lJq TUH=9;ADN=gM<XTUH=9OCfeh?m�b?MZ]Q=CE?PN=?PCGFo9XgB��:=?MH=IB?�N=?�IMTUZ[Z�:JLcF¡L\ADT@H

Page 96: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

{ � ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

α1,i αi,k αk,j αj,l αl,nN=?YCGF � �U:=<;? q9lE~ � l C TU:=<]N=gMLX?B<;Z]AEH=?B<oCD?M9]gmLcFaLX9�N=?jN=gMQwF@<;L]N=? Gn

|}H=TU:=9N=?M>@TUH=9KN=gmL\?B<;Z]AEH=?B<OIB?M:b�YN=? Gl

l8V ?M9�gML\FaL\9�N=?�NJgBQwF@< L�NJ? Gl9;TUHdL�N=gmL\?M<XZ[ADH=gM9�?MHt_pTUH=ImL\ADT@HtN=?

IB?B:S��N=? Gj��:=AR9;TUHdLi?B:S��F@:J9X9XA�_pTUH=ImL\ADT@H�N=?�IB?B:S��N=? Gk

|b?M:b��k¦Z Z[?B9rNJgML\?M<XZ[ADH=gM9 � Q=F@<;LXAD<}N=?B9gMLcF¡L\9�N=?�N=gBQwFa<;LiN=? Gi

l=� H � H�CE?B9�gMLcF¡L\9�N=?�N=gBQwFa<;L�NJ? Gi9XTUHdL�NJgML\?M<XZ[ADH=gM9 � QwFa<;L\AE<�NJ:�Z]TSN u CE?

G1AEH=AELXAGF@CE?BZ[?BHdL�F@IMLXAE_ l�q ?B9WN=gmL\?M<XZ[ADHwFaLXADTUHJ9�9;:=IBIM?B9X9;AE>@?B9[ADZ[Q=CDAE�S:J?BHdL�NJ?uN=gMLX?B<;Z]AEH=?B<M|�IMTUZ]Z[?

QRTU:J<�CfevF@Q=QJ<XTSI s ? � N=?B:S� Z[TbNJ?B9B|�CE?]9;:=AE>SA�N=?B9�gM>UT@CD:JLXADTUH=9�N=?M9�<X?M9X9XT@:=<XIM?B9�IMTUZ]Z�:=H=?B9 � N=?M:b�Z]TSN=?B9^9;:=IBIM?B9X9;AE_p9 l

� eh:=H=?KZ]F@H=A u <;?�_pTU<XZ[?BCECD?OCfeh?BH=9;?BZ�xJCD?�N=?M9igML\FaL\9iN=?KNJgBQwF@< L^NwF@H=9rCD?�Z[TbNJ? n 9X?M<\F�N=TUHJH=gKQwF@<CGFWQ=<XT@QRTU9;AELXADTUHu�@gBH=gM<\F@CEAD9XgM?P9X:=An>@FaH�LX? l

� �SR aKR7cfWJPXWYR7N � �"&� ��� ) �#" 9;1!�)�"�� �2" 3� 1%:�1��#"%$&"��! 9

s1 α1,i si αi,k sk αk,j . . . sl αl,n

$&"����$�! 35" + 1� ��$ � �!� "�"��+�3�)$ ��35"

G1

� 9;1%+,"��� "�����!�#1 � �!� �"��+,"%$&"��! � ��) $ ��35"Gn

��"� "%+�+," !�)�"5'∀ a, b ∈ {1, i, k, j, . . . , l, n}2

�sa ∈ L(Ga)

"� αa,b

"29� �+ 1%:�1��#"%$&"��! �35" ���*$ $ ) �$ "����� $&"����$�! �3�) $ ��35"Ga

��)!$ ��35"Gb

�� �*) � �2"� " " 9;1!�)�"�� �2"���+ 1� ��$ 35"�351 � �$�� 3 �$� 98+," $ ��35"

n"29� �3 ���!�#1 � �$�5'

δn,et(qn,in, αl,n) = δn(qn,0, π1,i(s1)πi,k(si)πk,j(sk)...πl,n(sl)) �

� AE?BH ?BHdLX?BH=N=: ADC�H8ev?M9;L�QwF@9P��:=?B9 L\ADT@H N�evF@Q=Q=CEAD��:=?M<KIB?ML;L\?oQ=<;TUQRT@9XAELXADTUH � Cfeh?BHJ9X?BZ�x=CD?WN=?M9�9;gmk�S:J?BH=IM?B9uQ�TU9X9;ADx=CE?B9M|�N8e�F@:bLcF@HdL]Q=CD:=9[��:=?jIB?B< LcF@AEH=?B9[9XgM��:=?BH=IM?B9�9;TUHdL�AEH � H=AE?B9 l l l�C :=AE9X��:=?jL\TU:JLX?B9CD?B9^9;gB��:=?BHJIB?B9 � Q=<;?BH=N=<;? � IBT@Z]QJLX?PQwF@<;LX?BHdLON=:tZ[TSN=?KADH=AnL\ADF@Cf|SH=TU:=9^Q=<;TUQ�TU9XTUHJ9�:=HJ?�N=gMZ�Fa<XI s ?Q=<XTU�@<X?B9;9XAn>U?^��:=AwQR?M<XZ[?ML¤NJ?OIBF@CDIM:=CD?M<¥gML\F@Q�?iQwF@<¤gML\F@Q�?iCD?B9�gMLcF¡L\9}N=?iN=gMQwF@<;L}NJ?B9}N=A � gB<;?BHdL\9}Z[TbNJ?B9N=:�9 �b9 L u Z]? lJV ?^Q=<XAEH=IBAEQR?^IMTUH=9XAE9;LX? � I¢FaCDIB:JCD?B<}N�evF@x�TU<XN[CD?M9}gMLcF¡L\9�N=?^N=gBQwFa<;L�N=?B9�Z]TSN=?M9�Q�TU:J>aF@HdL L\<;?�9;gBCD?MIMLXADTUH=HJgB9 � QwFa<;L\AE<^N=?�C evgmLcFaLOAEH=AELXAGF@C |bQ=:JAD9OIB?B:S�tQ�TU:J>aF@HdL LX<X?�9XgBCE?BImL\ADT@H=H=gB9 � QwF@<;LXAD<^N=?IB?B9]Z]TSN=?M9[?mLuFaADH=9;AiN=?Y9;:=AELX? l}� � H N�ehgM>SAELX?B<oN=?j<X?m_`F@AD<;?jCE?B9oZ Z[?B9[I¢F@CEIB:=CE9WADC�_`F@:JL[?MH TU:JLX<X?>UgB<;A � ?M<�Fa:y_p:J<i?ML � Z]?M9X:=<;?�9MevAEC�<X?M9;L\?PN=?M9�IMTUZ[Z�:JLcF¡L\ADT@H=9 � L\<XF@AELX?B< l

� �SR aKR7cfWJPXWYR7N � � �� ��� "��! �+,"298$ ��3��%+,"29

G1

�G2

�&� � � �Gn

� �$� � �� 1����,9 �$�! ��� ��!�)�"8$ ��35"�35"�- ��� �� �����!�#"%$&"��! &�( ��� 1� "��%$ � �#"��

C) �#" - ��� �� "����� � �$�� "� "%+�+," 351*) �!�,929 �$�! �+,"29����*$ $ ) ��$ ����� 9 �!�;929�� '�+,"29��

i → j��� � �$�� � "��! �%C9�� "� �9;"%)5+,"%$&"��! �9�� ��+ "#"��,9� " ) �#" ���*$ $ ) �$ "�����(3�)!$ ��35"

Gi

:�"��79Gj

�/ �

I = {1}�I�2" ���7129;"��! " + "�� 9;"%$ '�+," 35"29 � � 3$���2"29 35"29 $ ��35"29�% � �$�� "� � 35"296!�)�"%+ 9 � �*) 9 ��+�+ ��� 9

����� 9�� 351��7"�� +,"29 1%:�1��#"%$&"��! 9 35" ���*$ $ ) ��$ "����� � ���*) 9 � �$�� ��� 9�3�)!$ ��35" � �!� "�"��+D�� ��� �$�! 0!�)�"

I 6= {}- �$� �2"5'

+ � - L = {}�L"29� ) � "�� 9;"%$ '�+," "%$ �!���#�$� �7" ��"��0$&"� ��$�! �35" 351� "��0$ � �#"�� +,"29 � � 3$���2"29 35"29

$ ��35"29 % � �$�� "� � 35"296!�)�"%+ 9�9;"�� ���! �"���: �,9 � �512"29 +,"29 ���*$ $ ) �$ "����� 9���) � �*9 9%) ��:��$�! &�

Page 97: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5���5� � � �������� ���N�*������ { �

+ ' - � �*) � ��� ��!�)�"i ∈ I

'9 ��� Li

+ "�� 9;"%$ '�+," 35"29 $ ��35"29 "%+�!�)�" !�)�"%+�!�)�"�9 ��� j��� � �$��

"����$�! �%Li

��+ � ���*$ $ ) �$ "�����i → j

- �*929;" � �$�� "� "�35"C

���� � �*) � �*)

Gj

"%+�!�)�"j ∈ Li

'� � � 1� "��0$ � �#"�� + "�� 9;"%$ '�+," 35"29 1� ��$ 9 35"�351 � �$�� �"�� ��� � + � !�) �$�! '

δj,et(qj,in,αi,j) = δj(qj,0,πi,j(Kq,q′))���Kq,q′

"29� +," + �$��� � �5" �����! "����$�! �*) "29 +,"29 9;1!�)�"�� �2"29 ���$�$�! ���*$ $&" 1� ��$ 3� ����� �$� �#"�) � 1� �$ �35" 351 � �$��

q3�) $ ��3��%+,"

Gi

"� ���*$ $&" 1� �$ �) ����+ ) � 1� ��$ 35"&351 � �$��

q′35" �2" $ ��3��%+," +

∀ s ∈ Kq,q′�αi,j ∈ suiv(s) - � ��"�����3 ��� �� "�7"

- �$� ��!�*) � �*) 9 +,"29 + �$��� � �5"29Kq,q′

+ ��+ � � � + ) 9�� "%) �79 1� ��$ 9q"�

q′�!�;929�� '�+,"29 - �

� �*) � ��� ��!�)�"&1� ��$ 35" 351 � �$�� 35"Gj

351� "��0$ � �#1���+ � ���%) ���2"�� �2" 35" + 1%:�1��#"�$&"��!

αi,j

9;"��#� + � '%"%+�+ �,9;12"�9%) ��:��$�! �+ � � �$��+,"&'αi,j = αi,j,k

9��δj,et(qj,in, αi,j) = qj,k

�?�C = C − {i → j} .i → j

�7" ���7129;"��! " + � ���*$ $ ) ��$ "����� 3�) $ ��35"i:�"��79 +,"8$ ��35"

j�

� ���L = (L ∪ Li) ∩ dom(C) �+#� - - �$� �2"I = L �

C �YC � � � < ��+68 -98�0�+;5Q0�� ��? � -�AG2�AGi,et

V F{QJ<XTUQ�TU9XAnL\AETUH Q=<XgMIBgBNJ?BZ[Z]?MH�L�gML\F@x=CDAE?�QR?M<XZ[?ML[N=?jIBTUZ[Q=CEgML\?M<oCGF IBTUH=9 L\<;:=IMLXADTUH N=?B9]Z]T¡kN u CD?M9�gMLX?BH=NJ:=9�Q�TU:=<�I s F@��:=?�Z[TbN=?�N=?�_pTUH=IMLXADTUHJH=?BZ[?BHdL i

l8� F@H=9�IM?���:=A�9X:=AnL¢|�H=TU:=9�N=g � HJAD9X9;TUH=9_pTU<;Z]?MCDCE?BZ[?BHdL�CE?B9iZ[TbN u CD?M9igML\?MH=N=:=9 � Gi,et � QRT@:=<^I s F@��:=?�Z]TSN=?KN=?K_pTUH=ImL\AETUH=H=?MZ]?MH�L i �

Gi,et = (Qi,et, Σi,et, δi,et, qi,0,et, Qi,m,et)T +�

�Qi,et = Qi ∪ {qi,in}

��

Σi,et = Σi ∪ Σ′iT +

Σ′i?M9;LWC ev?MH=9X?MZ�x=CE?�N=?M9WgM>UgMH=?BZ[?BHdLX9WQR?M<XZ[?MLXL\F@HdLWN=?]�S:JAELXLX?B<�T@: N=?

<;?M>@?BH=AE<�Fa:jZ[TSN=? i�

�qi,0,et =

{

qi,09XA i = 1

qi,in9XA i 6= 1�

Qi,m,et = Qi,m

�� CDF�_pTUH=ImL\ADT@H�gML\?MH=N=:=?�N=?�CGF�LX<\F@H=9;AELXADTUH δi,et

?B9 L�NJTUH=H=gM?�IMTUZ[Z]?K9;:=AEL�

~,l∀q ∈ Qi

?mL ∀σ ∈ Σi9XA δi(q, σ) ?m�bAD9 L\?a|RFaCDTU<;9 �

δi,et(q, σ) := δi(q, σ)7/l � TU:bL\?B9rCD?B9�F@:JL\<;?B9rLX<\F@HJ9XAELXADTUHJ9�9;?B<XT@H�L�N=gMLX?B<XZ[ADHJgB?B9r?BH�:JLXADCDAE9\F@HdL�CGF�Q=<XT@QRTU9;AELXADTUH q�lrz9l

� � 6., E�A �;E/$&���9$-%*>��3�#+&� ��� 6�, E ��(���� 6�� �!�2B ,#�F= +&( ,#�C

)�= J �3>�+ ; ��; 6.(�$-� � J ���2>��#E @���� 6.�*>�( �96�( =��3>i

+-��� 0�'��i → j�����2��$-+-(�����+ �

C�

Page 98: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

{mv ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

C �YC � � � � A � ��? AG2�HJ>�� ��?�8�5 >E-98�0@+� � � � � � Z � � �/c `/NQPXb�PXWYR7N

q ?mLr?��J?MZ]QJCD?^L\<\FaAEL\?^CE?OIBF@9�N=:u9;�S9 L u Z[?�<;?BQ=<;gB9;?BHdL\g � �U:=<X? q�ln~Xv�lBE C£9BevF@�UAnL�N=:�9 �b9 L u Z]?�gML\:JN=ADgNwF@H=9uCE?YIBF@9uQwFa<;L\AEIB:=CEAD?M<[T + H=TU:J9uH�evFz>SAETUH=9�IMTUH=9;ADN=gM<Xg���:=?�NJ?B:b� Z]TSN=?M9]N=?Y_pTUH=IMLXADTUHJH=?BZ[?BHdLF@:b�b��:=?BCE9�F gmL\g�F � T@:JL\gjCGF{Z�F@I s ADH=? M4

��:=A�QR?M<XZ[?ML]N=?tQ=<;?BH=NJ<X?�?MH IBTUZ[QJLX?tCD?y_`F@AnL]��:=?YCGFZ�F@I s ADH=? M2

QR?M:JLugM�dF@CE?BZ[?BHdL�LXTUZ�x�?B<[?BH QwF@HJH=? lrV F Z�F@I s ADH=? M4?B9 L�N=TUHJI�:=H=?�Z]F@I s AEH=?

<X?BNJTUH=NwF@HdLX?�F¢>U?MI�CDF�Z�FaI s ADH=? M2

l

������������

������������

������������

������������

S

d

d

1

f

f

1

33

Machine

Machine

M

M

2dMachine M 2

Machine M 4

1

3

4d

f4

f2

perturbation 2perturbation 1

�������7q�ln~Xv�� � �;9� �%$&"8$ �$��)%- � �� ) ��� "�� %9!�) �$ "�2"�$ � ��� � �#"29�"� �9� � ��� � �! "��%$&143$�"�$� �7"

V ?�Z[TSN u CE?�Fa:JL\TUZ]FaLX? Gi = (Qi, Σi,δi,qi,0,Qi,m) N=?�I s F@IM:=H=?�NJ?B9�Z]F@I s AEH=?B9 Mi?M9;L�<;?BQ=<;gmk

9X?BHdLXg�QwF@<iCDF � �U:=<;? q�lE~Xx9l

d dfr

i fi

p

Ai

Mi

iii

i

Mi Pi

Ai

Modèles G (i = 3, 4)iModèle G (i=1,2)i

������� q�ln~Sx�� � ��3��%+,"29���) �*$ �$ "29�35"29 $ � ��� � �#"29Mi

+i ∈ {1,2,3,4} -

V ?B9jN=A � gM<X?BHdLX9YZ[TbNJ?B9yN=? _pTUH=IMLXADTUHJH=?BZ[?BHdLyQ=<;AD9y?BH�IBTUH=9;ADN=gM<\FaLXADTUH 9;TUHdLtAEIBA�L\<;TUAD9yZ[TbNJ?B9N=gB�U<XF@N=gM9�?ML�:=H�Z[TSN=?}H=TUZ[ADHwF@C � >UT@AD< � �U:=<;? q�ln~Xz � l¡� F@H=9�CD?�Z]TSN=?}H=TUZ[ADH=F@CUIB?�9XTUHdL�CD?M9�Z]F@I s AEH=?B9M1

?mL M2��:=A�Q=<;TbN=:JAD9X?MHdL l V ?}Q=<X?MZ]AE?B<�Z[TbN=?¤NJgB�U<XF@N=g}IBTU<;<X?M9XQ�TUH=N � C ev:JLXADCEAD9\F¡L\ADT@H�N=?}CDF^Z]F@I s AEH=?

M3

� CGFyQ=CGF@IM?oN=?�CDFyZ]F@I s AEH=? M1��:=A}?B9 L�?MH QwF@HJH=?@|�F@CETU<X9P��:=?�CDF�Z�F@I s ADH=? M2

?M9;L�?BH xRTUHgMLcF¡L lS� F@H=9�CD?ON=?B:S�JA u Z[?�Z[TSN=?^N=gB�U<XF@N=ga|bIaev?M9;L�C evAEHd>U?B<;9X?

�CGFKZ]F@I s AEH=? M1

?B9 L�?MHuxRT@H]gmLcFaLrF@CDT@<X9�S:J?[CDF�Z]F@I s ADHJ? M2

?BH QwF@H=HJ?W?B9;LP<;?BZ[Q=CGFaIBgB?�QwF@<KCGF]Z�F@I s ADH=? M4

l�� H � H�|�N=F@H=9KCD?�L\<XT@AD9XA u Z[?CD?B9^N=?M:b�jZ]F@I s ADHJ?B9 M1

?ML M2?BHjQwF@H=HJ?�9;TUHdL�<;?BZ[Q=CGFaIBgB?M9iQwF@<^CD?M9iZ�FaI s ADH=?M9 M3

?mL M4

l

Page 99: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5���5� � � �������� ���N�*������ {�x

V e�FaCDQ s FaxR?mL^�UCDTUx=F@C8?M9;L Σ = Σn ∪ Σd1∪ Σd2

∪ Σd3∪ Σ′ T +

Σn = {d1,d2,f1,f2} Σd1= {d3,d2,f3,f2}

Σd2= {d1,d4,f1,f4} Σd3

= {d3,d4,f3,f4} Σ′ = {p1,p2,r1,r2}

d 2 2f

f1

d

f4f4

f3

f3

r

p1

1

d1

22f

f1

dd 22f

f3

2 f 2

f3

d3

p r

4f

f

1

f4

1d3d

d3

d

d4d44d

d1

d

f1

d4

3

1

qn,0qn,1

qn,2 qn,3

q qq q

q q

q q

q q

d2,0 d2,1

d2,2 d2,3

d3,0 d3,1

qd3,2 d3,3

q

r 2p

p1

22 2

r1

d1,0 d1,1

d1,2 d1,3

������� q�ln~Xz�� "29 3$� ��1��7"��! "29 ���*$ $ ) ��$ "����� 9 �!�;929�� '�+,"29

V ?B9ON=A � gB<;?BHdL\?M9�IMTUZ[Z�:JLcF¡L\ADT@H=9�Q�TU9X9;ADx=CE?B9^9XTUHdLO_pTU:=<;H=AD?M9OQ=F@<^CD?KIBT@H=IB?MQJL\?M:=< lR� HY9;:=Q=Q�TU9\F@HdL��:=?�CE?�9 �b9 L u Z]?K9;?�L\<;TU:J>U?KAEH=AELXAGF@CE?BZ[?BHdL}NwF@HJ9�CD?�Z]TSN=?OH=TUZ[ADHwF@C |d:=H�?m�b?MZ]Q=CE?�N=?�IMTUZ[Z�:JLcF¡L\ADT@H?M9;LO<XgBF@CDAE9Xg�QwFa<OC evTSIBIM:=<X<;?BH=IM?PN=?PCGF�9XgM��:=?BH=IM?�N�ehgM>@gBH=?MZ]?MHdL\9�NJ?�IMTUZ[Z�:JLcF¡L\ADT@H p1p2r1

lw� H � H=F@CCE?�9;�S9 L u Z[?W?B9 LPF@CETU<X9�?BH=�dFa�Ug�NwF@HJ9�CD?�Z]TSN=?�NJgB�U<XF@N=g d2

l C F@<KCDF]9X:JAEL\?a|8H=T@:=9KF@CECDTUH=9�F@Q=QJCDAD��:=?M<CDFuQ=<XTUQ�TU9;AEL\AETUH q�l|z QRTU:J<KN=gMLX?B<XZ[ADHJ?B<KCfeh?BHJ9X?BZ�x=CD?WN=?M9�gmLcFaLX9PN=?oN=gBQwFa<;L�N=?B9PZ[TbN u CD?M9 Gn

| Gd1

|

Gd2

?mL Gd3� l E HJAEL\ADF@CD?MZ]?MHdL I = {n}

l @ TU:J9�FaCDCDT@H=9�N=T@H=IWN=gMLX?B<;Z]AEH=?B<KCE?B9KgML\FaL\9KNJ?WN=gBQwFa<;L�N=?B9Z[TbNJ?B9^F@IMIB?B9;9XAEx=CD?M9ONJAD<X?MIMLX?BZ[?BHdLON=?BQ=:JAD9^CD?KZ[TbNJ?KH=TUZ[ADHwF@C l

��� C 72� 6.��6.,#������$B'�� >-���9>B��' ��, E 6��3>�EB, 6�@����3>3) � �*> � ' EB%3$-,�> 6.,#����%*> �3� (��96.( =8� � '9>&0�' J � ��$&%3>-����+ >�,#�#+$-�#EB����� =8%*><�2,#'�$0=��8+ �8=.�<EB����� �9��$ ���3> (��96.( =8�*>

n)d1

)d3

��+d4

� � �#=�( EB,.6.( 72� ��'2>->-( ���3> ( �96�( =��3> '.+-(�� (!>-%3> 69���9>��,�+&$-�<��� "#,�$&( +�� EB����'9(�>&0�'�� � � EB,.6.�<(���( +&(����1�3>�+

Gn

��+/��,�� �9�#>G1

Page 100: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

{mz ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

� � � � � � kI = {n}

� :YN=gMQwF@< L C = {n → d1, d1 → n, n → d2, d2 → n, d1 → d3, d3 → d1, d2 → d3, d3 → d2}?ML L = {}

l� QwF@<;LXAD<�N=:uZ[TbN u CD? Gn

|SN=?B:S��Z[TbN u CD?M9�9;TUHdL^F@IBIM?B9;9XADxJCD?B9M| Gd1

?ML Gd2

|SQwF@<rCE?B9�gM>UgMH=?BZ[?BHdLX9N=?�IMTUZ]Z�:JLcFaLXADTUH p1

?ML p2|£?ML�IB?M9�IMTUZ]Z�:JLcFaLXADTUHJ9 n → d1

?mL n → d2_pTUHdL�QwF@< L\AD?PN=? C

l @ TU:=9Fz>@TUH=9WN=T@H=I Ln = {d1, d2}

l @ TU:=9�N=gmL\?M<XZ[ADH=TUHJ9�F@CETU<X9�Cfeh?BHJ9X?BZ�x=CD?]N=?B9�gmLcFaLX9�N=?]N=gBQwFa<;LWQ�TU:=<I s F@IB:JHtN=?M9�N=?M:b�yZ[TbN u CD?M9 l

��� i�N�c `�� � _J`�T�`/c � Pfb�PSc�T�`yT%� a�b �XPhT � � R=T $/_Y`Gd1

�V ehgM>UgMH=?BZ[?BHdLiNJ?�QwFaH=H=? p1

Q�?B:JL�9X?�Q=<XTSN=:=AE<X? � QwFa<;L\AE<¤N=?B9�gML\FaL\9 qn,1?ML qn,3

N=:�Z]TSN u CE? Gn

l@ TU:=9�I¢F@CEIB:=CETUH=9�CD?B9�CGFaH=�dF@�U?M9�Fa9X9XTSIBAEgB9 � I s F@IM:=H N=?uIM?B9�gmLcFaLX9B| Kn,1

QRT@:=< qn,1?mL Kn,3

Q�TU:=<

qn,3|JIB?P��:=A�F@Z u H=? � <XgM9XTU:=NJ<X?�<X?B9;QR?MIMLXAE>U?MZ]?MHdL�CE?B9i9;�S9 L u Z[?B9�N�ehgB��:wFaLXADTUH=9^9;:=AE>aF@HdL\9

Kn,1 :

qn,0 = d1 qn,1 + d2 qn,2

qn,1 = f1 qn,0 + d2 qn,3 + ε

qn,2 = d1 qn,3 + f2 qn,0

qn,3 = f1 qn,2 + f2 qn,1

Kn,3 :

qn,0 = d1 qn,1 + d2 qn,2

qn,1 = f1 qn,0 + d2 qn,3

qn,2 = d1 qn,3 + f2 qn,0

qn,3 = f1 qn,2 + f2 qn,1 + ε

@ TU:=9^TUxJLX?BH=TUHJ9�FaCDTU<;9iCD?B9i9;TUCD:bL\ADT@H=9i9X:=An>aF@HdL\?B9�

Kn,1 = [(d1d2 + d2d1)(f2d2 + f1d1)∗(f2f1 + f1f2) + d1f1 + d2f2]

.[(d1d2 + d2d1)(f2d2 + f1d1)∗f2 + d1]

Kn,3 = [(d1d2 + d2d1)(f2d2 + f1d1)∗(f2f1 + f1f2) + d1f1 + d2f2]

.[(d1d2 + d2d1)(f2d2 + f1d1)∗]

V ehgMLcF¡L¤N=?iN=gMQwF@<;L}N=F@H=9}CD?�Z[TSN u CE? Gd1

|U9X?MCDTUHWCDF�L\<XF@IB?i?MH=<X?M�UAD9 L\<XgM? Kn,1T@: Kn,3

|U?B9 L}TUxJL\?MH�:QwF@<^CfevF@Q=Q=CEADIBFaL\AETUH�N=?PCDF�_pTUH=IMLXADTUHyN=?PQ=<;T � ?BImL\AETUH πn,d1

lV ?B9�gmLcFaLX9�L\<;TU:J>UgM9�9;TUHdL�<X?M9XQ�?BIMLXAE>@?BZ[?BHdL qd1,0

?ML qd1,2

l¢V evF@:JLXTUZ]FaL\? Gn,et?B9 L�NJTUH=I¤?BHJ<XADI s AUN=?B9

L\<\FaH=9XAnL\ADT@H=9 δn,et(qn,1, p1,0) = qn,in?ML δn,et(qn,3, p1,2) = qn,in

lzV ?B9�L\<XF@H=9;AEL\AETUH=9 δd1,et(qd1,in, p1,0) =

qd1 ,0?mL δd1,et(qd1,in, p1,2) = qd1,2

9;TUHdL�F � TU:JLXgB?B9 � CfevF@:JLXTUZ]FaL\? Gd1,et

lV FWIBTUZ[Z�:JL\FaL\AETUH n → d1

?B9 LO<X?MLXAD<;gB?PN=?PCfeh?BH=9;?BZ�xJCD? C �

C = {d1 → n, n → d2, d2 → n, d1 → d3, d3 → d1, d2 → d3, d3 → d2}

��� i�N�c `�� � _J`�T�`/c � Pfb�PSc�T�`yT%� a�b �XPhT � � R=T $/_Y`Gd2

�V ehgM>UgMH=?BZ[?BHdL�N=?iQwFaH=H=? p2

Q�?B:JL¤9;?^Q=<XTSN=:=AE<X? � Q=F@<;LXAD<�NJ?B9}gML\FaL\9 qn,2?ML qn,3

l @ TU:J9¤I¢F@CEIB:=CETUH=9CD?B9PCDF@H=�dF@�@?B9PF@9;9XTSIBADgM9 � I s F@IB:=H N=?oIB?M9�gmLcFaLX9B| Kn,2

QRTU:J< qn,2?ML Kn,3

QRT@:=< qn,3

l�V ?[CDF@H=�dFa�U?Kn,3

F�gmL\giN=g � � N=gMLX?B<XZ[ADHJg l E CJ<X?B9 L\?OF@CETU<X9 � I¢F@CEIB:=CE?B< Kn,2|@IB?i��:=AwF@Z u HJ? � <XgB9;TU:=N=<;?iCD?�9 �S9;L u Z]?

Page 101: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5���5� � � �������� ���N�*������ {m{

N�ehgB��:wF¡L\ADT@H=9^9X:=An>@FaH�L�

Kn,2 :

qn,0 = d1 qn,1 + d2 qn,2

qn,1 = f1 qn,0 + d2 qn,3

qn,2 = d1 qn,3 + f2 qn,0 + ε

qn,3 = f1 qn,2 + f2 qn,1

@ T@:=9^TUxJL\?MH=TUH=9OF@CETU<X9iCDF�9XTUCE:JL\AETUH�9X:JAE>aF@HdL\?�

Kn,2 = [(d1d2 + d2d1)(f2d2 + f1d1)∗(f2f1 + f1f2) + (d1f1 + d2f2)]

.[(d1d2 + d2d1)(f2d2 + f1d1)∗f1 + d2]

V evgmLcFaL}NJ?iN=gBQwFa<;L}NwF@HJ9¤CD?�Z[TbN u CD? Gd2

|@9X?BCETUHWCGF�LX<\F@IM?i?BH=<;?B�UAE9;LX<XgB? Kn,2TU: Kn,3

|a?B9;L�TUxbL\?BH�:QwFa<rCfevF@Q=QJCDADIBFaL\AETUHoN=?�CDF�_pTUH=ImL\AETUH�N=?�Q=<XT � ?MIMLXADTUH πn,d2

lJV ?M9igMLcF¡L\9rT@xJL\?MHS:J9i9XTUHdLi<;?B9XQ�?BImL\An>U?BZ[?BHdLqd2,0

?mL qd2,1

l�V evF@:JLXTUZ]FaL\? Gn,et?B9 LoN=TUH=I�?MH=<XAEI s ArNJ?B9WL\<XF@H=9XAnL\AETUH=9 δn,et(qn,2, p2,0) = qn,in

?ML

δn,et(qn,3, p2,1) = qn,in

l�V ?B9�LX<\F@HJ9XAELXADTUHJ9 δd2,et(qd2,in, p2,0) = qd2,0?mL δd2,et(qd2,in, p2,1) = qd2,1

9;TUHdL�F � TU:JL\gM?B9 � CfevF@:JL\T@Z�FaLX? Gd2,et

lV FWIBTUZ[Z�:JL\FaL\AETUH n → d2

?B9 L�<;?ML\AE<XgM?KN=?PCfeh?BH=9;?BZ�x=CE? C �

C = {d1 → n, d2 → n, d1 → d3, d3 → d1, d2 → d3, d3 → d2}V ?i9XI s gMZ�FPN=?^CGF � �U:=<X? q9lE~X{ <;?BQ=<;gB9X?MHdL\?OCfeh?BH=9;?BZ�x=CE?iN=?B9}gmLcFaLX9�NJ?iN=gBQwFa<;L�N=?B9}N=?M:b�oZ[TbN u CD?M9

Gd1

?mL Gd2

l� TU:=9�CE?B9�gMLcF¡L\9�NJ?�N=gMQwF@<;L�N=?B9�Z]TSN=?B9�F@IMIB?B9;9XAEx=CD?M9 � QwFa<;L\AE<^N=? Gn

T@H�L�gMLXg�I¢FaCDIB:JCDg@|£C evgmLcF@Q�?

3.(b).i ?M9;L^L\?M<XZ[ADH=gM? l @ TU:=9^N=gmL\?B<;Z]AEH=TUH=9iNJTUH=I L = {d1, d2}� QJ:=AD9 I = {d1, d2}

l

� � � � � � �I = {d1, d2}

� QJ< u 9�F¢>UTUAE<[NJgML\?M<XZ[ADH=gjCfeh?BHJ9X?BZ�x=CD?jN=?B9[gML\FaL\9]N=?jN=gBQwFa<;LuNJ?B9[N=?B:b� Z[TbN u CD?M9]FaIBIB?M9X9;ADx=CE?B9N=?MQ=:=AE9iCD?�Z[TbN u CD? Gn

|=H=TU:J9^F@CDCETUH=9�Q=<;TbIMgBN=?M<iN=?PCGF�Z Z[?�_`F � TUHyQRT@:=<iCD?M9iZ]TSN u CE?B9iFaIBIB?M9X9;ADx=CE?B9N=?MQ=:=AE9 Gd1

?ML Gd2

l��� �&R=T�` W N�W PSWYb1_

Gd1

�i = d1� ?MQ=:=AD9 Gd1

|�N=?M:b� Z[TbN u CD?M9�9XTUHdL�F@IMIB?B9;9XAEx=CD?M9�Q=F@<KCD?M9KgM>UgMH=?BZ[?BHdLX9�N=?oIMTUZ]Z�:JLcFaLXADTUH r1?ML

p2

l=V evgm>UgMH=?BZ[?BHdL p2I¢Fa<\F@ImL\gB<;AD9;?�CGF�IMTUZ[Z�:JLcF¡L\ADT@H]N=:�Z[TSN=?�N=gM�U<\FaN=g d1

>U?M<X9^CD?�Z]TSN=?�NJgB�U<XF@N=g

d3|�?BH�<X?M>aF@HJI s ?�CfehgM>@gBH=?MZ]?MHdL r1

IBF@<\F@ImL\gM<XAD9;?�IM?BCDCE?^N=:uZ[TbN=?ON=gM�U<\F@NJg d1>@?B<X9rCD?OZ]TSN=?OH=TUZ[ADHwF@C

nlLd1

= {n, d3}l�� gMLX?B<XZ[ADHJTUH=9�F@CDTU<;9iCfeh?BH=9;?BZ�xJCD?�N=?B9�gMLcF¡L\9ON=?�NJgBQwF@< L�N=?M9�N=?M:b�YZ]TSN u CD?B9 Gn

?mL Gd3

l� �YZ � i�NVcO` � �V_Y`yT�`/c ��PXb�PSc T�` T%� a�b �XP T � � R�T%$/_J`

GnV evgm>UgMH=?BZ[?BHdL}N=?�<;gBQwFa<\FaLXADTUH r1Q�?B:JL¤9;?�Q=<;TbN=:JAD<X? � QwFa<;L\AE<�NJ?B9¤gML\FaL\9 qd1,0

?mL qd1,2N=:WZ[TSN u CE?

Gd1

l @ TaL\TUH=9^��:=?�CD?K<;?ML\T@:=<^N=: Gd1

>U?B<;9 GnFogML\gPQ=<;gB9;?BHdL\g�NwF@H=9OCD?KIBF@9^CDAEZ]AnL\g � N=?M:b�jZ[TbN=?M9

���Ln = {d1, d2}

�8+dom(C) = {d1, d2, d3}

Page 102: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ IJI ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

p1,0 p1,0

p2,0

p2,1

f4f4

f3

f3

d3

d

d4

d4

3

q qd3,0 d3,1

qd3,2 d3,3

q

p2,1

p2,0

p1

p1

p2

r1

r 2p

2r

2

qn,ind 2 2f

f1

d

d1

22f

f1

dd 22f

f3

2 f 2

f3

d3

1d3d

qn,0qn,1

qn,2 qn,3

q q

q q

d1,0 d1,1

d1,2 d1,3

pp1,2

1,2

4f

f

1

f4d44d

d1

d

f1

1

q q

q q

d2,0 d2,1

d2,2 d2,3

r1

qd1,in

qd2,in

�������7q�lE~f{ � � ���,9;" "�� ����� 9�� 351��#�$ ����� 35"29 ���*$ $ ) ��$ "����� 9n → d1

"� n → d2

N=?i_pTUH=IMLXADTUHJH=?BZ[?BHdL lUV eh?BHJ9X?BZ�x=CD?^N=?M9�gmLcFaLX9¥L\<;TU:J>UgM9�N=F@H=9¤IB?^IBF@9}?B9;L� qn,0

?mL qn,2

lUV ?M9}H=TU:J>@?BCDCE?B9L\<\FaH=9XAnL\ADT@H=9�NJ? Gd1

9XTUHdL δd1,et(qd1,0, r1,0) = qd1 ,in?mL δd1,et(qd1,2, r1,2) = qd1,in

l�q ?BCDCE?B9�N=? Gn

9XTUHdL δn,et(qn,in, r1,0) = qn,0?mL δn,et(qn,in, r1,2) = qn,2

l

@ TU:=9^TUxJLX?BH=TUHJ9 C = {d2 → n, d1 → d3, d3 → d1, d2 → d3, d3 → d2}l

� � k � i�N�c `�� �V_J` T�`9c ��PXb�PXc T�` T � aVb �XP T � � R=T%$/_J`Gd3

C TU:=<rNJgML\?M<XZ[ADH=?M<�CE?B9�gML\FaL\9�N=?�N=gMQwF@<;LrQRT@9X9XAEx=CD?M9�N=F@H=9rCE?�Z[TSN u CE? Gd3

|SN=?B:b��I¢Fa9rQ�?B:J>@?BHdLi9X?Q=<XgM9X?BHdLX?B<�9;?BCDT@H]CE?B9}gML\FaL\9�N=?^N=gBQ=F@<;L�NwF@H=9�CD?^Z[TbN u CD? Gd1

lS� F@HJ9�I s FaIB:=HuNJ?OIM?B9�N=?B:b�[IBF@9B|�N=?M:b�CGF@H=�UF@�U?B9�QRT@9X9XAEx=CD?M9�Q�?B:b>U?BHdL L\<X?�I¢F@CEIB:=CEgB9OQ=:=AD9;��:=?�CfehgM>@gBH=?MZ]?MHdLKN=?�IMTUZ]Z�:JLcFaLXADTUH p2

Q�?B:bL�9X?Q=<XTSN=:=AE<X? � QwF@<;LXAD<�N=?uN=?M:b� gMLcF¡L\9�N=A � gM<X?MH�LX9 qd1 ,2

?mL qd1,3

l @ T@:=9�TUxbL\?BHJTUH=9WF@CETU<X9 4 9 �b9 L u Z]?M9N�evgM��:wFaL\AETUH=9 l

� � k �YZ � � ����PXb�P T�` T � aVb �SP T�b N�cGd1

`/cOPqd1,0

Page 103: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5���5� � � �������� ���N�*������ ~ I ~

� F@HJ9OIM?�IBF@9^CD?M9iN=?B:b�j9 �S9;L u Z]?M9�N8evgM�S:=FaL\AETUH=9OF@9X9;TbIMADgM9O9;TUHdL�

Kd1,2 :

qd1,0 = d3 qd1,1 + d2 qd2,2

qd1,1 = f3 qd1,0 + d2 qd1,3

qd1,2 = f2 qd1,0 + d3 qd1,3 + ε

qd1,3 = f3 qd1,2 + f2 qd1,1

Kd1,3 :

qd1,0 = d3 qd1,1 + d2 qd2,2

qd1,1 = f3 qd1 ,0 + d2 qd1,3

qd1,2 = f2 qd1 ,0 + d3 qd1,3

qd1,3 = f3 qd1 ,2 + f2 qd1,1 + ε

V ?B:=<^<;gB9XT@CD:JLXADTUH�N=T@H=H=?P<X?M9XQ�?BIMLXAE>@?BZ[?BHdL�CE?B9^9XT@CD:JLXADTUH=9r9X:=An>@FaH�LX?B9�

Kd1,2 = [(d3d2 + d2d3)(f2d2 + f3d3)∗(f2f3 + f3f2) + d3f3 + d2f2]

.[(d3d2 + d2d3)(f2d2 + f3d3)∗f3 + d2]

Kd1,3 = [(d3d2 + d2d3)(f2d2 + f3d3)∗(f2f3 + f3f2) + d3f3 + d2f2]

.[(d3d2 + d2d3)(f2d2 + f3d3)∗]

V evgmLcFaL�N=?�N=gMQwF@< LuNwF@HJ9uCD?YZ]TSN u CE? Gd3

|�9X?BCETUH CDF{L\<XF@IB?Y?BH=<;?B�UAE9;LX<XgB? Kd1,2TU: Kd1,3

|r?M9;LTUxbL\?BH�:�QwFa<�CfevF@Q=Q=CEADIBFaL\AETUHoN=?�CGF�_pTUH=IMLXADTUH�N=?�Q=<;T � ?BImL\ADT@H πd1 ,d3

l=V ?B9igmLcFaLX9�IBTU<;<X?M9XQ�TUH=NwF@HdLX9i9XTUHdL<;?B9XQ�?BImL\An>U?BZ[?BHdL qd3 ,0

?ML qd3 ,1

l=V ?M9^H=TU:J>@?BCDCE?B9�LX<\F@H=9;AELXADTUH=9rN=? Gd1

9XTUHdL δd1 ,et(qd1 ,2, p2,0) = qd1,in

?mL δd1,et(qd1,3, p2,1) = qd1,in

l�q ?MCDCD?M9¤N=? Gd3

9;TUHdL δd3,et(qd3,in, p2,0) = qd3,0?mL δd3,et(qd3,in, p2,1) =

qd3,1

l� � k � k � � � ��PXb9P T�` T � aVb �XP T�b1NVc

Gd1

`/cOPqd1,2� F@HJ9OIM?�IBF@9^CD?M9iN=?B:b�j9 �S9;L u Z]?M9�N8evgM�S:=FaL\AETUH=9OF@9X9;TbIMADgM9O9;TUHdL

Kd1,2 :

qd1,0 = d3 qd1,1 + d2 qd2,2

qd1,1 = f3 qd1,0 + d2 qd1,3

qd1,2 = f2 qd1,0 + d3 qd1,3 + ε

qd1,3 = f3 qd1,2 + f2 qd1,1

Kd1,3 :

qd1,0 = d3 qd1,1 + d2 qd2,2

qd1,1 = f3 qd1 ,0 + d2 qd1,3

qd1,2 = f2 qd1 ,0 + d3 qd1,3

qd1,3 = f3 qd1 ,2 + f2 qd1,1 + ε

V ?B9�9 �S9;L u Z]?M9KN�ehgB��:wFaLXADTUH=9�9XTUHdLKAEN=?BHdL\AE��:=?B9KFa:�I¢F@9�QJ<XgBIMgBN=?MZ]Z[?BHdLB|8CD?M9�9XT@CD:JLXADTUH=9OQ=:=AE9�CD?M9LX<\F@H=9;AELXADTUH=9r9XTUHdLON=TUH=IPCE?B9iZ Z[?B9 l

� TU:=9^CD?M9OgmLcFaLX9^N=?PN=gBQwFa<;L^N=:jZ]TSN u CD? Gd3

TUHdLON=TUHJI�gmL\gPN=gmL\?B<;Z]AEH=gB9 lF@ TU:J9�F¢>@TUH=9C = {d2 → n, d3 → d1, d2 → d3, d3 → d2}

Q=:=AE9 L = {} ∪ {n, d3} ∩ {d2, d3} = {d3}l

V ?�9;I s gBZ]F�N=? � �U:=<;? q�l�7 I�QJ<X?BHJN�?BHuIMTUH=9XAEN=gB<XFaL\AETUH[CGF�IMTUZ[Z�:JLcF¡L\ADT@H[NJ:uZ]TSN=? d1F@:�Z[TSN=?

n ?mL�NJ? d1>U?M<X9OZ]TSN=? d3

l

��� �&R=T�` W N�WJPXWYb _Gd2

�i = d2� ?MQ=:=AD9 Gd2

N=?M:b��IBTUZ[Z�:JL\FaL\AETUH=9}9XTUHdLrgB�dF@CE?BZ[?BHdL�Q�TU9;9XADxJCD?B9 lSV F�Q=<X?MZ]A u <X?O?B9 LiI¢Fa<\F@ImL\gB<;AD9;gB?QwFa<�CfehTbIMIB:=<;<X?MH=IB?WN=?WC evgm>UgMH=?BZ[?BHdL p1

��:=A¥Z u H=?�>@?B<X9PCE?�Z]TSN u CD? Gd3

l�V FuN=?M:b�bA u Z[?W?B9 LPN=:=? �C evTSIBIM:=<X<;?BH=IM?�N=? r2

��:=A£Z u H=?i>U?B<;9rCE?OZ[TSN u CE? Gn

lSq TUZ[Z]?^Q=<;gBIBgMN=?BZ[Z[?BHdLrQ�TU:=<}I s FaIB:=HuNJ?OIM?B9Z[TbN u CD?M9B|bH=TU:=9ON=gMLX?B<;Z]AEH=TUH=9iCE?B:=<;9igMLcF¡L\9^N=?PN=gBQ=F@<;L l

Page 104: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ I 7 ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

p1,0

p2,0

p2,1

p2,1

p2,0

p1

p1

p2

r1

r 2p

2r

2

1d

d1

r1

p1,0

p1,2

p2,0

p2,1

p2,1

p2,0

d 2 2f

f1

d22

f

f1

dd 22f

f3

2 f 2

f3

d3

3d

qn,0qn,1

qn,2 qn,3

q q

q q

d1,0 d1,1

d1,2 d1,3

p1,2

4f

f

1

f4d44d

d1

d

f1

1

q q

q q

d2,0 d2,1

d2,2 d2,3

r

r1,0

1,2

r

r

1,0

1,2

f4f4

f3

f3

d3

d

d4

d4

3

q qd3,0 d3,1

qd3,2 d3,3

q

qn,in

qd2,in

q

q

d1,in

d3,in

�������7q�l�7 I � � ���,9;" "�� ����� 9�� 351��#�$ "����� 35"29 ���*$ $ ) �$ "����� 9d1 → n

"� d1 → d3

V eh?BH=9;?BZ�x=CE?WN=?B9PgmLcFaLX9KN=?oN=gBQwFa<;LPN=: Z[TbN u CD? Gn

� <X?B9;Q l Gd3� QR?M:JL LX<X?oN=gmL\?B<;Z]AEH=g�N�eh:=H=?

Z�F@HJA u <;?]AEN=?BHdLXAD��:=? � IB?BCECD?[T + TUH FYCGFjIBTUZ[Z�:JL\FaL\AETUH{N=: Z[TbN=?[N=gM�U<\F@NJg d1F@: Z[TSN=?]HJTUZ]A k

HwF@C n� <;?B9;Q l NJ: Z]TSN=?oN=gM�U<\F@NJg d1

F@: Z]TSN=? d3 � l�q ?B9�gmLcFaLX9�9;TUHdL qn,0?ML qn,1

� <;?B9;Q l qd3 ,0?ML

qd3 ,2 � l¤V evF@:JLXTUZ�F¡L\? Gd2,et?B9 L[N=TUH=I�?MH=<XAEI s AiQwF@<�NJ?B9WL\<XF@H=9XAnL\AETUH=9 δd2,et(qd2,0, r2,0) = qd2 ,in

?ML

δd2 ,et(qd2,1, r2,1) = qd2,in

l=V ?B9�L\<\FaH=9XAnL\ADT@H=9 δn,et(qn,in, r2,0) = qn,0?mL δn,et(qn,in, r2,1) = qn,1

9XTUHdLF � TU:JLXgB?B9 � CfevF@:JL\T@Z�FaLX? Gn,et

lwV ?B9OH=TU:J>@?BCDCE?B9iL\<XF@H=9;AEL\AETUH=9iN=? Gd2

9;TUHdL δd2,et(qd2,1, p1,0) = qd2,in

?ML δd2,et(qd2,3, p1,2) = qd2,in

l�q ?MCDCE?B9¤N=? Gd3

9;TUHdL δd3,et(qd3,in, p1,0) = qd3,0?ML δd3,et(qd3,in, p1,2) =

qd3 ,2

l=V ?B9^IBF@CDIM:=CD9�N=TUH=H=?MHdL C = {d3 → d1, d3 → d2}Q=:=AE9 L = {d3} ∪ {n, d3} ∩ {d3} = {d3}

l� Q=F@<;LXAD<�N=?�Cfeh?BHJ9X?BZ�x=CD? I = {d1, d2}

|aL\T@:=9¥CD?M9¥gML\FaL\9�N=?�N=gMQwF@<;L¥TUHdL¤gMLXg�I¢F@CEIB:=CEgB9 lUV ?�9XI s gBZ]FN=?PCGF � �U:=<;? q�l 7S~ <;?BQ=<;gB9;?BHdL\?�IB?mLXL\?�9XAnL\:wF¡L\ADT@H l � AEHwF@CE?BZ[?BHdL I = {d3}

l

� � � � � � �I = {d3}

� H � H8|RCE?B9�IMTUZ[Z�:JLcF¡L\ADT@H=9^�S:JA�H=T@:=9�<X?M9;LX?BHdL � NJg � H=AE<�9;TUHdL�CDF]IMTUZ]Z�:JLcFaLXADTUHyN=:tZ]TSN=? d3

>U?B<;9¥CD?�Z[TbN=? d19;:=AELX? � C evTSIBIM:=<X<;?BH=IM?rN=? r2

?mL¥N=:�Z]TSN=? d3>U?M<X9�CE?�Z[TSN=? d2

9X:=AnL\? � CfehTbIMIB:=<;<X?MH=IB?N=? r1

�Ld3

= {d1, d2} � l

Page 105: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5���5� � � �������� ���N�*������ ~ I q

p1,0

p2,0

p2,1

p2,1

p2,0

p1

p1

p2

r1

p2

r2

1d

d1

r1

p1,0

p1,2

p2,1

p2,0

p2,0

p2,1r

2 r2

r2

r2,1

r 2

p1,0

p1,0

p1,2 p

1,2

d 2 2f

f1

d22

f

f1

dd 22f

f3

2 f 2

f3

d3

3d

qn,0qn,1

qn,2 qn,3

q q

q q

d1,0 d1,1

d1,2 d1,3

p1,2

4f

f

1

f4d44d

d1

d

f1

1

q q

q q

d2,0 d2,1

d2,2 d2,3

r

r1,0

1,2

r

r

1,0

1,2

f4f4

f3

f3

d3

d

d4

d4

3

q qd3,0 d3,1

qd3,2 d3,3

q

,0

,0,1

q q

qq

n,in d1,in

d3,ind2,in

������� q�l 7S~ � � ���,9;" "�� ����� 9�� 351��#�$ ����� 35"29 ���*$ $ ) ��$ "����� 9d1 → n

"� d1 → d3

��� i�N�c `�� � _J` T�`/c���PXb�PXc�T�` T � aVb �XP T � � R=T $9_J`Gd1

V ?B9}gML\FaL\9¤Q�TU9;9XADxJCD?B9¤NJ?ONJgBQwF@< L}NwF@H=9}CE?�Z]TSN u CD? Gd1

9;TUHdL}N=gMLX?B<;Z]AEH=gB9}9X?MCDTUHWC evgmLcFaL}NJ?iN=gBQwFa<;LNwFaH=9�CE?tZ[TbN u CD? Gd3

l�C :=AD9;��:=?�CD?YZ]TSN u CD? Gd3

F@NJZ]?mL�N=?M:b� gmLcFaLX9�N=?tN=gBQwFa<;L qd3 ,0?ML qd3,2

|H=T@:=9�F¢>@TUH=9�N=?M:b�YI¢F@9 � gmL\:=N=AE?B<M|���:=?�H=TU:=9�H=?�QJ<XgB9;?BHdL\?M<XTUHJ9�QwF@9�ADIBA�Q=:JAD9X��:=?�CGFoN=gBZ]F@<;I s ?�?M9;LZ]F@ADHdLX?BHwF@HdL�x=AD?MH�F@9;9XADZ[ADCEgB? l C F@<�IBF@CDIM:=C�H=TU:=9�LX<XTU:b>UTUH=9��S:J?WCD?B9�gML\FaL\9�N=?�N=gMQwF@<;L�9XTUHdL qd1,0

?ML

qd1,1

l�V ?B9WHJTU:J>U?MCDCE?B9�LX<\F@HJ9XAELXADTUHJ9�N=? Gd3

9XT@H�L δd3,et(qd3,0, r2,0) = qd3 ,in?mL δd3,et(qd3,1, r2,1) =

qd3,in

l�q ?MCDCD?M9�NJ? Gd1

9XT@H�L δd1,et(qd1 ,in, r2,0) = qd1,0?mL δd1,et(qd1,in, r2,1) = qd1,1

l�@ TU:=9�Fz>@TUH=9C = {d3 → d2}

l��� i�N�c `�� � _J` T�`/c���PXb�PXc�T�` T � aVb �XP T � � R=T $9_J`

Gd2

V ?B9OgML\FaL\9^N=?�N=gBQ=F@<;LON=:jZ]TSN u CD? Gd2

9XT@H�L qd2,0?ML qd2,2

l£V ?M9�H=T@:J>U?MCDCD?M9iL\<\FaH=9XAnL\ADT@H=9iN=? Gd3

9;TUHdL δd3,et(qd3,0, r1,0) = qd3,in?ML δd3,et(qd3,2, r1,2) = qd3,in

lzq ?BCDCE?B9�NJ? Gd2

9XTUHdL δd2,et(qd2,in, r1,0) =

qd2,0?mL δd2,et(qd2,in, r1,2) = qd2,2

l£� F@H=9^IM?�IBF@9 C = {}l

L = ({} ∪ {d1, d2}) ∩ {} = {}l E C�H�e �yFoQwF@9ON=?PH=TU:J>@?¢F@:YQwF@9ON=?PI¢F@CEIB:=C lwV ?�9;I s gBZ]F]NJ?�CDF

� �@:=<X? q�l�7U7 <X?MQ=<XgM9X?MH�LX?�N=T@H=IPCD?B9^Z[TbN u CD?M9�gMLX?BH=NJ:=9�IMTUZ[Q=CD?mL\9iN=?M9�Q=<;TbIMgBN=gM9 l

Page 106: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ I � ����� � ����� �5� ����� �� �����7� � � ����� � � � � ���

p1,0

p2,0

p2,1

p2,1

p2,0

p1

p1

p2

r1

p2

r2

1d

d1

r1

p1,0

p1,2

p2,1

p2,0

p2,0

p2,1r

2 r2

r2

r2,1

r 2

r1,2

r1,2

r1,0

r1,2

r1,0

r2,1

r2,0

r2,0

p1,0

p1,0

p1,2

p1,2

r1,0

d 2 2f

f1

d22

f

f1

dd 22f

f3

2 f 2

f3

d3

3d

qn,0qn,1

qn,2 qn,3

q q

q q

d1,0 d1,1

d1,2 d1,3

p1,2

4f

f

1

f4d44d

d1

d

f1

1

q q

q q

d2,0 d2,1

d2,2 d2,3

r

r

1,0

1,2

f4f4

f3

f3

d3

d

d4

d4

3

q qd3,0 d3,1

qd3,2 d3,3

q

,0

,0,1

,1r

2

q q

q q

n,in d1,in

d3,ind2,in

�������Qq9l 7U7�� � ��3��%+,"29 1� "�� 3�) 9 ���*$ � +,"� �9�35"29 ��� � �21435129

�&��� � �)(�*�� 9�#�,-�O(

� :�L\<XFz>@?B<;9¥N=?rIM?�I s F@QJAEL\<;?@|¡CGFO�U?B9 L\ADT@H�N=?M9¥Z]TSN=?M9�F�gmL\grF@xRT@<XN=gM?r?BHW9;?rxwFa9\F@HdL¤9;:=<�CDFOL s gBTU<;AD?N=?�IMTUHdL\< s CD?PQwF@<^9X:JQR?M<;>SAD9;ADTUHYQRTU:J<^_pT@:=<XH=AE<i:=HtIBF@N=<;?�_pTU<;Z]?MC�QRT@:=<�CDFWZ]TSN=gBCEAD9XFaL\AETUHu?ML�Q�TU:=<^CGFIBTUZ[Z�:JL\FaL\AETUH l

V ?B9rZ]TSN u CE?B9�IBTUHJ9XADNJgB<XgM9�ADIMAR9;TUHdLiIB?M:b��N=:uQ=<;TbIMgBN=ga|JQ=CE:=9�Q=<;gBIBAE9XgMZ]?MH�LrCD?M9r<X?M9X9;TU:=<XIM?B9^?BHJ�dF¡k�UgB?M9�NwFaH=9^:=HYZ[TSN=?KN=?K_pTUH=ImL\ADT@H=H=?BZ[?BHdL l

V evF@Q=Q=<;TbI s ?tZ�:=CELXAnklZ]TSN u CE?uIBT@H=9XAE9;L\? � <X?MQ=<XgM9X?BHdLX?B<�:=H 9 �b9 L u Z]?�IMTUZ[Q=CD?��J?YQwF@<]Q=CD:=9;AD?M:=<X9Z]TSN u CE?B9^9XAEZ]QJCD?B9 l£qrs F@��:=?�Z]TSN u CD?K?B9 L�?MHt<;g¢F@CEAEL\gK:JH=?�NJ?B9XIM<XAEQJL\AETUHyQwF@<;LXAD?MCDCD?�N=:t9 �b9 L u Z]?�NwF@H=9:=HtZ[TbNJ?KN=?K_pTUH=IMLXADTUHJH=?BZ[?BHdL^N=TUHJH=g lFE H=AnL\AGFaCD?BZ[?BHdLB|JTUHy9X:JQ=QRT@9X?��S:8ev:=HY9X?M:=C�Z]TSN u CE?K?B9 L�FaIML\An_ |�UgBH=gM<\F@CE?BZ[?BHdL}CD?rZ]TSN=?�N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL¤H=TUZ[ADH=F@C l¡� Ho<X?M>aF@HJI s ?iL\TU:=9¤CE?B9¤Fa:JL\<;?B9¤Z[TbN=?M9¤9XTUHdLN=gB9;gBCD?MIMLXADTUH=HJgB9 l N¥LcFaH�L�N=TUHJH=goCGF�QRT@9X9XAEx=ADCEAELXg�N�evF¢>UTUAE<�NJ?B9�<X?B9;9XTU:J<XIB?M9�IMTUZ]Z�:=H=?B9PNwFaH=9PI s F@IB:JHN=?B9oZ[TbN=?M9�IBT@H=9XAEN=gB<;gB9B|¤HJTU:=9[F¢>UTUH=9oAEH�LX<XTSN=:=AnL�CDF�H=T@L\AETUH N=?�9;:=AE>SA lE C�9BevF@�UAnLWN=?�IMTUH=9X?M<;>@?B<oCGFL\<\FaIB?WN=?M9�gm>UgMH=?BZ[?BHdL\9�F¢�dF@HdL�Z[?BH=gWC ev:=HJ?WN=?WIB?M9�<;?B9;9XTU:=<;IB?M9�IMTUZ]Z�:=H=?B9 � :JH=?oIBTUZ[Z�:JL\FaL\AETUHN=?uZ[TbN=? l�� ?uIB?]_`F@AELB|�H=TU:=9WF¢>@TUH=9�gmL\?BHJN=: I s F@IM:=H N=?B9�Z[TSN u CE?B9�N=?�Q=<;TbIMgBN=g�IBTUH=9;ADN=gM<XguN8ev:=H

Page 107: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�5� � � ����� � � � ����� ~ I �

gmLcFaL}QwFa<;L\AEIB:=CEAD?M<B|aF@Q=Q�?BCDgrgMLcF¡L}ADHwF@ImL\An_ l@V eh?BH=9;?BZ�x=CE?^N=?B9}gM>@gBH=?MZ]?MHdL\9�QR?M<XZ[?MLXL\F@HdL}N=?^QwF@9;9X?B<}N�eh:=HZ[TbN u CD?KNJ:�Q=<XTSIBgMN=g � CfevF@:JLX<X?a|�Iaev?M9;L k � klN=AD<;?�N8ev:=HtZ]TSN=?K>U?M<X9�:JH�F@:JLX<X?�Z]TSN=?@|w?M9;L�F@Q=Q�?BCDgPC ev?MHbk9;?BZ�x=CE?�N=?M9�gM>@gBH=?MZ]?MHdL\9oN=?�IMTUZ[Z�:JLcF¡L\ADT@H l�V FtN=A � IM:=CELXg�N�eh:=H=?�LX?BCECD?]F@Q=Q=<;TbI s ?�<X?BC u >@?uN�eh:=H=?QwFa<;L¤N=?iCDF�IBT@H=9;LX<X:=ImL\ADT@H[NJ?B9}Z]TSN u CD?B9�gMLX?BH=N=:J9�IBF@<\FaIML\gM<XAE9\F@HdL}CD?M9¥N=A � gM<X?BHdLX9�Z[TSN=?B9¥NJ?�_pTUH=IMLXADTUHSkH=?MZ]?MHdL�?mL�N�e�Fa:JL\<;?[Q=F@<;LPN=?[CGFuNJg � H=AnL\AETUH N�ev:JH Z[gBIBF@H=AD9;Z]?WNJ?[IMTUZ[Z�:JLcF¡L\ADT@H�QR?M<XZ[?MLXL\F@HdLPN=?9;:=AE>S<X?r?m�bQ=CDAEIBAnL\?BZ[?BHdL�CD?�IBTUZ[QRT@<;L\?MZ]?MHdL¥N=?�I s F@IB:=HoN=?M9¤Z]TSN u CD?B9�N=?M9¤Q=<XTSIBgMN=gB9 l�q ?�Z[gBI¢FaH=AD9;Z]?a|IBF@<\F@ImL\gM<XAD9;g^QwF@<�N=?B9�I¢F@H=F@:b�[N�ehADHJ_pT@<XZ]FaL\AETUH�|@9;?�x=F@9X?O9X:=<�:=H]?BH=9;?BZ�x=CE?�NJ?OLX<\F@IM?B9��UgBH=gM<XgM?B9rN=F@H=9CE?�Z[TbN u CD?�Q=<XgMIBgBNJ?BZ[Z]?MH�L�ADHwF@ImL\An>UgKF � H�N=?�N=gmL\?B<;Z]AEH=?B<r:=H�gML\FaLiN=?�NJgBQwF@< LiTU:�<;?ML\T@:=<iF@N=gM��:wFaLNwFaH=9^CD?KZ[TbN u CD?�HJTU:J>U?MCDCE?BZ[?BHdLOF@IMLXAE>@g l

Page 108: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 109: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ I x

� � ����'7%�)�� �

�� � % � ("h� !� � � � %�)�� ��� !)�"

� �� > (/+��� ��9�*�+�,-�)(A evF@�UAE9X9\FaH�L�N=?�CGFK9;�SHdL s1u 9X?KN=?�IBTUHdLX< s CE?B:=<;9B|�ADCw9;?�<Xgm> u CD?�Q=F@<;_pTUAE9¤L\< u 9rN=A � IBADCE?@|U?MHu9BevF@Q=QJ:J�dF@HdL

9;:=<iN=?B9iZ[gML s TSN=?B9iN=?KIMTUHdL\< s CD?M9iIBCGFa9X9XAE��:=?B9 � IBTUHdL\< s CD?M:=<i:=H=AE��:=?PF@9X9;TbIMADgKFa:j9 �S9;L u Z]? � |wN=?KIMTUZWkZ]F@H=N=?M<uIBT@H�>@?BHwFax=CD?MZ]?MH�Lj:=H 9 �b9 L u Z]? IBT@Z]Q=CE?m�b? �h� ?BC {�x�� � ��?M< {d7�� ��� �6{m{�� � � ��{mz�� liV ?B9y9;TakCE:JL\AETUH=9�QJ<XTUQ�TU9XgM?B9 � >@TUAD<WI s F@Q=AELX<X?M9 1 ?ML 2 � IMTUH=9XAE9;LX?BHdL � Z]?mLXL\<;?�?BH � :J>S<X?�:=H ?BH=9;?BZ�xJCD?�N=?9;:=QR?M<;>SAD9;?B:=<;9�gMCDgMZ]?MH�L\F@AD<;?B9^F@�@AD9X9XF@HdL^9X:=<^:=HJ?P_p<XF@IMLXADTUHyN=?PC ev?M9XQwF@IM?PN�evgmLcFaLX9^IBTUZ[Q=CD?mL l� F@Q=Q�?BCDT@H=9���:=?WCE?�IBTUZ[Q�TU<;LX?BZ[?BHdL�N=gM9XAE<Xg�N=: Q=<;TbIMgBN=g�NwF@H=9K:=H�Z[TSN=?�N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL

?M9;L}N=gMIB<XAnL}QwF@<¤N=?M9}9XQ�gBIBA � I¢F¡L\ADT@H=9¤��:=AwCD:=AJ9XTUHdL}Q=<;TUQ=<X?M9 l�� CDCE?B9¤Q�?B:J>@?BHdL�N=TUH=I L\<X?^IMTUH � AEIML\:J?BCDCE?B9M|?mLy?BHdL\<XFa�GH=?M<�:=H x=CDTSI¢Fa�U?�N=: 9;�S9;L u Z[? lOq ?MIBA � :=9 L\A � ?�CGF Q=<;TUQRT@9XAELXADTUH N�ev:JH=?{F@<XI s AnL\?MIML\:J<X? N=?IMTUZ]Z]F@H=NJ?j?MZ]QJCDTz�dF@HdL]:=H ?MH=9X?MZ�x=CE?tN=?Y9X:=Q�?B< >bAE9X?M:=<X9M|rT + I s F@IB:JH N�eh?BHdL\<;?t?B:S� ?M9;L]gBCGFaxRTU<;g9;QRgMIBA � �S:J?BZ[?BHdL � :=H�Z[TSN u CE?iN=:�Q=<;TbIMgBN=g � � �U:=<X? � ln~ � l�V ?O< s CE?^N=?�I s F@IB:=H�N=?�IM?B9�9X:=Q�?B< >bAE9X?M:=<X9IMTUH=9XAE9;LX? � _`F@AE<X?�<X?M9XQ�?BIMLX?B<�CE?B9�IBTUHdL\<XF@ADHdLX?B9�AEZ]Q�TU9XgM?B9ONwF@H=9�I s F@IB:JH�N=?B9�Z[TSN=?B9�<X?MLX?BH�:=9 l�q ?ML;L\?F@QJQ=<XTSI s ?�QRTU:J<�CDFO9 �SH�L s1u 9;?�N=?M9�IBT@H�LX< s CE?B:=<;9�?M9;L�N=TUH=I�IBT s gB<;?BHdL\?iF¢>@?BIrC e�FaQ=Q=<XTSI s ?}Z�:=CnL\A k¦Z[TbN u CD?<;?ML\?MH�:=?�Q�TU:=<iCE?KQ=<XTSIBgMN=g l@ T@:=9iZ]T@H�LX<XTUHJ9�NwF@H=9rIB?KI s F@QJAEL\<;?���:=?PCD?M9rL\?MI s H=AD��:=?M9^N=?�9;�SHdL s�u 9X?�?BZ[Q=CET �@gB?M9iQR?M<XZ[?MLXLX?BHdL

N�ehTUxJLX?BH=AE<�NJ?B9�IMTUHdL\< s CD?B:J<X9�9;ADZ[Q=CD?M9�?mL�Q�?B<;_pT@<XZ]F@HdL\9 � TUQJLXADZ]F@CDAnL\g@|RH=TUHbklx=CDTSI¢Fa�U?@| l l l � ?mLW��:=?uCD?M9IMTUHdL\< s CD?B:J<X9�<;gB9X:JCELcFaH�LX9�<X?M9;LX?BHdLON=?�LcFaADCDCE?OF@N=Z[AD9X9;ADx=CE? lG@ T@:=9i<\F@QJQR?MCDTUH=9���:=?KCGF�HJTU:J>U?MCDCE?�Q=<XT@x=CDg�kZ]FaL\AE��:=?]IMTUH=9;ADN=gM<XgB?�AEIBA�N=TUAnL�Q=<;?BH=NJ<X?�?BH IMTUZ[QJL\?a|¥F@:bklN=?BC � N=: Z[gBIBF@H=AE9XZ[?�N=?uIMTUZ[Z�:JLcF¡L\ADT@HN=?M9�Q=<;TbIMgBN=gM9B|�IM?BCE:=A�NJ?B9W9X:JQR?M<;>SAD9;?B:=<;9 l¤V ?�QJ<XTUx=C u Z[?]Z]F � ?M:=<�N=?�CGFY9 �SH�L s1u 9;?yN=?�IMTUHdL\< s CD?B:J<X9NwFaH=9�CfevF@Q=Q=<;TbI s ?�Z�:=CnL\AnklZ]TSN u CD?yQ=<XT@QRTU9;gB?�AEIBA�IMTUH=9;AD9;LX? � F@9X9;:=<X?M<yCD?�<XF@IBIMTU<XN=?MZ]?MHdLy?BHdL\<;?{CDFNJ�SHwFaZ]AE�S:J? � CD?KIMTUZ[QRTU< L\?MZ]?MH�L � N=:jQ=<XTSIBgMN=gP?MLOCfevF@IMLXADTUH�N=?PIBTUHdL\< s CD? � Z[?BH=?M< l

� F@HJ9KCGF]9;?BImL\ADT@H � l 7 H=TU:=9�NJgBZ[TUHdL\<XT@H=9���:�ehADC�?��bAD9;LX?�:=H�9;:=QR?M<;>SAD9;?B:=<K:JH=AD��:=?�Q=F@<�Z[TbN=?�N=?_pTUHJIML\AETUH=H=?MZ]?MHdL¢|BxJAD?BHP��:=?}CD?¤QJ<XTSIBgBNJg�NJ?¤I s F@��:=?�Z]TSN=?¤F@AnL�Q=CE:=9XAE?B:=<;9�gMLcF¡L\9�N=?¤N=gMQwF@<;L�Q�TU9X9;ADx=CE?B9 l� H=9;:=AELX? � 9X?BImL\AETUH � l|q � H=TU:=9�N=g � HJAD9X9;TUH=9�CD?B9�Z[gBI¢FaH=AD9;Z]?M9�N=?]IBTUHJ9;L\<;:=IMLXADTUH N=?B9�9XQ�gBIBA � I¢F¡L\ADT@H=9gmL\?BHJN=:=?B9]N=?yI s F@��:=?YZ]TSN=? l¤q ?B9�Z[gBIBF@H=AE9XZ[?B9B|�x=AD?MH ��:=?jN=A � gB<;?BHdL\9M|}<XgBQ�TUH=NJ?BHdLuFa:b� Z Z]?M9

Page 110: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ I z ������������� � � 5� ��� � � �7��� ������� � ��� ��

Modèle 1 modèle nModèle 2

Superviseur 1 Superviseur 2 superviseur n

infocont infocont infocont

Mode 1 Mode 2 Mode n

������� � lE~��� � ��� � "��� ) �7" 35" ���*$ $ �$� 35" ��� ���!�;9;12"

TUx � ?BImL\An_p9�N=?[N=gmL\?B<;Z]AEHwFaLXADTUH N=?M9�gML\FaL\9�N=?[N=gBQ=F@<;L�?ML�N=?[<X?MLXTU:=<���:=?�IM?B:b� Z[AD9K?BH Q=CGFaIB?[NwF@H=9CD?�I s F@Q=AELX<X? 3

l¤q ?mLXLX?u9X?MIML\AETUH ?M9;LWAECDCD:J9;L\<;gB?[QwF@<�:=H ?m�b?MZ]Q=CE? l�� H � H CGFj9X?BImL\AETUH � l � F@x�TU<XNJ?�CGF>UgB<;A � IBFaL\AETUHyN=?B9OQ=<;TUQ=<XAEgMLXgB9^N=?PIBTUHdLX< s CDF@x=ADCEAELXg�?mL�NJ?�HJTUHbk¦xJCDTSI¢F@�U? l

� ��� 4 �M, # +�!�( *�! !1+ 9�(�, * , + � ��� 9�( #�9�� ! ���5, # !�9 ��� 8 �3. � ��!

� ��� �~B 8��/A A=+ �/8 -94�>E-98 0�+V ?KQ=<;TUx=C u Z]?KQ�TU9;g�N=F@H=9^IB?mLXL\?P9;?BIMLXADTUHyIMTUH=9XAE9;LX? � Z[TUHdL\<;?B<iCfeh:=H=AEIBAnL\g�N�eh:=Hj9X:=Q�?B< >SAD9X?M:=<^QwF@<

Z]TSN=? l�C CD:=9]Q=<XgMIBAE9XgBZ[?BHdLB|�9XF@I s F@HdL���:=?�I s F@IB:=H NJ?B9uZ[TbN u CD?M9]NJ?B9uQ=<;TbIMgBN=gM9uQ�?B:JLyFaN=Z]?mLXLX<X?Q=CD:=9;AD?M:=<X9�gMLcF¡L\9�N=?�N=gBQ=F@<;LB|J?m�bAE9;L\?�k¦AEC�:JH �VN�W � ��` 9X:JQR?M<;>SAD9;?B:=<�Q=F@<rZ[TbNJ? � Z]TSN u CE? � Q�?B<XZ[?ML;LcF@HdLN�e�FaxRTU:bL\AD<^Fa:jCDF@H=�dFa�U?�N=gM9XAD<;gP�S:J?BC���:=?P9XTUAnL^CfehgMLcF¡L^N=?PN=gBQwFa<;LON=:jQ=<XTSIBgMN=g �

� eh:=H=? Z]F@H=A u <X?�_pT@<XZ[?BCDCE?@|�gML\F@HdLYNJTUH=H=g :=H�F@:JLXTUZ�F¡L\? Gj = (Qj, Σj, δj, Qj, ��� ����� , Qj,m)QRTU9;9XgMNwF@HdL[:=H ?BH=9;?BZ�x=CE?uN�ehgML\FaL\9WN=?�NJgBQwF@< L � Qj, ��� ����� � |�?��JAE9;LX?mk¦AECr:=H :JH=AD��:=?�9;:=QR?M<;>SAD9;?B:=< Sj

|L\?BCO��:=? ∀ q ∈ Qj, ��� ����� |�CD?�_pTUHJIML\AETUH=H=?MZ]?MHdL�?MH xRT@:=IBCE?j_p?M<XZ[gB?j9XTUAnL�CE?YCDF@H=�dF@�@?�N=gB9;AD<Xg Kj,q

|�L(Sj/Gj) = Kj,q ? � |£F¢>@?BI Kj,q

CDF@H=�dF@�@?�N=gB9;AD<;g�gMCGF@x�TU<;g � QwF@<;LXAD<iN=?PC evgmLcFaL^N=?PN=gMQwF@< L ql

j ��� NVW PSWJR7N � �YZ� ���

Gi

) �($ ��3��%+," ��) �*$ �$ " �������7"29 �!��� 3 �$�! G% ) � $ ��35" 35"�- ��� �� �����!�#"%$&"��! &� " $ ��3��%+,"Gj��"%) ���*$ �!���� "�� � + ) 9�� "%) �79 1� ��$ 9 35" 351 � �$�� ,+ :$��� � ��� ����� "�2"

3 - ��� �*) � ��� ��!�)�" 1� ��$ 35" 351 � �$�� q35"

Gi

) �#" 3�������$ � !�)�" � �$�� ���%)5+ � ���7" 9;"��#� 3 ���!�#12"�� �$� +," + �$��� � �5"L(Gi,q)

� � ��:�"��Gi,q =

(Qi, Σi, δi, q, Qi,m)+ ��) �*$ �$ " � �$�#� �� 1����,9;1 � �$�8) � 9;"%)5+ 1� �$ 35"�351 � �$��

q�

p� " "%$ � +,"� ��� �) � ��) �*$ �$ "

Gi

�!�;929;143 �$�! 35"%)D" 1� �$ �9 35" 351 � �$�� q1

"� q2

+Qi, ����������� = {q1, q2} - � "29

���L(Gi,q)

�3>�+5� J �3�9>��#E @���� 6��<+-,#'.+-�*>/���3>5>-%30�'��3�F=8�*>56�J %<L#%����#EB����+&>5�9��$-+&���#+56�����'�(!>�� J %8+ � +q

�8+ E �3�9����+ L���$ >'9� %�+&��+56.'���$-, =�%36.%

Gi,q

Page 111: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � � ��� ���� � � ��� � ����� ����� � � ��� ����� �� � � �� � ����*����� ~ I {

+ �$��� � �5"29L(Gi,q1

) = {s ∈ Σ∗i | δi(q1,s)!}

"� L(Gi,q2

) = {s ∈ Σ∗i | δi(q2,s)!}

�2" ���7129;"��! "��! 35"%)D" 3�������$ � !�)�"29 3$� ��1��7"��! "29 3�) ��� � �214351

Gi

�L(Gi,q1

)"29� .+ � 3�� ����$ � !�)�" �*929 � ��� 12" % + 1� ��$

q1

�L(Gi,q2

)"29� �+ � 3�������$ � !�)�"�3 ���!�#12" � �$� + 1� ��$

q2

�y

V ?WQ=<XT@x=C u Z]?�gm>UTS��:=g]NJ?W9;�SHdL s1u 9X?�NJ?WIBTUHdL\< s CD?M:=<KIBT@H=9XAE9;L\? � IMTU:=Q=CE?B<KCD?WQJ<XTSIBgBNJg Gi

� :=H:=HJAD��:=?y9X:=Q�?B< >SAD9X?M:=<��UF@<\F@HdLXAD9X9XF@HdL[CD?B9ox�TUH=H=?M9]Q�?B< _pTU<XZ]F@H=IM?B9o��:=?BCECD?y��:=?j9XTUAnLo9\F Nb�bH=F@Z]AE��:=?IMTU:=<\FaH�LX? � � �U:J<X? � l�7 � l E C¤9Me�F@�@AELKN=?[N=g � H=AD<KQ�TU:=<PI s Fa�S:J?]gmLcFaL�N=?oN=gMQwF@<;L q N=:{Q=<;TbIMgBN=g Gi

CE?CDF@H=�dF@�@?�NJgB9XAE<Xg Ki,q

l @ TU:=9�NJ?M>S<XTUHJ9�?BH=9;:=AELX?�>@gB<XA � ?B<�CD?M9�IBT@H=N=AELXADTUHJ9�H=gMIB?M9X9\FaAD<X?M9�?ML�9X: � 9XF@HdL\?B9N�eh?m�bAE9;L\?MH=IB?�?MLON�eh:=H=AEIBAnL\gKN�eh:=HyL\?BC�9;:=Q�?B<;>SAE9X?B:J< l

Plusieurs états de départ

Modèle G

Mode i

Superviseur S

i

i

������� � l�7 � " ��� ��'�+��%$&" 35" 9 ���! � �29;" 35" �����! �76*+,"%) �

� ������� � ��<=0K. � � AA TUAE?BHdL Ki

CD?iCDF@H=�dFa�U?iN=gB9;AD<;g�Fa9X9XTSIBAEgOF@:]Z[TSN u CE? Gi?mL {Ki,q | q ∈ Qi, ��� ����� } Cfeh?BH=9;?BZ�x=CE?^N=?B9

CDF@H=�dF@�@?B9�NJgB9XAE<XgM9KIBTU<;<X?B9;QRT@H=NwF@HdL � Cfeh?BHJ9X?BZ�x=CD?�NJ?B9KgML\FaL\9KNJ?�N=gBQ=F@<;L q ∈ Qi, ��� ����� N=: Q=<XTSIBgMN=g

Gi

l� F@Q=Q�?BCDT@H=9���:=?�N=F@H=9�C e�FaQ=Q=<XTSI s ?�IBCGFa9X9XAE��:=?�N=?�CGF[L s gBT@<XAD?�N=?�IMTUHdL\< s CD?�QwF@<�9;:=Q�?B<;>SAE9XADT@H�|RCE?

IMTUH=IB?MQJLKN=?�IBTUHdL\< s CGFax=ADCEAEL\gK?M9;LK9;: � 9\F@HdLPQ�TU:=<�N=gBZ[TUHdL\<;?B<�C ev?��JAE9;LX?BH=IM?�N�eh:=H�9X:=Q�?B< >SAD9X?M:=< S ��:=AF@�@AEL�9;:=<^:=HjQ=<XTSIBgMN=g G F@N=Z[?ML;LcF@HdL^:=Hj9X?M:=C�gML\FaL^N=?PN=gMQwF@<;L � ���nz�x F � l�q ?BQ�?BHJNwF@HdL¢|£CD?�IBTUH=IM?BQJLN=?jIBT@H�LX< s CDF@x=AECDAELXg�9Me�F¢> u <X?�AEH=9X: � 9XF@HdLuQ�TU:=<oQ=<;TU:J>U?M<�C ev:=HJADIBAnL\g�N=? Si

� ��:=?BCE��:=?t9;TUAEL[CfehgML\FaL[N=?N=gMQwF@< L q NJ: Q=<XTSIBgMN=g Gi

| L(Si/Gi) = Ki,q � l�� H ? � ?ML¢|�Q=:=AE9X��:=?�CD?YQ=<XTSIBgMN=g GiIBT@Z]Q�TU<;LX?

:=H�?MH=9X?MZ�x=CE?WN�evgmLcFaLX9KN=?�N=gMQwF@< L¢|�CE?�9X:=Q�?B< >SAD9X?M:=< Si?M9;LPADHJI¢F@QwFax=CD?�N�evAEN=?BHdLXA � ?M<�CfehgML\FaL � QwF@< L\AE<

N=:J�S:J?BC Gi9;?B<XF@AELOF@ImL\An>Ug l

Page 112: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~U~ I ������������� � � 5� ��� � � �7��� ������� � ��� ��

0

2q q3

1qq

σ

σ

α

α

γββγ

������� � lrq��� ) �*$ �$ " �!�;929;143 �$�! �35"%)�" 1� ��$ 9 35" 351 � �$��

E HuT@<XN=?M<�LXT�x�?MLXLX?B<�:=H=N=?M<X9;L\F@H=N=AEH=��L s AD9�Q=<XT@x=CD?MZY|dCE?ML�:=9rIMTUH=9XAEN=?B<�L s ?�F@:JLXTUZ�F¡L\TUH[T@_ � �@:=<X?��� l �is AD9}Fa:JL\TUZ]FaLXTUH�Q�TU9X9;?B9;?B9}L��rTK9 LcF@< L\ADHJ��9;L\FaL\?M9 q0

F@H=N q1|UF@9;9X:=Z[Z]AEH=��L s FaL�L s ?iTSIBIB:J<X<X?MH=IB?

C TU:=<iZ[AD?B:S�uIMTUZ]QJ<X?BHJN=<X?KIM?KQ=<XTUxJC u Z[?@|bIBTUHJ9XADNJgB<XT@H=9^CfevF@:JL\T@Z�FaLX?�NJ?�CDF � �U:J<X? � l|q�lwq ?mL�F@:bkL\TUZ]FaL\?�F@N=Z[?ML¤N=?M:b�WgmLcFaLX9¤N=?iN=gMQwF@<;L q0

?ML q2

lBA :=QJQRTU9;TUH=9¤��:=?^CD?M9¥TSIBIB:J<X<X?MH=IB?M9}N=?iCfehgM>@gBH=?MZ]?MH�Lα� QwF@<;LXAD<PN=?M9�gML\FaL\9 q0

?ML q2Z u H=?MHdL�>U?M<X9�N=?B:b� gML\FaL\9�N=A � gM<X?BHdLX9B|�<X?B9;QR?MIMLXAE>U?MZ]?MHdL q1

?ML q3

l� F@H=9�IB?[I¢F@9PCE?W9X:=Q�?B< >bAE9X?M:=<�?M9;L�ADH=IBF@QwF@xJCD?WN=?oN=gmL\?B<;Z]AEH=?B<KC evgmLcFaLPN8e�F@<;<XAn>UgB?[F@QJ< u 9�TSIBIB:J<X<X?MH=IB?N=? α

l£� ?PIB?K_`F@AnLi9XA�C evgm>UgMH=?BZ[?BHdL σ ?M9;L�F@:JLXTU<XAE9Xg � QwF@< L\AD<rN=? q1

�ασ ∈ Kq0

� FaCDTU<;9�CfehgM>@gBH=?MZ]?MH�Lσ NJTUAEL L\<;?yF@:JLXTU<XAE9Xg � QwFa<;L\AE<�N=?�C evgmLcFaL q3

l¥� H <X?m>aF@H=I s ?y9XArN=?BQ=:JAD9WCD?M9�N=?M:b� gML\FaL\9 q0?ML q2

CD?B9ogm>UgBHJ?BZ[?BHdL\9]N=?yN=gBQwFa<;L[9XTUHdL[N=A � gM<X?BHdLX9B|}F@CETU<X9WNwFaH=9oIB?yI¢F@9oCDF 9 �SH�L s1u 9;?t9Mev? � ?MIML\:J?YN�eh:=H=?Z�F@HJA u <;?^IBCGFa9X9XAE��:=? lSV ?iL s gMTU< u Z]?O9X:=An>aF@HdL�gmLcF@xJCDAEL}CE?B9}IBT@H=N=AELXADTUHJ9�HJgBIB?M9X9XF@AD<;?B9r?mL�9X: � 9\FaH�LX?B9���:=?H=TU:=9O<X?MI s ?B<;I s TUH=9 l� � �/R � $�� `�� �YZ� ��� "��! '

� Gi

) � ��) �*$ �$ " �!�;929;143 �$�! �) � "�� 9;"%$ '�+," 3� 1� ��$ 9 35"�351 � �$�� q ∈ Qi, ������� ���

�� {Ki,q | q ∈ Qi, � � � � ��� }

+ "�� 9;"%$ '�+," 35"298+ �$��� � �5"29835129�� �7129 �������2"29 �!��� 3 �$�! %��� ��!�)�" 1� ��$ 35"351 � �$��

q�

�0+ "#"��,9� " ) � ) �!� !�)�" 9%) ��"��0: �,9;"%) �Si

"%+�!�)�"∀q ∈ Qi, ������� ��� , L(Si/Gi) = Ki,q9�� "� �9;"%)5+,"%$&"��! �9��7'

( �∀ q ∈ Qi, ��� � � ���

�Ki,q

"29� �����! "�26*+ � '�+," � �$� �#��� �!���� 0%L(Gi,q)/ �

∀ s ∈ Ki,q

"� ∀s′ ∈ Ki,q′

"%+ 9 !�)�"s = s′

�∀σ ∈ Σi,c �

'sσ ∈ Ki,q

"� s′σ ∈ L(Gi,q′) ⇔ s′σ ∈ Ki,q′ �

E HdL\:JAEL\An>U?MZ]?MH�LB|£CGFoIBTUH=NJAEL\AETUH 7 <;?BC u >U?�N=:t_`F@AnL���:=?�CD?P9X:JQR?M<;>SAD9;?B:=< SiH=?�N=AD9;QRTU9;?�N8e�F@:JIB:=H=?

ADHJ_pTU<;Z�F¡L\ADT@HjQ�TU:=<�IBTUHJHwFa�DLX<X? � ����������� QwF@<;Z]A�Cfeh?BH=9;?BZ�xJCD?�NJ?B9�gmLcFaLX9�N=?�NJgBQwF@< L¢|RCfehgMLcF¡L � Q=F@<;LXAD<N=:=��:=?BCRCD?OZ]TSN u CD? Gi

9X?M<\F@AnL�FaIML\An>Ug lS� ADH=9;Af|d9MevAEC�?��bAD9;LX?�N=?MQ=:=AE9rN=?M:b�]gMLcF¡L\9rNJ?�N=gMQwF@< L q1?ML q2

:=HgM>UgMH=?BZ[?BHdL σ Fa:JL\TU<;AD9;gKN=?BQ=:JAD9^CfehgML\FaL q1

|=AEC�N=?m>b<XF[gM�dF@CE?BZ[?BHdL LX<X?�F@:JLXTU<XAE9XgKN=?MQ=:=AD9^C evgmLcFaL q2

l�.�

Σi,c

�3>�+/� J ���9>-�<E0@���� 6��3>;%<L#%����#EB����+&>5=�,���+-$ ���!� @����3>;6.' EB,.6.@����Gi

Page 113: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � � ��� ���� � � ��� � ����� ����� � � ��� ����� �� � � �� � ����*����� ~U~U~

� �����YC � < � 0�+ ��-9.�>E-�8�0�+V ?B9^N=A � gM<X?BHdLX?B9OgMLcFaQR?M9ONJ?�HJT@L\<;?�NJgBZ[TUH=9;LX<\FaLXADTUH�9;TUHdL

�~,l N¥LX?BH=N=<;?�CE?KQ=<XTSIBgMN=g Gi

F¢>U?MI�CD?M9iL\<\FaH=9XAnL\ADT@H=9�N=?�IBTUZ[Z�:JL\FaL\AETUH�QwF@< LcF@HdLON=?PCfehgML\FaL^ADH=F@IMLXAE_?mL^Z]?MHwF@HdL^>U?M<X9O:=HYgmLcFaL^NJ?�NJgBQwF@< L �

7/l�� gML\?M<XZ[ADH=?M<iCD?KCDF@H=�dF@�@?�N=gB9;AD<;g K N=:yQ=<XTSIBgMN=g Gi,et

�q9lO� Q=Q=CEAD��:=?B<PCE?oL s gBT@< u Z[?oIBCDF@9X9;AD��:=?[N�ev?��bAD9;LX?BH=IM?�N�eh:=H 9X:=Q�?B< >bAE9X?M:=<�:=HJAD��:=? Si,et

9X:=< Gi,et

?mL K�

� l�A ?�<\F@Z[?BHJ?B< � Si��:=A=H8evTUxJ9X?B< >U?^QwF@9¤CE?B9¥gm>UgMH=?BZ[?BHdL\9�N=?�IMTUZ[Z�:JLcF¡L\ADT@H l @ TU:=9¥Z[TUHdL\<;?B<;TUH=9

FaCDTU<;9O��:=?�H=T@L\<;?�QJ<XTUx=C u Z[?�Q�?B:bL�9X?�<\F@Z[?BHJ?B< � CfehgMLX:=N=?�NJ?�Cfeh?m�bAE9;L\?MH=IB?�N�eh:=H�9X:JQR?M<;>SAD9;?B:=<F¢>@?BI�TUx=9X?M<;>aFaLXADTUHyQwF@< L\AE?BCDCE? �

� l�� gBZ[TUHdL\<X?M<�CfehgB��:=An>aF@CD?MH=IB?�?MHdL\<X?KCDF�IBT@H=N=AELXADTUH 1 N=:uL s gBTU< u Z[? l � lE~ ?mL^IB?MCDCD?�N=:uL s gBTU< u Z[? l� l 7 �

v9l�� gBZ[TUHdL\<X?M<�CfehgB��:=An>aF@CD?MH=IB?�?MHdL\<X?KCDF�IBT@H=N=AELXADTUH 2 N=:uL s gBTU< u Z[? l � lE~ ?mL^IB?MCDCD?�N=:uL s gBTU< u Z[? l� l 79l

� � k � � �YZ i ��PX`/NVc WYR7NT �a �SR=U �/T �Gi

A TUAE?BHdL Gi = (Qi, Σi, δi, Qi, � � ��� � , Qi,m) ?mL T = {τ1, τ2,..., τn}Cfeh?BH=9;?BZ�x=CE?PN=?B9�gM>UgMH=?BZ[?BHdLX9

N=?[IBT@Z]Z�:bLcFaLXADTUH ��:=A�QR?M<XZ[?MLXLX?BHdL�N8e�F@ImL\An>U?B<�CD?[Z[TbN u CD? Gi

l�V FYN=g � H=AELXADTUH{N=?]Cfeh?BH=9;?BZ�x=CE?]NJ?B9gm>UgBHJ?BZ[?BHdL\9�NJ?�IBT@Z]Z�:bLcFaLXADTUH T 9X?�xwF@9;?�9X:=<OIB?MCDCE?�N=?�Cfeh?BH=9;?BZ�xJCD?�N=?B9�gMLcF¡L\9�NJ?�N=gMQwF@<;L lFE C��YFF@:bLcF@HdL^N�ehgM>@gBH=?MZ]?MH�LX9�N=?PIMTUZ]Z�:JLcFaLXADTUH���:=?PN�ehgML\FaL\9ON=?PN=gMQwF@<;L lC Fa<�FaHwF@CDT@�UAD?�Fz>@?BI[CD?WI s FaQ=AELX<X? 3 |�CE?WZ]TSN u CD? Gi

Q�?B:bL L\<;?ogML\?MH=N=: N=?oCGFu_`F � T@H{9;:=AE>aF@HdLX?�

Gi,et = (Qi,et, Σi,et, δi,et, qi,in, Qi,m,et)F¢>U?BI

��

Qi,et = Qi ∪ {qi,in}�

�Σi,et = Σi ∪ T

��

Qi,m,et = Qi,m

�� CDF�_pTUH=ImL\ADT@H�N=?KL\<\FaH=9XAnL\ADT@H�?B9;L�N=g � H=AD?KIMTUZ[Z]?K9;:=AEL

~,l∀ σ ∈ Σi

?ML ∀ q ∈ Qi9;A δi(q, σ)! F@CDTU<;9 δi,et(q, σ) := δi(q, σ)

�7/l

∀ τi ∈ T ?ML ∀ qi ∈ Qi, ��� ����� | δi,et(qi,in, τi) := qi

lp� " "%$ � +,"� ��� �+,"8$ ��3��%+,"���) �*$ �$ "

Gi

35"8+ � ) ��) �2"�� ��� �� ����� �29�+ � ) ��) �7"�� ����� +," $ ��3��%+,"

Gi

� 3�$&"� �35"%)�" 1� �$ �9 35" 351 � �$�� q0

"� q2

� � �*) 9 351*) �!�,9�9 ��� 9 � �$������� 9;1!�)�"��! + "�� 9;"%$ '�+," 35"29 1%:�1��#"%$&"��! 9 35" ���*$ $ ) ��$ �����

T = {τ0, τ2}� " $ ��3��%+,"

��) �*$ �$ " 1� "�� 3�) "29� �7" ���7129;"��! 1 � �$�8+ ��) ��) �7"�� � �1�

y

Page 114: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~U~ 7 ������������� � � 5� ��� � � �7��� ������� � ��� ��

d

f

2

0

2q q3

1qq

d3

d 3

f 22f d2

3

f 3

������� � l � � � ��3��%+," ��) �*$ �$ " � ��� 1� "�� 3�)Gi

f3

0

2q q3

1qq

q d2

d3

d3

f3

f2f2 2d

τ0

τ2

i,in

������� � l � � � ��3��%+," ��) �*$ �$ " 1� "�� 3�)Gj,et

V evF@:JL\T@Z�FaLX?�gMLX?BH=NJ:�Q�TU9X9 u N=?^:=H[9X?M:=C£gMLcF¡L}N=?^N=gBQwFa<;L qi,in?ML}QwFa<¤IBTUH=9;gB��:=?MH�Lr:=H=?^9X?M:=CD?^NJ�dk

HwF@Z[AD��:=? L(Gi,et)l=q ?BCGF�Q�?B<;Z]?mL�N�evF@Q=QJCDAD��:=?M<iF@AE9XgBZ[?BHdLiCE?B9�Z]gmL s TSN=?B9iIMCGF@9;9XAE�S:J?B9�N=?KCDF�L s gBTU<;AD?

N=?PIBTUHdL\< s CD?PQwFa<i9X:=Q�?B< >bAE9XAETUH l

�� k � � � k j ��PX` � � WYN�b9PSWYR7NFT � _Jb N � b�� ` T%�/cfW � �K

� � H�N8e�F@QJQ=CDAE�S:J?B<�IB?M9YZ[gML s TSN=?B9M|iH=TU:=9jN=?M>@TUH=9yL\TU:bLYN8e�F@x�TU<;N�N=g � H=AE<�CD?�CGFaH=�dF@�U?�NJgB9XAE<XgIBTU<;<X?B9;QRT@H=NwF@HdL�F@: Z]TSN u CD?�gmL\?BHJN=: l�� ?oIB?�_`FaAEL¢|RH=TU:=9�F@CECDTUHJ9�gMLX?BH=NJ<X?ogB�dFaCD?BZ[?BHdLKCE?B9KCDF@H=�dF@�@?B9N=gB9;AD<XgM9 Ki,q

N=?WI s F@��:=?ogML\FaLKN=?�N=gBQwFa<;LPN=:�Q=<;TbIMgBN=g GiQwF@<�CfevF � TU:JL�N=?�CfehgM>@gBH=?MZ]?MHdL�NJ?�IBTUZWk

Z�:JLcF¡L\ADT@H τqIBT@<X<X?M9XQ�TUH=NwFaH�L l�� ev:JH=?]Z]F@H=A u <;?�_pTU<XZ[?BCECD? ∀ q ∈ Qi, ��� ����� |�CD?WCDF@H=�dFa�U?�gMLX?BH=NJ: N=?

Ki,q?B9 L τqKi,q

|£Fz>@?BI�

τqKi,q := {s | s = τqs′ T +

s′ ∈ Ki,q}

C F@<^IBT@H=9XgM�S:J?BHdL¢|�CD?KCDF@H=�dF@�@?KN=gB9;AD<XgK�@CDTUxwFaC�N=:yZ]TSN u CD? Gi,et?B9 LON=TUH=H=g�QwF@<

∪q∈Qi, ���������� τqKi,q

Page 115: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � � ��� ���� � � ��� � ����� ����� � � ��� ����� �� � � �� � ����*����� ~U~Xq

C Fa<O9;ADZ[Q=CDA � I¢F¡L\ADT@H�|�H=TU:=9^H=T@LXTUH=9^N=gM9XTU<;Z�F@AE9 ∪q∈Qi, ���������� τqKi,qQ=F@< K

l

� � k � � � � i ��W cIPX`/NVUm`�T � ��N c ��aK` �Xe�WYc ` � � �VN�W � ��`Si,et

C :=AD9;��:=? CfevF@:JL\T@Z�FaLX? Gi,etF@NJZ]?mL�:=H 9X?M:=CKgML\FaLyN=?�N=gMQwF@<;L � gML\FaLyADH=AnL\ADF@C � |}F@CDTU<;9uN�evF@Q=< u 9

� ���nz�x F � ADC�?m�bAE9;L\?�:=H�9X?M:=C�9;:=Q�?B<;>SAE9X?B:J<�H=T@LXg Si,et|�LX?BC��S:J? ∀ q ∈ Qi, ��� ����� , L(Si,et/Gi,et) = K9���"� .9;"%)5+,"%$&"��! .9��

K ?M9;L�IBTUHdLX< s CDF@x=CD?�QwF@<i<\FaQ=QRT@<;L � L(Gi,et)l

� � k � � ��� �A� c ` �Xe1b9PSWYR7N#a�b �XPSWJ`/_ _J`C :=AD9;��:=?�C ev?MH=9X?MZ�x=CD?oN=?M9�gm>UgBHJ?BZ[?BHdL\9 T ?B9;L�ADH=F@IBIM?B9X9;ADx=CE?�Fa: 9;:=QR?M<;>SAD9;?B:=< Si

|�H=TU:J9�F@CECDTUHJ9N=g � H=AE<�CGF�_pT@H=IMLXADTUH�N=?�Q=<XT � ?MIMLXADTUH Pi

�S:JA�QR?M<XZ[?MLiN8evTUxJ9X?B< >U?M<O9;?B:=CE?BZ[?BHdL^CfehTSIBIB:J<X<X?MH=IB?KNJ?B9^gM>@gmkH=?MZ]?MHdL\9�N=?�CfevF@CDQ s F@xR?mL Σi �

L\T@:=9�CD?M9�gm>UgBHJ?BZ[?BHdL\9oN=? T 9;?B<;TUHdLoIBTUH=9;ADN=gM<XgM9�H=TUHbklTUx=9;?B<;>aF@xJCD?B9 lq ?mLXL\?K_pTUHJIML\AETUHy?B9 L�NJTUH=H=gM?�IMTUZ[Z]?K9;:=AEL

A TUAEL Pi : Σ∗i,et −→ Σ∗

iL\?MCDCE?K�S:J? ∀ σ ∈ Σi

?ML ∀s ∈ Σ∗i :

Pi(ε) = ε

Pi(sσ) =

{

Pi(s)σ9XA σ ∈ Σi

Pi(s)9XA σ ∈ T

A TUAnL Si : Pi(Σ∗i,et) −→ Γ := {γ ∈ Pwr(Σi,et) : Σi,et,u ⊆ γ} � LX?BCK��:=? ∀ s ∈ Σ∗

i,et|

Si(Pi(s)) = Si,et(s)l£V F � �U:=<;? � lrv Z]T@H�LX<X?KCE?�_pTUH=IMLXADTUHJH=?BZ[?BHdLO?BHjxRT@:=IBCE?P_p?M<XZ[gB?KN=:Y9X:=Q�?B< >SAnk

9;?B:=< SiF¢>U?BI�CD?KQJ<XTSIBgBNJg�gmL\?MH=N=: Gi,et

l

G

S

P

s

S

i, et

i

(P(s))i

������� � lrv��Gi,et

���*) � +,1 ��:�"��8+,"�9%) ��"��0: �,9;"%) �Si

: �"� + � - ��� �� ����� 35" �������/"��� "�����P

� evF@Q=< u 9oCGF � �U:=<X? � lrv |�H=TU:=9WIMTUH=9;L\FaL\T@H=9W��:=?yCfehgML\:JN=?�N=?�Cfeh?m�bAE9;L\?MH=IB?�NJ? SiH=TU:=9o<\FaZ u H=?

F@:yIBF@9iN=?PCfehgMLX:=N=?KN=?PCfeh?m�bAE9;L\?MH=IB?PN�eh:=Hj9X:=Q�?B< >SAD9X?M:=<^TUx=9;?B<;>aF@HdLOQwF@< L\AE?BCDCE?BZ[?BHdL�:JHYQ=<;TbIMgBN=g l£V ?B9IMTUH=N=AnL\ADT@H=9�N�eh?m�bAD9 L\?MH=IB?�N=?�IB?P9X:=Q�?B< >SAD9X?M:=<O9XTUHdLON=g � H=AD?M9ON=F@H=9^CD?�L s gBTU< u Z[?P9X:=An>@FaH�L l� �%� R � $ � ` � � k1�tT�� b1a � $/c � ���;[ ��� � � � �7k�� ��0+ "#"��,9� " ) � ) �!� !�)�" 9%) ��"��0: �,9;"%) �

Si

� "%+�!�)�"L(Si/Gi,et) = K

9���"� �9;"%)5+,"%$&"��! �9��7'( �

K"29� �����! "�76*+ � '�+," � �$� � ��� �!���� 0%

L(Gi,et) .:��

Σi,et,u

$&����$&%3>-����+&����+ � J �3�9>-�<E @9� �<6.�*> %<L#%����#E �3��+&>;(��F=8,#�#+&$��#��� @����3>

Page 116: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~U~ � ������������� � � 5� ��� � � �7��� ������� � ��� ��

/ �K

"29� ��'%9;"��0:�� '�+," � �$� �#��� �!���� �%L(Gi,et)

"� Pi

��

V ?uL s gBTU< u Z[? � lE~ ?M9;L[N=TUH=Iu>S<XF@Ai9XA�CE?B9WN=A � gM<X?MH�LX?B9[IBTUHJN=AELXADTUH=9�N=?B9oN=?M:b� L s gBTU< u Z[?B9o9XTUHdLgB��:=AE>aF@CE?BHdL\?M9 l

�� k � � � � � � ��WJe�b _Y`/N�Um`yT�`/c UmR7N�TVW PSWJR7NVc1

q ?mLXL\?�gM��:=AE>aF@CE?BH=IM?��S:JA�IBTU<;<X?M9XQ�TUH=N F@: CD?MZ]Z[? � l|q |¥HJgBIB?M9X9;AEL\?�LXTU:JLWN�evF@x�TU<XN N8evAEH�LX<XTSN=:=AE<X?N=?B:b�YFa:JL\<;?B9^gB��:=An>@FaCD?BHJIB?B9M|£�S:JA�9XTUHdLOCD?M9iCD?BZ[Z[?B9 � ln~ ?ML � l�79l�@`�� � ` � � Z

∪q∈Qi, ���������� Ki,q,et = ∪q∈Qi, ���������� Ki,q,et

j ��� R7N�cOP �Sb�PSWJR7NC TU:=<^N=gBZ[TUHdL\?M<^CfehgB�dF@CEAELXg@|SH=TU:=9OF@CECDTUH=9rN=gBZ[TUHdL\<;?B<iN=?M:b�jADH=IMCD:=9;ADTUHJ9

�~ml

∪q∈Qi,dpartKi,q,et ⊆ ∪q∈Qi,dpart

Ki,q,et

79l∪q∈Qi,dpart

Ki,q,et ⊆ ∪q∈Qi,dpartKi,q,et

~ml∀q ∈ Qi,dpart

| Ki,q,et ⊆ ∪q∈Qi,dpartKi,q,et ⇒ ∪q∈Qi,dpart

Ki,q,et ⊆ ∪q∈Qi,dpartKi,q,et

l79l

s ∈ ∪q∈Qi,dpartKi,q,et ⇒ ∃ q ∈ Qi,dpart

L\?MC���:=? s ∈ Ki,q,et

⇒ ∃ u ∈ Σ∗i,et

L\?MC��S:J? su ∈ Ki,q,et

⇒ su ∈ ∪q∈Qi,dpartKi,q,et

⇒ s ∈ ∪q∈Qi,dpartKi,q,et

V ?M9�NJ?B:b�yAEZ]QJCDADIBFaL\AETUH=9�9XTUHdL^>S<\F@AE?B9^N=TUHJI�C evgM�dF@CEAEL\g�?B9 LO>@gB<;A � gM? l ♦

�@`�� � ` � � k

∀q ∈ Qi, � � � � ��� , τqKi,q = τqKi,q

j ��� R7N�cOP �Sb�PSWJR7N� eh:=H=?P_`F � TUHy9XADZ[ADCDF@AD<;?@|�H=TU:J9�FaCDCDT@H=9�Z[TUHdL\<X?M<i��:=? ∀q ∈ Qi, ��� ��� � �~ml

τqKi,q ⊆ τqKi,q

79lτqKi,q ⊆ τqKi,q

~mls ∈ τqKi,q ⇒ s = τqs1

Fz>@?BI s1 ∈ Ki,q

⇒ ∃u ∈ Σ∗i,et

LX?BC���:=? s1u ∈ Ki,q

⇒ τqs1u ∈ τqKi,q

⇒ s = τqs1 ∈ τqKi,q

Page 117: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � � ��� ���� � � ��� � ����� ����� � � ��� ����� �� � � �� � ����*����� ~U~ �

7/ls ∈ τqKi,q ⇒ u ∈ Σ∗

i,etLX?BC���:=? su ∈ τqKi,q

⇒ su = τqs1u ∈ τqKi,qF¢>U?BI s1u ∈ Ki,q

⇒ s1 ∈ Ki,q

⇒ τqs1 ∈ τqKi,q

⇒ s = τqs1 ∈ τqKi,q

V ?B9^N=?M:b�jADZ[Q=CEADI¢F¡L\ADT@H=9}9XTUHdLO>b<XF@AD?M9iN=TUH=IPC evgM�dF@CDAnL\g�?B9;L^>@gB<XA � gB? l ♦

��`�� � ` �� �K

"29� �����! "�76*+ � '�+," � �$� �#��� �!���� 5%L(Gi,et)

9�� "� 9;"%)5+,"%$&"��! 9��∀q ∈ Qi, ������� ���

�Ki,q

"29� �����! �76*+ � '�+,"� �$� �#��� �!���� G%

L(Gi,q)�

j ��� R7NVcIP �Sb�PSWJRQNC T@:=<^N=gBZ[TUHdL\<;?B<^CfehgB��:=An>@FaCD?BHJIB?@|JH=TU:=9OF@CECDTUH=9rN=gBZ[TUHdL\<;?B<iN=?M:b�jADZ[Q=CDAEI¢FaLXADTUHJ9

�~ml

K IBTUHdL\< s CGFax=CD?OQwF@<�<XF@Q=Q�TU<;L � L(Gi,et) ⇒ ∀q ∈ Qi, ��� ����� | Ki,q?M9;LiIMTUHdL\< s CGF@x=CE?�QwFa<

<\FaQ=QRT@<;L � L(Gi,q)79l

∀q ∈ Qi, � � ��� � | Ki,qIBT@H�LX< s CDF@x=CE?�QwF@<^<\FaQ=QRT@<;L � L(Gi,q) ⇒ K ?M9;L�IBTUHdLX< s CDF@x=CD?KQ=F@<

<\FaQ=QRT@<;L � L(Gi,et)~,l

s ∈ Ki,q ⇒ τqs ∈ τqKi,q

⇒ τqs ∈ τqKi,q

� CE?BZ[Z]? � l 7 �⇒ τqs ∈ ∪q∈Qi, ���������� τqKi,q

⇒ s ∈ K� CD?BZ[Z[? � l�7 �

A TUAEL σ ∈ Σi,et,uLX?BC���:=? τqsσ ∈ L(Gi,et)

lK IBT@H�LX< s CDF@x=CE?�QwF@<^<\FaQ=QRT@<;L � L(Gi,et) ⇒ τqsσ ∈ K

⇒ τqsσ ∈ ∪q∈Qi, ���������� τqKi,q

� CE?BZ[Z]? � lE~ �⇒ ∃q ∈ Qi, ��� ����� L\?MC���:=? sσ ∈ Ki,q

7/l∀q ∈ Qi, ��� ��� � | Ki,q

IMTUHdL\< s CGF@xJCD?�QwFa<O<XF@Q=Q�TU<;L � L(Gi,q)

⇒ τqKi,q = τqKi,q

� CE?BZ[Z]? � l 7 � ?M9;LOIBT@H�LX< s CDF@x=CE?�QwF@<^<\FaQ=QRT@<;L � L(Gi,et)QJ:=AD9;�S:J? ∀q ∈ Qi, � � ��� � | τq

?M9;L�9X:=Q=Q�TU9;g�:JHYgm>UgBHJ?BZ[?BHdLKF@:bL\TU<;AD9XgKQ=F@<iN=gM_`Fa:JL

⇒ ∪q∈Qi, ���������� τqKi,q?B9 LOIBTUHdL\< s CGFax=CD?KQwFa<i<\F@Q=Q�TU< L L(Gi,et)

� � k � � � � � � �VW e1b1_Y`/N�Um`yT�`/c UmR7N�TVW PSWJRQN�c2

��`�� � ` ����K

"29� ��'%9;"��0:�� '�+," � �$� �#��� �!���� 0%L(Gi,et)

"� P9�� "� �9;"%)5+,"%$&"��! �9��7'

( �∀ s ∈ Ki,q

"� ∀s′ ∈ Ki,q′

"%+ 9 !�)�"s = s′

�∀σ ∈ Σi,c

8 '� �

Σi,c

�3>�+/� J ���2>��#E @����<6.�3> %#L�%3���<EB����+ > =�,���+-$ ���!� @9� �*> 6�'�EB,.6.@3� �Gi

Page 118: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~U~Xv ������������� � � 5� ��� � � �7��� ������� � ��� ��

sσ ∈ Ki,q

"� s′σ ∈ L(Gi,q′) ⇔ s′σ ∈ Ki,q′

j ��� R7N�cOP �Sb�PSWJR7N@ TU:=9}F@CECDTUH=9�Z�FaADHdL\?MHwF@HdL¤gML\F@x=CEAD<�:JH=?^<X?BCDFaL\AETUH�N�ehgB��:=An>aF@CD?MH=IB?i?MH�LX<X?^CGF�IMTUH=N=AnL\AETUH 2 N=:oL s gBTak

< u Z[? � ln~ ?MLPC evTUxJ9X?B< >aF@x=ADCEAELXg�N=? Kl @ T@LXTUH=9K��:=? K ?B9;L�TUxJ9X?B< >aF@x=CD?�QwF@<K<\FaQ=QRT@<;L � L(Gi,et)

?ML

P | 9�� "� .9;"%)5+,"%$&"��! .9���

~ml(∀s,s′ ∈ Σ∗

i,et)(P (s) = P (s′))(∀σ ∈ Σi,et,c) ⇒ s ∈ K | s′ ∈ K ?ML sσ ∧ s′ ∈ K ?ML

s′σ ∈ L(Gi,et)|wF@CDT@<X9 s′σ ∈ K

�79l CfehADHd>U?M<X9;?�?M9;LO>S<\F@A lA :JQ=QRT@9XTUH=9^��:=? K ?M9;LOTUx=9;?B<;>aF@xJCD?KQwF@<^<XF@Q=Q�TU<;L � L(Gi,et)

?mL Pl

A T@AEL s ∈ Ki,q?mL s′ ∈ Ki,q′

LX?BC���:=? s = s′l

A A sσ ∈ Ki,q?ML s′σ ∈ L(Gi,q′)

|=Z[TUHdL\<;TUH=9i��:=? s′σ ∈ Ki,q′l

� eh:=H=?�QwF@< L s ∈ Ki,q ⇒ τqs ∈ τqKi,q = τqKi,q

� CD?MZ]Z[? � l�7 �⇒ τqs ∈ ∪q∈Qi,dpart

τqKi,q = K� evF@:JLX<X?PQwF@< L s′ ∈ Ki,q′ ⇒ τq′s ∈ ∪q∈Qi,dpart

τqKi,qC :=AE9X��:=? s = s′ F@CDT@<X9 P (τqs) = P (τq′s′)

L�< sσ ∈ Ki,q ⇒ τqsσ ∈ ∪q∈Qi,dpartτqKi,q = K

⇒ τq′s′σ ∈ ∪q∈Qi,dpart

τqKi,q = K� Q=:JAD9X��:=? K ?B9;LOTUxJ9X?B< >aF@x=CD? �

⇒ τq′s′σ ∈ ∪q∈Qi,dpart

τqKi,q

� CD?MZ]Z[? � ln~ �E C�?BHj<XgB9;:=CELX?P�S:J?

τq′s′σ ∈ τq′Ki,q′ = τq′Ki,q′ ⇒ s′σ ∈ Ki,q′

� IBTUH=NJAEL\AETUH 7 N=:�L s gMTU< u Z]? � ln~ � l

� FaADHdL\?MHwF@HdLO9X:=Q=Q�TU9;TUH=9^CGFWIBT@H=N=AELXADTUH 7 >@gB<XA � gB?�?ML^Z[TUHdL\<;TUH=9^CfehTUx=9;?B< >@Fax=ADCEAEL\g�N=? Kl

A T@AEL s ∈ K ?mL s′ ∈ K L\?BCE9i��:=? ∀σ ∈ Σi,et,c| sσ ∈ K

l� T@H�LX<XTUHJ9O��:=?�9XA s′σ ∈ L(Gi,et)

F@CETU<X9 s′σ ∈ Kl

� eh:=H=?�QwF@<;L sσ ∈ K = ∪q∈Qi,dpartτqKi,q ⇒ ∃u ∈ Σ∗

i,etL\?BC���:=? sσu ∈ ∪q∈Qi,dpart

τqKi,q

⇒ ∃q ∈ Qi,dpartL\?MC���:=? sσu ∈ τqKi,q

⇒ sσu = τqs1σu ∈ τqKi,q ( F¢>U?MI s = τqs1)

⇒ s1σu ∈ Ki,q ⇒ s1σ ∈ Ki,q� ?PZ Z]? s′ ∈ K = ∪q∈Qi,dpartτqKi,q ⇒ ∃v ∈ Σ∗

i,etL\?MCP�S:J? s′v ∈ ∪q∈Qi,dpart

τqKi,q

⇒ ∃q′ ∈ Qi,dpartL\?BCP��:=? s′v ∈ τq′Ki,q′

⇒ s′v = τq′s2v ∈ τq′Ki,q′ (F¢>@?BI s′ = τq′s2)

⇒ s2v ∈ Ki,q′ ⇒ s2 ∈ Ki,q′

LKH F s1 = s2QJ:=AD9;�S:J? P (s) = P (s′)

l C F@<�IMTUH=9;gB��:=?BHdL�?ML�9X?MCDTUH�CDF]IMTUH=N=AnL\ADT@H 7 N=:YL s gMTU< u Z]?� lE~

s2σ ∈ Ki,q′l=� TUH=I τq′s2σ = s′σ ∈ τq′Ki,q′

� ��� "��s′σ ∈ K

l♦

Page 119: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� ��� � � � � ��� ��� ��� � � ��� ��������� � ���� � ��� ~U~Sx

V ?B9iCE?BZ[Z]?M9 � ln~ | � l�7 | � lrq ?mL � l � HJTU:=9^TUHdLiN=TUHJI�Q�?B<;Z]AE9rN=?PN=gMZ]T@H�LX<X?M<�CfehgB��:=An>@FaCD?BHJIB?�?MH�LX<X?CE?B9iIBT@H=N=AELXADTUHJ9iN=?B9iL s gBTU< u Z[?B9 � ln~ ?mL � l 7 |=?MLON=TUHJI�NJ? � :J9;L\A � ?B<^H=TaL\<X?KQJ<XTUQ�TU9XAnL\AETUH l

� ��� � ( . � ��� �-! �"! # � ��*�,���*18 +�, �O( � 8 � . � �"!

� F@HJ9�CGF^9X?MIMLXADTUH�Q=<XgMIBgBNJ?BHdL\?�HJTU:=9¥F¢>@TUH=9�NJgBZ[TUHdL\<Xg�Cfeh?m�bAE9;L\?MH=IB?�N�eh:=H�9;:=QR?M<;>SAD9;?B:=<�:=H=AE�S:J?@|¡IB?��:=AS?BHdL\<XFa�GHJ?rCfeh?m�bAE9;L\?MH=IB?rN�ev:JHoF@:JL\T@Z�FaLX?�NJ?r9XQ�gBIMA � IBFaL\AETUH�:=HJAD��:=?rQ=F@<�Z[TbNJ? l'C F@<¥F@ADCECD?B:J<X9B|zN=F@H=9CE?�I s F@Q=AnL\<;?WQ=<XgMIBgBNJ?BHdL�HJTU:=9�F¢>UTUH=9KLX<\F@AnL\g�CE?WZ]gMI¢F@H=AE9XZ[?�N=?WIMTUZ]Z�:JLcFaLXADTUHt?BHdL\<;?[CE?B9KZ[TbN u CD?M9N=?M9iQ=<XTSIBgMN=gB9O?BHyCE?B9igMLX?BH=N=F@HdL�F � H�N=?PN=gMLX?B<;Z]AEH=?B<�CE?B:=<;9igML\FaL\9iIMTUZ]Q=FaL\AEx=CD?M9rN=?P<\FaIBIBT@<XN=?MZ]?MH�L l

� F@HJ9�CE?KZ Z]?P?B9;Q=<XAnLOH=TU:=9OF@x�TU<XNJTUH=9^NwF@H=9OIB?mLXLX?�9;?BIMLXADTUHjCD?KZ[gBIBF@H=AE9XZ[?KN=?�IMTUZ[Z�:JLcF¡L\ADT@H?MH�LX<X?�CD?B9�Z]TSN u CD?B9^N=?�9XQ�gBIMA � IBFaL\AETUH=9 l E C�9BevF@�UAE<\F]NJ?�<X?MI s ?B<;I s ?B<KCE?B9OgML\FaL\9 � QwF@< L\AE<ONJ?B9X��:=?MCD9�IM?B9Z[TbN u CD?M9�NJTUAE>@?BHdL LX<X?uAEH=AELXAGF@CEAD9;gB9PF � H N=?u�dF@<XF@HdL\AE<�:=HJ?uIBT s gB<X?MH=IB?�?MHdL\<X?�CGFYNb�bH=F@Z]AE��:=?uIBT@:bk<XF@HdL\?PN=:tQJ<XTSIBgBNJg�?mL�CE?B9OF@IMLXADTUHJ9ONJ?�IMTUHdL\< s CD?P9XTU: s F@AELXgB?M9 � CD?B9OF@ImL\AETUH=9^N�ehADHdL\?M<XN=AEIML\AETUHyTU:jN�e�Fa:bkLXTU<XAE9\FaLXADTUH � l C :JAD9X��:=?WI s F@��:=?WZ]TSN u CD?�NJ?�9XQ�gBIMA � IBFaL\AETUH�?B9 L�F@9X9;TbIMADg � :JH{Z[TSN u CE?�N=: Q=<;TbIMgBN=ga|:=HYI s F@H=�@?BZ[?BHdL�NJ?�Z[TbNJ?�NJ?�_pTUH=ImL\AETUH=H=?MZ]?MH�LOQ�?B<;Z]?mL�N8evTUxbL\?BHJAD<ON=?B9ONJ�SHwF@Z[AD��:=?M9�N=AE9;LXADH=ImL\?B9 l@ evTU:Jx=CDAETUH=9�QwFa9[��:=?yH=T@:=9oN=?M>@TUH=9]F@IMLXAE>U?M<oI s F@��:=?jZ]TSN u CE?uN=?y9XQ�gBIMA � IBFaL\AETUH N=?BQJ:=AD9o:=H gML\FaLQ�?B<;Z]?mLXLcFaH�L�N�e�F � :=9;LX?B<PCD?M9PF@IMLXADTUH=9�N=?WIBTUHdLX< s CE?WIBTUZ[QwFaLXADx=CE?B9�F¢>@?BIoCGFuH=T@:J>U?MCDCD?�NJ�SHwF@Z[AD��:=?WN=:Q=<;TbIMgBN=g l8V ?�Z]gMI¢F@H=AE9XZ[?�NJ?�IBT@Z]Z�:bLcFaLXADTUHy:JLXADCDAE9XgPQ=<;gBIBgMN=?BZ[Z[?BHdLKQ�TU:=<OCD?B9�Z]TSN u CD?B9ON=?M9�Q=<;TakIMgBN=gM9 � I s F@Q=AnL\<;? 3 � H=?WQ�?B:JLPQ=F@9 L\<;?oF@Q=Q=CEAD��:=g�Q�TU:=<KCE?B9KZ[TbN u CD?M9�N=?W9;QRgMIBA � I¢FaLXADTUH l8� H ? � ?mL¢|CETU<X9;�S:8evAEC8�jF]:=HJ?�IMTUZ]Z�:JLcFaLXADTUH�N8ev:=HtZ]TSN u CE? Gi

� :=HtZ[TbN u CD? Gj|£CGFWL\<\FaIB?P�UgBHJgB<XgM?�NwFaH=9 Gi

Q�?B:JLoIMTUZ[QRTU< L\?M<WN=?B9ogM>@gBH=?MZ]?MHdL\9���:=Ai9;TUHdL[ADHdL\?M<XN=AnL\9 � QwF@< L\AD<WNJ?jC evgmLcFaL�ADH=AnL\AGFaC�N=?yCDF�9XQ�gBIBA k� IBFaL\AETUH Ej

|�?ML�N=TUHJI]��:=A}H�evF@Q=QwFa<\F@AE9X9X?MHdL�QwFa9�NwFaH=9�IM?ML;L\?�9;QRgMIBA � I¢FaLXADTUH l�� evT + CfehADZ[Q�TU9X9;ADx=AECDAELXgN�eh:JLXADCDAE9X?M<�CD?KZ[gBIBF@H=AD9;Z]?�N=?P9X:=An>bA�NJ:YQ=<;TbIMgBN=gPQ�TU:=<iCDFo9;QRgMIBA � I¢FaLXADTUH lA TUAnL Ei = (Xi, Σi, ξi, xi,0, Xm,i)

CDFW9XQ�gBIBA � I¢F¡L\ADT@HYFa9X9XTSIBAEgB?�F@:yQ=<;TbIMgBN=g

Gi = (Qi, Σi, δi, qi,0, Qi,m)l E H=AnL\ADF@CD?MZ]?MH�LB|bCE?KZ]TSN=? 1 ?M9;LO9X:JQ=QRT@9Xg L\<;?P9XgBCE?BImL\ADT@H=H=gKN=TUHJI�C e�Fa:bk

LXTUZ�F¡L\?WN=?oQ=<;TbIMgBN=g G19X?oL\<;TU:J>U?[NwF@HJ9�9;TUH gmLcFaL�AEH=AELXAGF@C q1,0

l�V ?[Z]TSN u CE?�N=?[CGF�9XQ�gBIMA � IBFaL\AETUHE1

9;?[LX<XTU:J>@?]gM�dF@CE?BZ[?BHdL�F@IMLXAE>@g@|�9XTUH Z]TSN u CD?W?B9 L�N=F@H=9�CfehgMLcF¡LPADH=AnL\AGFaC x1,0

l�� CfehTbIMIB:=<;<X?MH=IB?[N=?C evgm>UgBHJ?BZ[?BHdLPN=?oIBTUZ[Z�:JL\FaL\AETUH α1,j

|�CD?�Z]TSN u CE? G1,et9X?M<\FyIBTUHJN=:=AEL�>U?B<;9P9XTUH gML\FaLPADH=F@IMLXAE_ q1,in� >UTUAE<iI s F@Q=AnL\<X? q � l£V FW9;QRgMIBA � I¢FaLXADTUH E1

H=? � TU:wF@HdLOQ=CD:J9ONJ?�< s CD?a|=9XTUHYZ]TSN u CD?�N=T@AEL LX<X?PgMLX?BH=N=:QwFa<O:JHYgmLcFaL�ADHwFaIML\An_ x1,in

FaLXLX?BADHdL^QwFa< α1,j

l�q ?ML�gMLcF¡L�9;?B<\FoIBT@H=9X?M<;>Ug � :=9X��:�e � C evTSIBIM:=<X<;?BH=IM?�N�eh:=Hgm>UgBHJ?BZ[?BHdL�N=?�IBT@Z]Z�:bLcFaLXADTUH αk,1

� CE:=A�QR?M<XZ[?ML;LcF@HdL�F@ADHJ9XA�N=?�<X? � TUADH=NJ<X?P:=HtgmLcFaL x ∈ X1

l � FaQbkQ�?BCETUH=9}��:=?�CETU<X9;�S:J?�CE?�Q=<;TbIMgBN=g G1

9X?OL\<XT@:J>U?�NwF@H=9�:=H�gmLcFaL q ∈ Q1 6= q1,in|�CD?B9�F@:JLX<X?M9�Z[TbN u CD?M9

Gj

�j 6= 1 � 9XTUHdLO_pTU<XIMgBZ[?BHdLOQ=CDT@H=�UgB9^NwFaH=9�CE?B:=<;9^gMLcF¡L\9OADHwF@ImL\An_p9i<X?B9;QR?MIMLXAE_p9 l£� ?�_`F � TUHj9XADZ[ADCDF@AD<;?@|

CETU<X9;�S:J?�CGF�9XQ�gBIBA � I¢F¡L\ADT@H E19;?�L\<XT@:J>U?�N=F@H=9i:=H�gmLcFaL x ∈ X1

|JCE?B9�9;QRgMIBA � I¢FaLXADTUHJ9iF@:JLX<X?B9r�S:J? E1

.� � J (��96.( =8�k

0�'�(.����'.+ 48+&$-�;6.( H�%3$-�3��+ 6.�j=���$ ��� > �.>�+-@#E � ����'.+ �9�#>->-��$��9��$�����'9>-( �3'�$&>�EB,.6.�3> � L ����+ 6.� $-�#L����9( $

6����2>;� � EB,.6.�<( �9( +&(���� �

Page 120: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~U~Xz ������������� � � 5� ��� � � �7��� ������� � ��� ��

9X?PL\<XT@:J>U?MH�L�NwF@H=9OCD?M:=<X9^gmLcFaLX9OAEHwF@ImL\AE_p9 l£q ?�Q s gBHJTUZ u H=?�N=?�IMTUZ[Z�:JLcF¡L\ADT@Hu<X?M9;L\?�H=g¢FaH=Z]T@ADH=9i:=HQ=<XTUxJC u Z[?oH=TU:J>@?¢F@: l�� H ? � ?mL¢|�9XA�CD?oZ[TbN u CD?WN=: Q=<XTSIBgMN=g Gi

QRTU9;9 u N=?�Q=CE:=9XAE?B:=<;9�gmLcFaLX9�NJ?�<\FaImkIBTU<;N=?BZ[?BHdL � N=gBQwFa<;Li?mL � TU:�<X?MLXTU:=< � |SCGF�9;QRgMIBA � I¢FaLXADTUH�IBTU<;<X?B9;QRT@H=NwF@HdL\?�N=TUAEL�Q�TU9X9;gBN=?M<igB�dF@CE?BZ[?BHdLQ=CD:=9;AD?M:=<X9�gML\FaL\9�N=?oN=gBQ=F@<;L�?ML � TU:{N=?]<;?MLXTU:=<�F � H{N=?]9;:=AE>S<;?]IMTU<X<;?BIMLX?BZ[?BHdL�CfehgM>UT@CD:JLXADTUH N=?[9XTUHZ]TSN u CE?K?ML^QwFa<OIMTUH=9;gB��:=?BHdL�F@�UAD<rIBTUHd>U?MHwF@x=CE?BZ[?BHdL�9X:=<^IB?MCD:=A k¦IMA l

� ?OIB?^_`F@AnL¢|UCE?B9}N=?B:S�[9X?BImL\AETUH=9�IBAnk¦F@Q=< u 9}Q=<XgM9X?MH�LX?BHdLi:=HJ?�Z[gML s TbNJ?^_pT@<XZ[?BCDCE?�Q�TU:=<}CGFKN=gmL\?B<;Z]A kHwFaL\AETUHoN=?B9�gML\FaL\9}N=?^<XF@IBIMTU<XN=?MZ]?MHdL�NJ?�CDF�9XQ�gBIBA � I¢F¡L\ADT@H[HJTU:J>U?MCDCE?BZ[?BHdL�F@IMLXAE>UgM?^QwF@<}CfehTbIMIB:=<;<X?MH=IB?N�ev:JHtgM>@gBH=?MZ]?MHdL�N=?PIMTUZ]Z�:JLcFaLXADTUH l

� �YC �~B D -9>E-F2�A 26< ��>K.9-F264 � 032 �=? A}2�A � � � <=5Q8���5 >E-98�0�+ �Ej

� TU:JL�N�e�FaxRTU<;N�CD?M9�Z[TbN u CD?M9�N=?�9XQ�gBIBA � I¢F¡L\ADT@H=9�N=?�I s F@��:=?WZ[TbNJ?�N=TUAn>U?MH�L L\<;?�gmL\?BHJN=:=9PF � HN=?P�dF@<\FaH�LXAD<iCDF�9XgBCE?BImL\ADT@HjN8ev:=Hj9X?M:=C�Z]TSN=? � CGF�_pT@AD9 lA T@AELiCDFo9;QRgMIBA � I¢FaLXADTUH Ei = (Xi, Σi, ξi, xi,0, Xm,i)

|w9;TUHYZ[TSN u CE?�gMLX?BH=N=:j?B9 L �)" C @ I q$��

Ei,et = (Xi,et, Σi,, ξi,et, xi,0,et, Xm,i,et)F¢>U?BI

�Xi,et = Xi ∪ {xi,in}

��

Σi,et = Σi ∪ Σ′i �

�xi,0,et =

{

x1,09;A i = 1

xi,in9;A i 6= 1�

Xm,i,et = Xm,i

�� V Fo_pTUHJIML\AETUH�N=?KL\<XF@H=9;AEL\AETUH ξi,et

?B9 L�NJg � H=AE?PIBTUZ[Z]?K9;:=AEL�

~ml∀ x ∈ Xi

?ML ∀σ ∈ Σi9;A ξi(x, σ) ?��JAE9;LX?�FaCDTU<;9 �

ξi,et(x, σ) := ξi(x, σ)79l

∀ x ∈ Xi

� Q=F@<;LXAD<�N=:J�S:J?BC�CfehgM>@gBH=?MZ]?MH�L�N=?PIBT@Z]Z�:bLcFaLXADTUH αi,jQ�?B:bL L\<;?��@gBH=gM<Xg

ξi,et(x, αi,j) := xi,inq�lOV evgmLcFaLOFaL;L\?MADHdL^QwF@<^CGF�LX<\F@HJ9XAELXADTUH ξi,et(xi,in, αj,i)?B9;L � N=gMLX?B<;Z]AEH=?B< l

� "%$ �$�#!�)�" ����*) 9 9%) � �!�;9;"�� ��� 9&3 �$� 9 + � 351%$ ��� 9� �#�$ "����� !�) ����� �29 + � �51��#1�� �$ "����� 35" + �!9;1!�)�"�� �2" 3� 1%:�1��#"�$&"��! 9

s3 �$� 9 +," ��� � �214351 9%) ��"��0: �,9;1

Si/Gi

��+ 1%:�1��#"%$&"��! 35" ���*$ $ ) ��$ �����αi,j

9 "29� ������3�) � &���"� " 9;1!�)�"�� �2"

s��"%) ���*$ �!���� "�� ) � "�� 9;"%$ '�+,"&3� 1%:�1��#"%$&"��! �9���*$ $ ) � 9!"��! "�7" +,"29 $ ��3��%+,"29

35"29 ��� � �21435129Gi

"� Gj

+ 3 �$� 9�+," � �*9 ��� ��+ "#"��,9� " 35"29 �7"2929 �*) � �2"29 ���*$ $ ) �#"29 - � � �$� 9 �2" � �*9���+,"���*$ �!���� "%$&"��! 35129�� �21 35"

Gj

351 ��"�� 3 35" + � �#� �2"s

�51��#1��712" 3 �$� 9 +," ����� �214351 9%) ��"��0: �,9;1Si/Gi

�� �*) �(351� "��%$ � �#"�� + 1� �$ 35" 351 � �$�� 35" + � 9 ��1���� ) � �$ ������� ��+ "29� 3 ��� � �#1��2"2929 �$� �7" 35" � ��+ �%)5+,"�� ��

Σ′

i

�3>�+ � J �������9� @2��+56.�3>;%#L�%��9�<EB����+&> 6�� =8, EGE '.+&��+-(�,�����H �#= + ����+ � � EB,.6.�i

Page 121: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� ��� � � � � ��� ��� ��� � � ��� ��������� � ���� � ��� ~U~X{

�*) "29 +,"29 "� � �2"29s

�51��#1��712"29 3 �$� 9�+," $ ��3��%+,"Si/Gi

"� .$&"����$�! �:�"��79835"29 1� �$ �9 ��� + 1%:�1��#"%$&"��! 35" ���*$ $ ) ��$ �����

αi,j

"29� �2"�� 3�) �!�;929�� '�+,"���

A TUAnL Q′ C ev?MH=9X?MZ�x=CE?WN=?B9�gML\FaL\9PN=? Si/Gi

� QwF@< L\AE<�N=?B9;��:=?BCE9�C evgm>UgBHJ?BZ[?BHdL�NJ?[IMTUZ[Z�:JLcF¡L\ADT@H

αi,jQ�?B:bL�9;?PQ=<XTSN=:=AE<X? lJ� CDT@<X9 Ki,Q′ := {s ∈ L(Si/Gi) | δi × ξi((qi,0,xi,0), s) ∈ Q′} <X?MQ=<XgM9X?BHdLX?

C ev?MH=9X?MZ�x=CD?iNJ?B9}L\<\FaIB?B9�F¢�dF@HdL�CDAE?B:WNwF@HJ9 Si/Gi?mL�Z[?BH=F@HdL�>@?B<;9�N=?M9�gmLcFaLX9�N8evTSIBIM:=<X<;?BH=IM?�Q�TU9X9;ADx=CE?

N=? αi,j

lV ?]CDF@H=�dFa�U? Ki,Q′

Q�?B:JL�9X?[N=gMIBTUZ[QRT@9X?B<�?BH 9XTU:J9 k¦CDF@H=�dFa�U?B9 Ki,q

�Ki,Q′ = ∪q∈Q′Ki,q � L\?BCE9

��:=?PI s F@��:=? Ki,qF[Q�TU:=<igmLcFaL^AEH=AELXAGF@C qi,0

?ML q IMTUZ[Z]?KgmLcFaL^N�evF@<;<XAE>@gB? l � T@<XZ[?BCDCE?BZ[?BHdL �Ki,q := {s ∈ L(Si/Gi) | δi × ξi((qi,0,xi,0), s) = q}

l@ T@:=9^IBTUH=9;ADN=gM<XTUHJ9OCE?B9 s �SQRT@L s1u 9;?B9�9X:=An>@FaH�LX?B9

�~,l�V ?KCDF@H=�dF@�@? Ki,q

N=gMQR?MH=NjN=:YCDF@H=�dFa�U?�N=gM9XAD<;gPN=?BQ=:JAD9^CfehgML\FaL δj,et(qj,0, πi,j(s))�

7/l∀s ∈ Ki,q

CE?KCGF@HJ�dF@�U?�NJgB9XAE<XgPN=?MQ=:=AD9^C evgmLcFaL δj,et(qj,0, πi,j(s))?B9 L�9;:=Q=Q�TU9Xg�:=H=AE��:=? l

qrs F@��:=?�gMLcF¡LrN=?�N=gBQ=F@<;L q NJ:�Q=<;TbIMgBN=g Gj?B9 L�IBF@<\F@ImL\gM<XAD9;g�QwFa<�:=H�CGF@H=�UF@�U?^N=gB9;AD<;g�gMCGF@x�TU<Xg �

QwFa<;L\AE<¤N=?�IM?MLrgMLcF¡L l A TUAnL qj,mC evgmLcFaL�N=?ON=gBQwFa<;L�N=:uQ=<;TbIMgBN=g Gj,et

|�N=gmL\?B<;Z]AEH=TUH=9�CfehgML\FaL�N=?ON=gBQwFa<;LIMTUZ]Q=FaL\AEx=CD?�N=?PCGFW9XQ�gBIMA � IBFaL\AETUH Ej,et

lA TUAnL qj,m

CfehgML\FaL�NJ?�N=gBQ=F@<;L�N=: Q=<XTSIBgMN=g Gj,et

l C TU:=<uNJgML\?M<XZ[ADH=?M<�C evgmLcFaL]N=?�N=gMQwF@< LuN=?�CDF9;QRgMIBA � I¢FaLXADTUH Ej,et

F@N=gM�S:=FaL�F¢>@?BIOCfehgMLcF¡L}N=?�NJgBQwF@< L�N=:�Q=<;TbIMgBN=g GjH=TU:=9�I¢Fa<\F@ImL\gB<;AD9;TUH=9}NwF@H=9�:=H

Q=<;?BZ[AD?M<}LX?BZ[Q=9�CD?OCGF@H=�UF@�U?iN=gM9XAD<;g Kj,qgBCGFaxRTU<;g � QwF@< L\AE<�NJ?�C evgmLcFaL qj,m

lb� F@HJ9r:=H]9X?BIMTUH=N�LX?BZ[Q=9H=T@:=9^<X?BI s ?B<XI s TUH=9�C evgmLcFaL^IMTUZ[QwFaL\AEx=CD?�N=?PCGF�9;QRgMIBA � I¢FaLXADTUH Ej,et

lV FKH=T@L\AETUHoN=?^IBTUZ[QwFaLXADx=AECDAnL\g�?B9;L�N=g � H=AE?�AEIBA=N=?iLX?BCDCE?r_`F � TUH]��:=?OCfehADHdLX?B<X9;?BImL\ADT@H[NJ:]CDF@H=�dF@�@?�N=?

CDF�9;QRgMIBA � I¢FaLXADTUH]F¢>U?BI�IB?BCE:=A£N=:�QJ<XTSIBgBNJg�9XT@AEL�CD?OCGF@HJ�dF@�U?iN=gM9XAE<Xg Kj,q

lS� � HuN=?Ox=AE?BHuFaQ=Q=<Xg s ?BHJN=?B<CDF�QRTU< L\gM?�N=?^H=TaL\<X?^Q=<;TUQ�TU9XAnL\ADT@H�|@9;:=Q=Q�TU9XTUHJ9���:=?OCD?^Q=<;TbIMgBN=g Gj

F@N=Z[?MLXLX?iN=?B:S�[gMLcF¡L\9�N=?^N=gBQwFa<;L

qj,1?ML qj,2

|}F@CDTU<;9 � Q=F@<;LXAD<WN=?yCfevF@:JLXTUZ]FaL\? GjH=T@:=9]Q�TU:=<;<XTUHJ9[NJg � H=AE<oN=?B:b� Fa:JL\TUZ]FaLX?B9 G1,j

?mL G2,jF¢�dFaH�L�<;?B9XQ�?BImL\An>U?BZ[?BHdL�CfehgML\FaLPN=?oN=gBQ=F@<;L qj,1

?mL qj,2 � G1,j = (Qj, Σj, δj, qj,1, Qj,m) ?ML

G2,j = (Qj, Σj, δj, qj,2, Qj,m)l C TU:=<KI s F@��:=?WgML\FaLKN=?WN=gMQwF@< LK?MLPN=T@H=I�Q�TU:=<�I s Fa�S:J?]Fa:JL\TUZ]FaLX?

H=T@:=9iN=g � H=AD9;9XTUH=9i:JHjCDF@H=�dFa�U?�N=gM9XAE<Xg Kj,1

l C F@<iIBTUHJ9XgB��:=?MHdL�9;A�CfehgML\FaL�N=?KNJgBQwF@< L^N=:yQ=<XTSIBgMN=g Gj

?M9;L qj,1|SAECJ_`F@:JL�<;?BI s ?M<XI s ?M<�:=H[gMLcF¡L xl

NJ?�CDFP9;QRgMIBA � I¢FaLXADTUH Ej>UgM<XA � F@HdL L(Gj,qj,1)∩L(Ej ,xl) =

Kj,1|£T +

L(Gj,qj,1)?M9;L�CD?KCDF@H=�dF@�@?KN=:tQ=<;TbIMgBN=g�N=gM�U<\F@NJg�F¢�dFaH�L�IBT@Z]Z[?KgML\FaL�AEH=AELXAGF@C�CfehgML\FaL qj,1

lV ?�L s gBTU< u Z[?�IMAnklN=?B9;9XTU:=9^Q=<;gB9;?BHdL\?�CD?KI¢FaN=<X?K_pTU<;Z]?MC�N=?PIB?mLXL\?PN=gmL\?M<XZ[ADHwFaLXADTUH l� �%� R � $ � ` � � �� ���

qm

) � 1� �$ 35" 351 � �$�� 83�) ��� � �214351Gj

� �%+�"#"��,9� " ) � 1� ��$ ) �!� !�)�"xl

35"&+ � 9 ��1���� ) � �$ "�����Ej

"%+ !�)�"L(Gj,qm

) ∩ L(Sj,xl) = Kj,m

� ��:�"��Kj,m

+ �$��� � �5" 35129�� �21���*$ � �$ "� '�+,"���:�"��qm

� ��"+ �$��� � �5" 35129�� �71

Kj,m

"29� 3 ���!�#1 � �$� � ��� �!���� 2% + "�� 9;"%$ '�+," 35"29 9;1!�)�"�� �2"29 3� 1%:�1��#"%$&"��! �9{s ∈

L(Si/Gi) | δi × ξi((qi,0,xi,0), s) = q}���

αi,j ∈ suiv(s)"�

δj,et(qj,0, πi,j(s)) = qm

��

j ��� R7NVcIP �Sb�PSWJRQN� gB9X:JCEL\?PHwF¡L\:=<;?BCDCE?BZ[?BHdLiN=:yL s gBTU< u Z[? � lE~,l ♦

Page 122: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ 7 I ������������� � � 5� ��� � � �7��� ������� � ��� ��

� �YC � � D -9>E-F2�AG.�A -�0�4�.#264 � � <=5Q8���5 >E-98�0�+Ei

V ehgMLcF¡L]NJ?Y<;?ML\T@:=<oNwF@H=9[CD?yZ[TbN u CD?�N=?jCGF�9;QRgMIBA � I¢FaLXADTUH EiN=TUAnL LX<X?jIBTUZ[QwFaLXADx=CE?yFz>@?BIjCGF

NJ�SHwF@Z[AD��:=?[IBTU:=<XF@HdL\?[N=: QJ<XTSIBgBNJg Gi

� CfehgML\FaL�N=?[<X?MLXTU:=<PN=: Z]TSN u CE?WN=: QJ<XTSIBgBNJg�FygMLXg]gmLcF@x=CEANwF@H=9OCD?�I s F@Q=AELX<X?PQ=<;gBIBgMN=?BHdL � lC F@<iF@HwFaCDTU�UAE? � CGF�N=gMZ�Fa<XI s ?�QJ<XgBIMgBN=?MHdL\?@|wC evgmLcFaLrN=?K<X?mL\TU:J<�N=?�CDF�9XQ�gBIMA � IBFaL\AETUH Ei

?B9 LiIBTUZWkQwFaL\AEx=CD?�F¢>U?BIKCDF�LX<\F@IM? s �@gBH=gM<XgB?KN=F@H=9�CE?�Q=<;TbIMgBN=g�9;:=Q�?B<;>SAE9Xg Sj/Gj

Q�TU:=<rCDF@��:=?BCECD?OCfehgM>@gBH=?MZ]?MH�LN=?�IBT@Z]Z�:bLcFaLXADTUH αj,i

?M9;L¤Q�TU9;9XADxJCD? l'C TU:=<�I s F@��:=?igML\FaL q ∈ QjT + C evgm>UgMH=?BZ[?BHdL¤N=?rIBTUZ[Z�:JL\FaL\AETUH

αj,i?B9 L�Q�TU9X9;ADx=CE?@|wH=T@:=9�IBF@CDIM:=CDTUHJ9OC ev?MH=9X?MZ�x=CE?�N=?M9�LX<\F@IM?B9��@gBH=gM<XgB?M9�NwF@HJ9 Sj,et/Gj,et

?ML�Z[?BHwF@HdL>U?B<;9�C evgmLcFaL q |=L\?MC���:=? Kj,q := {s ∈ L(Sj,et/Gj,et) | δj,et × ξj,et((qj,in,xj,in), s) = q}

lA :JQ=QRT@9XTUH=9�Z]F@ADHdL\?MHwF@HdL}��:�e � C evTSIBIM:=<X<;?BH=IM?ONJ?�C evgm>UgBHJ?BZ[?BHdLrNJ?OIMTUZ[Z�:JLcF¡L\ADT@H αj,i

|dCfehgML\FaL}N=?<X?MLXTU:=<�NJ:�Q=<XTSIBgMN=g Gi,et

9XTUAnL qlR� CDTU<;9�C evgmLcFaL�N=?�<;?ML\T@:=<�N=?�CGF[9XQ�gBIBA � I¢F¡L\ADT@H Ei

?B9 L xl′L\?MC���:=?

L(Si,xl′) ∩ L(Gi,q) = Ki,qV F�N=gMZ�Fa<XI s ?�QJ<XTUQ�TU9XgM?�NwF@HJ9�CD?�L s gMTU< u Z]? � l|q |aQ�TU:=<�N=gMLX?B<;Z]AEH=?B<�CD?B9�gML\FaL\9¥NJ?�<\F@IMIBTU<;N=?BZ[?BHdL

N=?B9P9XQ�gBIMA � IBFaL\AETUH=9M|8?m�bAE�U?W:=H�I¢FaCDIB:JC¥N=?�L\T@:=9�CD?M9KCGF@HJ�dF@�U?M9�N=?�LXTU:=9KCD?M9�gML\FaL\9KNJ?W9XQ�gBIBA � I¢F¡L\ADT@H lq ?BIBA¤<;?BH=N IM?MLXLX?oN=gBZ]F@<XI s ?WIBTUZ[Q=CD?��b? l @ TU:=9KQ=<;TUQRT@9XTUH=9KNJTUH=IW:=H{F@CE�UTU<XAnL s Z[?PQR?M<XZ[?ML;LcF@HdLPN=?N=gMLX?B<XZ[ADHJ?B<¤Cfeh?BHJ9X?BZ�x=CD?�NJ?B9}gML\FaL\9¤N=?i<XF@IBIMTU<XNJ?BZ[?BHdL}N�eh:=H=?^Z�FaH=A u <X?�Z[TUADHJ9�IBT@Z]Q=CE?m�b? l@� >aF@HdL}N=?Q=<XgM9X?BHdLX?B<�HJT@L\<;?[QJ<XTUQ�TU9XAnL\AETUH�|8HJTU:=9�N=?M>@TUH=9PL\TU:JL�N�evF@x�TU<XN{gML\F@x=CEAD<�:=H{?BHJ9X?BZ�x=CD?[N=?oH=T@L\FaL\AETUH=9�S:JA�9;?B<;TUHdL�:bL\ADCEAD9;gB?B9iN=F@H=9^CfevF@CD�@TU<XAnL s Z[? l

��R Pfb�PSWJRQN�c �Σ(q)

� <;?BQ=<;gB9;?BHdL\?�C ev?MH=9X?MZ�x=CE?�N=?M9�gm>UgMH=?BZ[?BHdL\9iQ s �S9;AD��:=?BZ[?BHdLrQRTU9;9XAEx=CD? � Q=F@<;LXAD<¤N=?OCfehgML\FaL q N=:Q=<XTSIBgMN=g �

Σa(x)� <;?BQ=<;gB9;?BHdL\?KC ev?MH=9X?MZ�x=CD?^N=?M9rgm>UgBHJ?BZ[?BHdL\9^F@:bL\TU<;AD9XgM9}N=?BQ=:JAD9rC evgmLcFaL x NJ?�CGFP9XQ�gBIMA � IBFaL\AETUH �

Re(x,E)� ?B9 L�C ev?MH=9X?MZ�x=CE?KN=?B9OgML\FaL\9^N=?PCGF�9;QRgMIBA � I¢FaLXADTUH E FaL;L\?BAE�UHwF@xJCD?B9rN=?BQ=:JAD9^CfehgML\FaL x

Re(q,G)� ?B9 L�C ev?MH=9X?MZ�x=CE?�NJ?B9^gML\FaL\9^N=?PQ=<;TbIMgBN=g G F@IMIB?M9X9XAEx=CD?M9^N=?BQ=:JAD9^CfehgML\FaL q

l� �SR aKR7cfWJPXWYR7N � �YZ� ���

ql, qk,...,qn

+ "�� 9;"%$ '�+,"835"29 1� �$ �9 35" 351 � �$�� �3�) ��� � �214351Gi

�( ��� 1� "��%$ � �#"�� �!�*) � ��� ��!�)�"&1� ��$ 35" 351 � �$��

qi

+," + �$��� � �5" 35129�� �71Kqi

1%+ � '����21 % � �$�� � � 35"�2"� 1� ��$ &� �$� �7"

H = X� ���!� �"��+,"%$&"��! �� "29� + "�� 9;"%$ '�+," 35" �*) 9 +,"29 1� ��$ 9 35" + �&9 ��1���� ) � �$ "�����

Ei�*929 � ��� 12"���) ����� �214351Gi

�/ �� �*) � ��� ��!�)�"

qi

- �$� �7"5'+ � - � ��+ �%) +,"��

Σ(qi) ∩ Kqi

�Σ(qi) ∩ Kqi

�2" ���7129;"��! "�+ "�� 9;"%$ '�+," 35"29 1%:�1��#"%$&"��! �9 � ��� 9�� !�)�"%$&"��! �!�;929�� '�+,"29 35" � ) �,9&+ 1� ��$

qi

3�) ��� � �214351 "� !�) � ��� � �$�� � "��!�#"��! ��) + �$��� � �5"35129�� �71

Kqi

Page 123: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� ��� � � � � ��� ��� ��� � � ��� ��������� � ���� � ��� ~ 7b~

+ ' - � �*) � ��� ��!�)�"x ∈ H

- �$� �7"5'��� � ��+ �%)5+,"��

Σa(x)�

� ��� � ��+ �%)5+,"��Σa(x) ∩ Σ(qi)

�Σa(x) ∩ Σ(qi)

"29� + "�� 9;"%$ '�+," 35"29 1%:�1��#"%$&"��! �9 � ���29�� !�)�"%$&"��! �!�;929�� '�+,"29 35" � ) �,9 + 1� �$

qi

"� �!�) �.9 ���! ��) �����,9;129 % � �$�� � � 35" + 1� ��$ x35"8+ � 9 ��1���� ) � �$ "����� �

� � ��� � �Σ(qi)∩Kqi

6= Σa(x)∩Σ(qi)��+ ���29

H = H −{x}�H −{x}

"29� �+ "�� 9;"%$ '�+,"H

351 �!�*) �0:;) 35" �*) 9 +,"29 1� �$ �9x

!�) � �#"8:�1���� ) "��! � �*98+ ������ 3$� ����� ���:9� � �$�! 0!�)�"

card(H) � 6= 1- �$� �7"5'

� � � ��+ �%)5+,"��Re(x,E)

��?� � ��+ �%)5+,"��

Re(qi,Gi)�

� � � ��!�)�"%+ !�)�" 9 ��� x′ ∈ Re(x,E)

"� 2!�)�"%+ !�)�" 9 ��� q′ ∈ Re(qi,Gi)

� ��+."#"��,9� ") �#" 9;1!�)�"�� �2" 3� 1%:�1��#"%$&"��! �9�:�1���� ) �$�!

δi(qi,s) = q′"�

ξi(x,s) = x′ � "%+�+,"!�)�"

sΣ(qi) ∩ Kqi6= s(Σa(x) ∩ Σ(qi))

��+ ���79H = H − {x}

�:9� 1� �$

x:�1���� ) �$�! !�)�"

card(H) = 1"29� !� �$� ����� 9;1!�)�"��! +," 9;"%)5+#1� ��$ �35" 351 � �$��

!�) � �������2"29 �!��� 3 %&+ 1� �$ qi

��

� �YC �YC � � A � ��?�A&2 HY>�� ��?�8 5Q>E-�8�0�+� � � � � �YZ �&R=T $/_Y`/c�N�R7N ��PX`/N�T ��c

V ev?��b?BZ[Q=CD?�<;?MLX?BH�: ?M9;LPIM?BCD:JA�Q=<;TUQRT@9XgWNwF@HJ9KCD?�I s FaQ=AELX<X?�Q=<;gBIMgBN=?MH�LB|�9X?MIML\AETUH q�l�79l � Q=F@�U? zmq |N=?OL\<;TUAD9�Z�FaI s ADH=?M9 M1

| M2?mL M3

?mL�N�eh:=Hu9 L\TSI � AEH�LX?B<;Z]gMN=AGF@AE<X? SlJV ?M9�Z]TSN u CD?B9�N=?M9�Z�FaI s ADH=?M9

� � �U:=<;? q�lrz |wQwF@�U? z � � ?MLOCD?M9igM>UgMH=?BZ[?BHdLX9�N=?PIBT@Z]Z�:bLcFaLXADTUH�IMTUH=9XAEN=gB<;gB9^9XT@H�L�ADNJ?BHdL\AE�S:J?B9 lq ?�9;�S9 L u Z[?�Q�TU9X9 u N=?�N=?M:b� Z[TbNJ?B9�NJ?u_pTUH=IMLXADTUHJH=?BZ[?BHdL¢|�CD?�Z]TSN=?�HJTUZ]AEHwF@C n ?ML�CD?�Z[TSN=?

N=gM�U<\FaN=g dl¤� � H NJ?YZ[?ML;L\<X?y?MH � :J>S<X?YCfevF@Q=Q=<;TbI s ?yQ=<;TUQ�TU9XgM?YH=T@:=9]?��bQ=<XAEZ]TUHJ9]Q�TU:=<oI s F@��:=?

Z[TbNJ?¥N=?¤_pTUH=ImL\ADT@H=H=?BZ[?BHdL � N=TUH=I}Q�TU:=<�I s F@��:=?�Z[TbN u CD?¥NJ:�QJ<XTSIBgBNJg � :=HPZ]TSN u CE?¥N=?}9XQ�gBIMA � IBFaL\AETUHF@9;9XTSIBAEg � >@TUAD< � �U:J<X? � lrx � lrV F 9;QRgMIBA � I¢FaLXADTUH En

?B9 LyF@ADHJ9XA�F@9X9;TbIMADgB?tF@: Z[TbNJ?tH=TUZ[ADH=F@Ci?ML�CDF9;QRgMIBA � I¢FaLXADTUH Ed

F@: Z]TSN=?jN=gB�@<\F@N=g l�q ?M9u9XQ�gBIMA � IBFaL\AETUH=9[9XTUHdL�gMIB<;AEL\?M9�?MH _pTUH=ImL\ADT@H N=?YCfehgML\FaLAEH=AELXAGF@C�N=:{Q=<XTSIBgMN=g[F@9X9;TbIMADg

�CE?�_`F@AELP��:=?oCD?oZ[TbNJ?WIBTUH=9;ADN=gM<XgoH�eh?B9 L�QwFa9�9;gBCE?BIMLXADTUHJH=g[F@: N=gBQwFa<;L

H�eh?BHdLX<X?KN=TUHJI�QwF@9i?MH�IBTUZ[QJL\?�NwF@H=9�C evgMIB<;AEL\:J<X?�N=?�CfevF@:JL\T@Z�FaLX?�NJ?KCGF�9;QRgMIBA � I¢FaLXADTUH�HJTUH�gMLX?BH=N=:J? l

� � � � � � k \]R7N�cOP � �VU,PXWYR7N#T�`Ed,et

V evTSIBIM:=<X<;?BH=IM?�N=?^C evgm>UgBHJ?BZ[?BHdLrNJ?�IMTUZ]Z�:JLcFaLXADTUH p1IMTUH=N=:=AnL�CfevF@:JL\T@Z�FaLX?iN=?^CGFK9XQ�gBIMA � IBFaL\AETUH

En,et>U?M<X9PCfehgML\FaL�AEHwF@IMLXAE_ xn,in

l�� H�<X?m>@FaH=I s ?@|8IB?WZ Z[?�gM>@gBH=?MZ]?MHdL�IMTUH=N=:JAEL�C e�Fa:JL\TUZ]FaLX?�N=?WCDF9;QRgMIBA � I¢FaLXADTUH Ed,et

NJ?BQ=:=AE9^9XTUHygML\FaLOADHwFaIML\An_ xd,in>U?M<X9O:=HYgmLcFaL x ∈ Xd

N=AnL^gMLcF¡L^N=?PN=gBQwFa<;L l� �

card(H)$-�3��$-%*>��3��+-� � � ��, E @�$&�<6�J %���%<EB����+&> 0�'�(:�8=.(�>�+-�3��+ 69���9>

H

Page 124: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ 7U7 ������������� � � 5� ��� � � �7��� ������� � ��� ��

En

GdGn

Ed

xn,0 xn,1

xd,0 xd,1

qn,0qn,1

qn,2 qn,3

qd,0qd,1

qd,2 qd,3

f f

f

f

d

dd

d

1

1

1

1

22 22 df f

f

f

2

d

d

d

3

3

3

3

2 22

d 2

f1

d }−{d ,−{f , d } 3d

f

2

3

Σ Σ Σ Σ

p

r

1

1

mode dégradémode nominal

spécification spécification

Procédé Procédé

1 2 2 1−{f ,, d }23 2−{d ,d }

������� � lrx�� � ��3��%+,"29 � ��� 1� "�� 3�) 9�3�) ��� � �214351 "� 35"29 9 ��1���� ) � �$ ����� 9

@ TU:=9�F¢>@TUH=9�Z[TUHdL\<;g�NwFaH=9rCE?�I s F@QJAEL\<;?�QJ<XgBIMgBN=?MHdL^�S:J?�CD?OZ]TSN u CD?^N=:uQ=<;TbIMgBN=g�NwF@H=9�CD?OZ]TSN=?N=gB�U<XF@N=gWQ�?B:JL�QRTU9;9XgMN=?B<PN=?M:b��gmLcFaLX9KN=?�N=gMQwF@<;L�H=T@L\gM9 qd,0

?ML qd,2

l C Fa<�IBTUHJ9XgB��:=?MHdL�IM?WZ]TSN u CE?F@N=Z[?ML^N=?M:b�jNJ�SHwF@Z[AD��:=?M9ONJA � gB<X?MHdL\?B9M| L(Gd,qd,0

) ?ML L(Gd,qd,2) |wF¢>U?MI �

L(Gd,qd,0) = {s ∈ Σ∗

d | δd(qd,0, s)!} = {d2, d3, d2f2, d3f3, ...}

L(Gd,qd,2) = {s ∈ Σ∗

d | δd(qd,2, s)!} = {f2, d3, f2d2, d3f3, ...}

A :JQ=QRT@9XTUH=9�Z]F@ADHdL\?MHwF@HdL���:�eh?BH�IMTU:=<;9�N=:�Z[TbN=?¤HJTUZ]AEHwF@C |BCfehgM>@gBH=?MZ]?MHdL�N=?}QwFaH=H=?�9X?}Q=<XTSN=:=AE9X?F@Q=< u 9¥CGFO9XgM�S:J?BH=IM?ON8evgm>UgBHJ?BZ[?BHdL\9 s = d1

� gM>@gBH=?MZ]?MH�L p1,0 � � laV ehgML\FaL¥NJ?�N=gBQ=F@<;L¤NJ:�Z]TSN u CD? Gd,et

N=gMLX?B<XZ[ADHJg�NwFaH=9�CE?^I s F@Q=AnL\<X? 3 ?B9 L qd,0

lbq ?���:=A£IMTU<X<;?B9XQ�TUH=N � :=H]9;LXTbI � >SADN=? lSV ?OCGFaH=�dF@�U?iNJgB9XAE<Xg?BH x�TU:=IBCE?[_p?M<XZ[gB?[N=?BQJ:=AD9�IB?ML�gMLcF¡L�N=T@AEL�Q=<X?MH=N=<X?]?BH IMTUH=9;ADN=gM<\FaLXADTUH CfehgMLcF¡L�>SADNJ?]N=: 9;L\TSI � |�LX?BC�S:J? Kd,0 = {d3, d3f3, d3f3d2, ...}

l� FaADHdL\?MHwF@HdL¢|SH=TU:=9�F@Q=Q=CEAD��:=TUH=9�CGF�Q=<XT@QRTU9;AELXADTUH � ln~ Q�TU:=<rNJgML\?M<XZ[ADH=?M<�C evgmLcFaL�N=?�NJgBQwF@< L�N=?�CGF

9XQ�gBIBA � I¢F¡L\ADT@H Ed

l���

p1,0

�3>�+ � J %<L#%����#E �3��+ 6�� �9�����9� 6�%879��( � �2��$-+-(�$ 6.�p1

�9��$ � J �8=.��$&�3>&>-( ,#� >-'�( L ���#+&�p1 = p1,i

>-(δd,et(qd,in,p1) = qd,i

Page 125: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� ��� � � � � ��� ��� ��� � � ��� ��������� � ���� � ��� ~ 7,q

xn,0xn,1

xd,0 xd,1

qn,0 qn,1

qn,2 qn,3

qn, in

qd,0qd,1

qd,2 qd,3

q ind,

f f

f

f

d

dd

d

1

1

1

1

22 22 df f

f

f

2

d

d

d

3

3

3

3

2 22

d 2

f1

1d }−{d ,−{f , d }1d }33−{f ,, d } −{d ,d

f

2

3

Σ Σ Σ Σ

x x

rr

Gd,et

Gn,etp1,0

1r

r1

p

p1,0 1 1

p1,2

p1,2

p1,0p

1,2

p1,2

1,0

E Ed,etn,et

n,ind,in

2 2 2 2

������� � l|z�� � � � �214351 "� .9 ��1���� ) � �$ ����� 9�1� "�� 3�) 9�3�)!$ ��35"�351$�$�#� 351

Page 126: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ 7 � ������������� � � 5� ��� � � �7��� ������� � ��� ��

E H=AnL\ADF@CD?MZ]?MH�L H = {xd,0, xd,1}l

C TU:=< xd,0 ∈ H _`F@AE<X?�

q FaCDIB:JCDTUH=9 Σa(xd,0) Σa(xd,0) = {d3,f2,f3}q FaCDIB:JCDTUH=9 Σa(xd,0) ∩ Σ(qd,0) Σa(xd,0) ∩ Σ(qd,0) = {d3}q FaCDIB:JCDTUH=9 Kd,0 ∩ Σ(qd,0) Kd,0 ∩ Σ(qd,0) = {d3}� ?B9 L Σa(xd,0) ∩ Σ(qd,0) = Kd,0 ∩ Σ(qd,0) H = H.

C TU:=< xd,1 ∈ H _`F@AE<X?�

q F@CDIM:=CDT@H=9 Σa(xd,1) Σa(xd,1) = {d2,f2,f3}q F@CDIM:=CDT@H=9 Σa(xd,1) ∩ Σ(qd,0) Σa(xd,1) ∩ Σ(qd,0) = {d2}q F@CDIM:=CDT@H=9 Kd,0 ∩ Σ(qd,0) Kd,0 ∩ Σ(qd,0) = {d3}� ?M9;L Σa(xd,1) ∩ Σ(qd,0) 6= Kd,0 ∩ Σ(qd,1) H = H − {xd,1} = {xd,0}.

� ADH=9;Af|JCDFW9XTUCE:JL\AETUH�N=?PCfehgB��:wFaLXADTUH L(Sd,xj) ∩ L(Gd,qd,0

) = Kd,0?B9;L xj = xd,0

l� ?�_`F � TUH�9XADZ[ADCDF@AD<;?@|aTUHuQ�?B:JLiZ[TUHdL\<;?B<���:�e � C evTSIBIM:=<X<;?BH=IM?�N=?�C evgm>UgMH=?BZ[?BHdLiN=?�IBTUZ[Z�:JL\FaL\AETUH

p1,2N=?MQ=:=AE9�C evgmLcFaL qn,3

?BH�Z]TSN=?¤H=TUZ[ADH=F@Cf|MCfehgMLcF¡L�N=?}N=gBQwFa<;L�N=?�CGFi9XQ�gBIMA � IBFaL\AETUHPgML\?MH=N=:=?�N=:�Z]TSN=?N=gB�U<XF@N=g�?B9 L xd,0

l£V ?�Z[TbN u CD?K�@CDTUxwFaC�gMLX?BH=N=:tN=?�CDF[9;QRgMIBA � I¢FaLXADTUHjN=:jZ]TSN=?PN=gM�U<\F@NJg�?M9;L�NJTUH=H=gQwF@<rCDF � �U:=<X? � l|z�l A :=<�IB?ML;L\? � �U:=<;?@|SCD?OZ]TSN u CE?^gML\?MH=N=:uNJ:uZ]TSN=?^H=TUZ[ADH=F@CwH=?�IMTUZ[QRTU< L\?^��:=?�CE?B9L\<\FaH=9XAnL\ADT@H=9�gm>SADN=?MH�LX?B9iZ[?BHwFaH�L � C evgmLcFaL�ADHwFaIML\An_ lSV ?M9�F@:bL\<X?M9rL\<XF@H=9;AEL\AETUH=9�9XTUHdLrN=gMLX?B<XZ[ADHJgB?B9rNwF@H=9CGFW9X?MIML\AETUHy9X:=An>aF@HdL\? l

V ?�QJ<XTSIBgBNJg�9XTU:J9�IBT@H�LX< s CE?�gmL\?BHJN=:�N=:�Z[TbNJ?�N=gM�U<\FaN=g@|RTUxJL\?MH�:�QwF@<�9;�SHdL s1u 9X?@|�?M9;L�Q=<XgM9X?BHdLXg� �U:=<;? � lr{�l E C8IBTUHdL\AE?BHdL 7 gML\FaL\9^?mL 12 L\<\FaH=9XAnL\ADT@H=9 l

�� � � � � � \ R7N�cOP � ��U,PSWYR7N T�`En,et

V ehTbIMIB:=<;<X?BHJIB?�NJ?�C evgm>UgBHJ?BZ[?BHdL�N=?OIBT@Z]Z�:bLcFaLXADTUH r1IBTUHJN=:=AEL�CfevF@:JLXTUZ]FaL\?�NJ?�CDF�9;QRgMIBA � I¢FaLXADTUH

En,etNJ?BQ=:=AE9�9;TUH�gmLcFaL�AEHwF@IMLXAE_ xn,in

>@?B<;9r:=H]gMLcF¡L x ∈ XnN=AEL�CfehgML\FaL�N=?O<X?MLXTU:=< l L�H[<\F@QJQR?MCDCD?i��:=?

CD?�Z[TbN u CD?ON=:yQ=<;TbIMgBN=gK?MH�Z]TSN=?�HJTUZ]AEHwF@C�QRT@9X9 u N=?KN=?M:b��gmLcFaLX9�N=?K<X?mL\TU:J< qn,0?ML qn,2

� I s F@Q=AELX<X?3 � lF@ TU:=9iL\<XF@AELXTUH=9�9;:=IBIM?B9;9XAE>@?BZ[?BHdLKCE?B9iN=?M:b�jI¢F@9 �\]b c�Z � ��PXb�P T�` �S`�PXR � � T�b N�c�_Y` � R=T $9_J`�T �a �SR=U �/T%�

Gn,et

`9cIPqn,0

� FaH=9yIB? I¢F@9M| ∀s ∈ L(Sd/Gd)|�LX?BC���:=? r1 ∈ suiv(s) |�CfehgML\FaLyN=: 9;LXTbI � ?M9;LjQ=CE?BADH l1C Fa<

IBTUH=9;gB��:=?MH�LOCE?�CGFaH=�dF@�U?ON=gM9XAD<;g�N=?MQ=:=AE9�IB?mLigML\FaL¢|S��:=A8N=T@AEL�Q=<X?MH=N=<X?K?MH�IBTUZ[QJLX?�IB?mLigML\FaL�QJCD?BAEH�N=:9;L\TSI � |£?B9;L Kn,0 = {d2, d2f2, d2d1,......}

l� F@ADHdLX?BHwF@HdLB|�HJTU:=9]F@Q=Q=CEAD��:=TUH=9oCDF{Q=<;TUQ�TU9XAnL\ADT@H � lE~ Q�TU:=<oN=gMLX?B<;Z]AEH=?B<oCfehgML\FaL[N=?j<X?MLXTU:=<oN=?jCGF9XQ�gBIBA � I¢F¡L\ADT@H En

lE H=AnL\ADF@CD?MZ]?MH�L H = {xn,0, xn,1}

l

Page 127: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� ��� � � � � ��� ��� ��� � � ��� ��������� � ���� � ��� ~ 7 �

C T@:=< xn,0 ∈ H _`F@AD<;?�

q FaCDIB:JCDTUH=9 Σa(xn,0) Σa(xn,0) = {d1,f2,f1}q FaCDIB:JCDTUH=9 Σa(xn,0) ∩ Σ(qn,0) Σa(xn,0) ∩ Σ(qn,0) = {d1}q FaCDIB:JCDTUH=9 Kn,0 ∩ Σ(qn,0) Kn,0 ∩ Σ(qn,0) = {d2}� ?B9 L Σa(xn,0) ∩ Σ(qn,0) 6= Kn,0 ∩ Σ(qn,0) H = H − {xn,0} = {xn,1}.

C T@:=< xn,1 ∈ H _`F@AD<;?�

q F@CEIB:=CETUH=9 Σa(xn,1) Σa(xn,1) = {d2,f2,f1}q F@CEIB:=CETUH=9 Σa(xn,1) ∩ Σ(qn,0) Σa(xn,1) ∩ Σ(qn,0) = {d2}q F@CEIB:=CETUH=9 Kn,0 ∩ Σ(qn,0) Kn,0 ∩ Σ(qn,0) = {d2}� ?B9;L Σa(xn,1) ∩ Σ(qn,0) = Kn,0 ∩ Σ(qn,1) H = {xn,1}.

� AEH=9XA |=CGF�9;TUCD:bL\ADT@H�N=?PCfehgB��:wFaLXADTUH L(Sn,xj) ∩ L(Gn,qn,0

) = Kn,0?M9;L xj = xn,1

l\]b c k �E_�� ��PXb9P�T�` �S`�PXR � �hT�b NVc _Y` � R=T�` T �a � R�U �9T �

Gn

`/cOPqn,2� F@HJ9iIB?KI¢Fa9B| ∀s ∈ L(Sd/Gd)

|J?mL r1 ∈ suiv(s) |SCfehgML\FaLiN=:�9 L\TSI � N=TUAnL�9;?�L\<XT@:J>U?M<iQ=CD?MADH l C F@<IMTUH=9XgM��:=?BHdL}CD?}CDF@H=�dF@�@?�N=gM9XAE<Xg�N=?BQ=:JAD9�IM?ML�gMLcF¡L¥N=TUAnL�Q=<X?MH=N=<X?r?BH�IMTUZ]QbL\?�IB?ML�gML\FaL�QJCD?BAEH�N=:�9;LXTbI � |?mL Kn,2 = {d1, f2, d1f1, d1f1d2,......}

lU� CDTU<;9B|¡CGF�9;TUCD:JLXADTUH�N=?iCfehgB��:wF¡L\ADT@H L(Sn,xj)∩L(Gn,qn,2

) =

Kn,2QR?M:JL LX<X?PN=gMLX?B<;Z]AEH=gKN=?PCGF�Z Z[?KZ�FaH=A u <X?K��:=?PNwF@H=9^CDFoIBF@9 ~ml

q ?MLPgmLcFaLPNJ?�<X?mL\TU:=<K?M9;L xj = xn,1

� CfehgMLcF¡LKN=?W<X?mL\TU:J<�N=?WCGFu9;QRgMIBA � I¢FaLXADTUH�gmL\?MH=N=:=? � QwF@< L\AE<N=:jZ[TbN=?�H=TUZ[ADHwF@CR?B9 L xn,1 � � >@TUAD< � �@:=<X? � ln~ I � lV ?�IBT@H�LX< s CE?B:=<�gML\?MH=N=:oN=:oZ[TbN=?�H=TUZ[ADHwFaCS?M9;L}N=T@H=H=giQwF@<�CGF � �@:=<X? � lE~U~,l E CJIMTUZ[QRTU< L\? 7 gML\FaL\9?mL 12 L\<\FaH=9XAnL\ADT@H=9 l

� � � � � ��� \]R � a�b �Sb WYc R7N#b�eQ`/U�_�� b1a�a �SR=U ��` Um`/NQP �Sb _YW c � `� � H[NJ?iZ]TUHdLX<X?B<�Cfeh? � I¢F@IMAELXg�?ML¤C evAEHdL\gB< L¤NJ?iH=T@L\<;?iF@Q=QJ<XTSI s ?iN=TUHdL}CD?M9¥Q=<;ADH=IMADQwF@:S�WF¢>aF@HdLcF@�@?B9

9;TUHdLPN�ev:JH=?]Q=F@<;LPCDFu�U?B9 L\ADT@H�N=?B9PZ[TbN=?M9KN=?W_pTUH=ImL\ADT@H=H=?BZ[?BHdLP?mLPN�e�Fa:JL\<;?[Q=F@<;LPCDFu9XADZ[Q=CEADIBAnL\g�N=?IMTUHdL\< s CD?B:J<X9�<;gB9X:JCELcFaH�LX9B|¥HJTU:=9oF@CECDTUH=9M| � Q=F@<;LXAD<�NJ?�Cfeh?m�b?BZ[Q=CD?�IBTUH=9;ADN=gM<Xga|¥? � ?BImL\:=?M<W:=H=?ygMLX:=N=?IMTUZ]Q=F@<\FaLXAE>@?�?MHdL\<X?�CD?M9�LX?BI s HJAD��:=?B9�IBCGFa9X9XAE��:=?B9�N=?�Z]TSN=gBCEAD9XFaL\AETUHK<X?MQRTU9XF@HdL�9;:=<�:=H�Z[TbN u CD?¤:=HJAD��:=?N=: Q=<XTSIBgMN=guIBT@:=Q=CDg � :=H 9;?B:=C�9X:=Q�?B< >SAD9X?M:=<�?mL�CD?M9�9 L\<\F¡L\gB�@AD?B9�N=?uIMTUZ]Z]F@H=NJ?]<;?BQ�TU9\F@HdL�9X:=<�CDF9 L\<X:JIML\:J<X?PQ=<XT@QRTU9;gB?�NwF@H=9^IM?�Z[gBZ[TUAE<X? l

V ?�Z[TbN u CD?�F@:JLXTUZ�F¡L\?rIMTU<X<;?B9;QRTUHJNwF@HdL � I s F@��:=?iZ]F@I s AEH=?rNJ:W9;�S9;L u Z[?i?B9;L¤LXTU: � TU:J<X9�CE?rZ Z[?� QRTU:J<�<XF@Q=Q�?BC

�� �@:=<X? q�l|z | QwF@�U? z � � lz� C e�F@AEN=?}N=:�CETU�UAEIBAD?MC � �Oq � � CD?}Z[TbN u CD?}�UCETUxwF@CUNJ:�Q=<XTSIBgMN=g

G ?B9 L¤TUxJLX?BH�:oQwF@<¥IMTUZ]Q�TU9;AEL\AETUH�Q=F@<\F@CEC u CD?}N=?iIB?M9¥L\<;TUAD9�Z]TSN u CE?B9 l�E C=?M9;L¤NJTUH=H=giQwFa<¥CGF � �U:=<X? � lE~z79l� H�gmLcFaL q N=:�Z[TSN u CE?��UCETUxwF@C G ?B9;L�I¢F@<XF@IMLXgB<XAE9Xg�Q=F@<rCE?�Q=<XTSN=:=AnLrIBF@<;LXgB9;AD?BH�NJ?�L\TU:J9�CD?M9�gML\FaL\9

Q�TU9X9;ADx=CE?B9�N=?�I s Fa�S:J?�Z]TSN u CD? Mi

l � TU<XZ[?BCECD?BZ[?BHdLB| q = (q1, q2, q3)|aT + I s F@��:=?igmLcFaL qi

F@Q=QwF@< L\AE?BHdL� C ev?MH=9X?MZ�x=CE?�N=?M9oF@IMLXAE>SAELXgB9�NJ?uCGFtZ]F@I s AEH=? Mi

l�V ?uZ[TSN u CE?��UCETUxwF@C G F@N=Z[?ML 12 gML\FaL\9�?ML 40

Page 128: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ 7,v ������������� � � 5� ��� � � �7��� ������� � ��� ��

r1,0

p1,0

f2

r1,2

p1,2

d d

d

f

f

2

2

2

f

fq

0 1 2 3

4

5

33

3

3d,in

������� � l|{�� � ���! "�76*+,"%) � 1� "�� 3�) 3�)!$ ��35"�351$�$�#� 351

r1,0

Gn,et

qn,0 qn,1

qn,2 qn,3

qd,0 qd,1

qd,2 qd,3

xd,0 xn,1xn,0

xd,1

f f

f

f

d

dd

1

1

1

22 22 df f

f

f

2

d

d

d

3

3

3

3

2 22

d 2

f1

1d }−{d ,−{f , d }1d }3d

f

2

3

Σ Σ Σ Σ

x x

r

Gd,et

p1,0r

p1,0

p1,0

p1,2

p1,2

p1,0p

1,2

p1,2

1,0

1,0

1,0r r

r1,2

1,21,2r

d1

r1,2

E Ed,etn,et

qq

n,in

n,ind,in

d,in

2 2−{f ,, d }3 2 −{d , 2

������� � ln~ I � � ��3��%+,"29 1� "�� 3�) 9 3�) $ ��35" � �*$ � ����+"� 351$�$�#� 351

Page 129: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ���5� ��� � � � � ��� ��� ��� � � ��� ��������� � ���� � ��� ~ 7mx

p1,0 r

1,0

1,2r

p1,2

f2

d d

d

f

f

1 2

1

2

2

f

f

1

1q

0 1 2 3

4

5

n,in

������� � ln~U~�� � ���! "�76*+,"%) � 1� "�� 3�) 3�)!$ ��35" � �*$ � ����+

AAA1 2 3

1 2AAM

3

1 3AMA

2

1 2AMM

3

MAM2 31

21MAA

3

21 3MMA

21 3MMM

PAM1 32

1PAA

2 3

1 2 3PMA

2PMM

31

d

d

d

d

d

d d d

ddf f f

fff

f f fd d d

ddd

r

r

r

r

22

1

1

1

2

1

1

1

1

p

p

p

p1

1

1

1

3 33333

2 22222

333333

1

������� � ln~ 7�� � ��3��%+," ��+ ��'���+ 3�) ��� � �214351

Page 130: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ 7,z ������������� � � 5� ��� � � �7��� ������� � ��� ��

L\<\FaH=9XAnL\ADT@H=9 lV ?B9�9XQ�gBIBA � I¢F¡L\ADT@H=9�ADZ[Q�TU9XgM?B9�Fa: Q=<XTSIBgMN=g G 9XTUHdLW<;?BCDFaL\An>U?B9�N�ev:JH=?uQwF@< L � CDFtI¢F@Q=F@IBAnL\g�NJ:

9;L\TSI � ?ML�N�e�Fa:JL\<;?YQwFa<;L�F@: _pT@H=IMLXADTUH=HJ?BZ[?BHdL�NJ?B9�NJ?B:b� Z]F@I s ADHJ?B9 M1?ML M3

l�� H ? � ?mL¢|�H=TU:=99X:=Q=Q�TU9;TUH=9���:=?�CD?K9 L\TSI � ?B9 L�N=?PIBF@QwF@IMAEL\gP:=HJAELcFaAD<X?�?ML�Q=:=AD9;��:=?PCGFWZ�FaI s ADH=? M3

?B9 L�<;?BN=T@H=NwF@HdL\?� CGFYZ]F@I s AEH=? M1

|�H=TU:J9WADZ[QRTU9;TUH=9�F@:=9;9XA���:�eh:=H=?�9;?B:=CE?uZ�FaI s ADH=?]N=TUAnL�_pTUH=ImL\AETUH=H=?M< � CGFy_pTUAD9 lE HJ_pTU<XZ[?BCECD?MZ]?MH�L�IB?B9O9XQ�gBIMA � IBFaL\AETUH=9i9;TUHdL�gMIB<;AEL\?M9^IBTUZ[Z]?K9;:=AEL

~ml^V FoZ]F@I s AEH=? M2H=?KIBT@Z]Z[?BH=IM? � L\<\F¢>aF@AECDCD?M<���:=?�9XA8?BCDCE?�Q�?B:JLOQ=<;?BH=N=<;?P:=H=?PQ=A u IB?KNwFaH=9^CD?

9;LXTbI � � CD?K9;LXTbI � ?B9;LON=?PIBF@QwF@IMAEL\gPCEADZ[AEL\g � :=H=?�9X?M:=CD?KQ=A u IM? � �79l^V F[Z]F@I s AEH=? M1

TU: M3H=?PN=gMQRT@9X?P:=H=?PQ=A u IB?PNwFaH=9^CD?K9;LXTbI � ��:=?P9;A�IB?BCE:=AnklIBA�?M9;L^>SADN=? �

q�l^V F[Z]F@I s AEH=?K<X?MN=TUH=NwFaH�LX? M3HJ?P_pT@H=IMLXADTUH=HJ?���:=?P9;A�CGF�Z]F@I s ADHJ? M1

?M9;LO?BHjQwF@H=HJ? �� l^V F[Z]F@I s AEH=? M1

H=?PQR?M:JL L\<;?P<XgBQ=F@<XgM?���:=?�9XA�CDF�Z�FaI s ADH=? M3?M9;L�NwF@H=9^CfehgML\FaLiN�evF@<;< L l

V ?B9^Z[TbN u CD?M9iIBTU<;<X?M9XQ�TUH=NwF@HdL�F@:b��9XQ�gBIBA � I¢F¡L\ADT@H=9i9XTUHdL�N=TUH=HJgB9^QwF@<^CGF � �U:=<X? � ln~Xq�lV ?rZ[TSN u CE?��UCETUxwF@CdNJ?rCGFO9XQ�gBIMA � IBFaL\AETUH�?M9;L¤TUxbL\?BH�:WQwFa<�Q=<;TbN=:JAEL�N=?�IM?B9 3 Z]TSN u CE?B9 l'E CSIBT@H�LXAD?MH�L

8 gML\FaL\9i?mL 46 L\<XF@H=9XAnL\AETUH=9 lJV ?�IMTUHdL\< s CD?M:=<�<XgM9X:=CnLcF@HdLON=:�_pTUH=ImL\AETUH=H=?MZ]?MH�L^?MHyxRTU:JIBCD?�_p?M<XZ[gB?KN=:Q=<XTSIBgMN=g G ?MLOIB?M9�9;QRgMIBA � I¢FaLXADTUHJ9iIBTUHdL\AE?BHdL 20 gML\FaL\9^?mL 42 LX<\F@HJ9XAELXADTUHJ9 l

� H{IBTUZ[QwF@<XF@HdLPCGFu9;LX<\FaLXgB�UAE?WN=?oIBTUZ[Z]F@H=N=?W<;?BQ�TU9\F@HdL�9X:J<�:JH Z[TbN u CD?�:=H=AD��:=?oN=: Q=<;TbIMgBN=gIBTU:=QJCDg}F¢>U?MI�:JH�Z[TbN u CD?�:=H=AE�S:J?¤N=?}CGFr9;QRgMIBA � I¢FaLXADTUHK?mL�CGF�9;LX<\FaLXgB�UAE?¥N=gm>U?BCETUQ=Q�gB?}NwF@HJ9�IM?¤I s F@Q=AnL\<;?@|H=TU:=9iIMTUH=9;L\FaL\T@H=9i:=H=?K9;ADZ[Q=CDA � I¢FaLXADTUH[N=?M9iZ]TSN u CE?B9�Z�F@HJADQ=:=CEgB9 lJV F�Q=<;?BZ[A u <;?�9 L\<X:JIML\:J<X?�F@x�TU:JL\AnL� :=H�IBT@H�LX< s CE?B:=<�N=? 20 gML\FaL\9�?ML 42 L\<XF@H=9;AEL\AETUH=9M|�CDF]9;?BIBT@H=N=? � 2 IBTUHdLX< s CE?B:=<;9�I¢F@<XF@IMLXgB<;AD9\FaH�L�CD?9;�S9;L u Z[?O9;gBQwFa<XgBZ[?BHdL¤N=F@H=9¤CD?M9�N=?M:b�WNJA � gB<X?MHdL\9¤Z[TbN=?M9�N=?�_pT@H=IMLXADTUH=HJ?BZ[?BHdL¢|¡T + I s F@IM:=HoIBTUHdLXAD?BHdL

8 gML\FaL\9K?mL 12 LX<\F@HJ9XAELXADTUHJ9 l8q ?W�dF@ADHt9X:=<�CDF�IBT@Z]Q=CE?m�bAELXg�N=?M9KZ]TSN u CD?B9�QRT@:=<X<XF@AEL LX<X?WNwF¢>aF@HdLcF@�@?IBTUH � <XZ[g�?MHYIMTUH=9;ADN=gM<\F@HdLON=?B9^9 �b9 L u Z]?M9�Q=CE:=9iADZ[QRT@<;LcFaH�LX9 l

� ��� � � � , ��*18 +�,-�O( �"! * �O(�+���� � 8�� , �-,-+ � !1+0("�O(���� �-� * 8��:!

E CS?B9 L¤H=gBIM?B9;9\F@AE<X?�OIB?�9 LcF@N=?rN=?�>@gB<XA�w?B<�CD?B9�Q=<;TUQ=<XAEgMLXgB9�_pT@H=NwF@Z[?BHdLcFaCD?B9�<X?MCD?M>aF@HdL�N=?rCDFOL s gBTU<;AD?N=?]IMTUHdL\< �UCD?WQwFa<K9X:=Q�?B< >bAE9XAETUH N=F@H=9PCD?WIBF@N=<X?oN=?oC e�F@QJQ=<XTSI s ?oZ�:=CnL\AnklZ]TSN��MCD?�� V ?B9PQ=<;TUQ=<;ADgMLXgB9PN=?H=TUHbklx=CDTSI¢F@�@?�?mL�N=?�IMTUHdL\< �UCGF@xJADCDAnL\gi9;TUHdL�CD?M9rQ=CE:=9rAEZ]Q�TU< LcF@HdL\?M9�� � H�N�evF@:JL\<;?B9rLX?B<;Z]?M9B|SADC�9BevF@�UAEL�N=?>UgB<;A�w?M<�IM?B9�N=?B:S�PQ=<XT@Q=<XAEgML\gM9�9X:=<�CD?¤IMTUHdL\<��@CD?B:J<�gML\?MH=N=:��`Q�TU:=<�I s F@��:=?�Z]TSN=?¤N=?¤_pTUHJIML\AETUH=H=?MZ]?MHdL��?BHj9X:=Q=Q�TU9XF@HdL���:=?�CD?KIMTUHdL\<��@CD?B:J<iH=TUHygMLX?BH=N=:Y?B9 L�NJg����oIBTUHdL\< �UCGFax=CD?�?mLOH=TUHbklx=CDTS��:wF@HdL��

� ?PIM?P_`FaAEL¢|bH=TU:=9�F@CECDTUH=9�_`F@AD<;?KCD?M9 s �SQ�T@L s �B9X?M9�9;:=AE>aF@HdL\?M9�

~ � L(Si/Gi)?M9;L�IBTUHdLX<��UCDF@x=CD?�QwF@<K<\FaQ=QRT@<;L�� L(Gi)

� L(Si/Gi)Σi,u ∩ L(Gi) ⊆ L(Si/Gi)�m|

Σi,u?B9 LoCfeh?BH=9;?BZ�x=CE?uN=?M9WgM>UgMH=?BZ[?BHdLX9[AEH=IBT@H�LX<��UCDF@x=CE?B9�N=: Q=<XTSIBgMN=g Gi

�`TUH 9;:=Q=Q�TU9X?���:=?

L(Si/Gi)?M9;LOQ=<;g�J�b?mklIBCETU9�� �

7 � L(Si/Gi)?M9;LOH=TUHSk¦x=CETb��:wF@HdL�� L(Si/Gi) = Lm(Si/Gi)

���

Page 131: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � � � � ���� ��� ��������� ��� ��� �/� � � � � � � ����� ��� � ��� � � �#� � ����� ~ 7��

@ TU:=9OF@CDCETUH=9�Z[TUHdL\<;?B<i��:=?�

� ������ �������� � ���( �

L(Si,et/Gi,et)"29� �����! �76*+ � '�+," � �$���#��� �!���� %

L(Gi,et)+L(Si,et/Gi,et)Σi,u,et ∩ L(Gi,et) ⊆

L(Si,et/Gi,et) -�./ �L(Si,et/Gi,et)

"29� � ��� '�+ �6!�) �$�! �+L(Si,et/Gi,et) = Lm(Si,et/Gi,et) - �

������������ �����������

V FOIMTUHdL\< �UCGF@xJADCDAnL\g�N=? L(Si,et/Gi,et)?B9 L¥F@9;9X:=<;gB?�QwF@<�CD?¥_`F@AnL���:=?�LXTU:=9�CD?M9�gm>UgMH=?BZ[?BHdL\9�N=?�IMTUZWk

Z�:bLcFaLXADTUHu9;TUHdL^9X:=QJQRTU9;gB9OF@:JLXTU<XAE9XgM9�� � Hy? �R?MLB|=CfehTbIMIB:=<;<X?MH=IB?KN�eh:=HygM>@gBH=?MZ]?MHdL�N=?KIMTUZ[Z�:JLcF¡L\ADT@HIMTUH=N=:=AnL¤CfevF@:JLXTUZ]FaL\?�N=:oQ=<XTSIBgMN=g Gi,et

>@?B<X9¤C evgmLcFaL¥ADHwF@ImL\An_ qi,in?ML}C e�Fa:JL\TUZ]FaLX?�N=?iCDF�9XQ�gBIMA�wIBFaL\AETUH

Ei,et>@?B<X9OCfehgML\FaL^ADH=F@IMLXAE_ xi,in

� C Fa<OIMTUH=9;gB��:=?BHdL�IB?ML;L\?�TbIMIB:=<;<X?MH=IB?�?B9 LOLXTU: �;TU:J<X9^F@:JLXTU<XAE9XgM?��C T@:=<^N=gBZ[TUHdL\<;?B<^��:=? L(Si,et/Gi,et)

?B9 LOH=TUHbklx=CDTS��:wF@HdL¢|=NJ?B:b�yIBF@9^9XTUHdL�QRT@9X9XAEx=CD?M9��! �"�$#��

Gi?M9;LOCD?�Z[TSN��BCE?�ADH=AnL\ADF@CD?MZ]?MH�L�F@ImL\An>Ug�� � wHyN=?PZ[TUHdL\<X?M<���:=? L(Si,et/Gi,et)

?B9;LOH=T@HbkxJCDTS�S:=F@HdL¢|=AECR_`F@:JLOZ[TUHdL\<;?B<i��:=? L(Si,et/Gi,et) = Lm(Si,et/Gi,et)

�C TU:=<^N=gMZ]TUHdLX<X?B<iC evgM�dF@CEAEL\ga|bHJTU:=9OF@CDCETUH=9�NJgBZ[TUHdL\<X?M<^N=?B:b�jAEH=IBCE:=9XAETUH=9

�~ � Lm(Si,et/Gi,et) ⊆ L(Si,et/Gi,et)

�7 � L(Si,et/Gi,et) ⊆ Lm(Si,et/Gi,et)

�~ � E C�?B9;LOgm>bAEN=?BHdL���:=? Lm(Si,et/Gi,et) ⊆ L(Si,et/Gi,et)

⇒ Lm(Si,et/Gi,et) ⊆ L(Si,et/Gi,et)

L(Si,et/Gi,et)?B9 LOQ=<Xg�J�b?mk¦IMCDTU9��pI¢F@< L(Si/Gi)

?B9 L�9;:=Q=Q�TU9XgPQ=<;g�J�b?mklIBCETU9��⇒ Lm(Si,et/Gi,et) ⊆ L(Si,et/Gi,et)

�7 �iQRTU:J<[NJgBZ[TUHdL\<X?M<]��:=? L(Si,et/Gi,et) ⊆ Lm(Si,et/Gi,et)

|¤AECi9X:�%oL]N=?jZ]TUHdLX<X?B<[��:=?

∀s ∈ L(Si,et/Gi,et)| s ∈ Lm(Si,et/Gi,et)

�s ∈ L(Si,et/Gi,et) ⇒ δi,et × ξi,et((qi,0, xi,0), s) = (qi, xi)

⇒ 9XTUAnL (qi,xi) = (qi,in,xi,in), textsoit (qi,xi) 6= (qi,in,xi,in)9XA (qi,xi) = (qi,in,xi,in)

⇒ ∃ u ∈ Σ∗i,et

L\?BC���:=? δi,et × ξi,et((qi,0, xi,0), su) = (q, x) ∈ Qi × Xi

L(Si/Gi)?M9;LOH=TUHbklx=CDTS��:wF@HdL

⇒ ∃ v LX?BCP��:=? N=?MQ=:=AE9YC evgmLcFaL (q, x) |=T@HjQ�?B:bL�FaxRTU:bL\AD<r:=HYgmLcFaLOZ]F@<X��:=g (qi,m, xi,m)

⇒ δi,et × ξi,et((qi,0, xi,0), suv) = (qi,m, xi,m)

⇒ suv ∈ (Lm(Si,et/Gi,et))

⇒ s ∈ Lm(Si,et/Gi,et)9XA (qi,xi) 6= (qi,in,xi,in)

⇒ ∃w L\?MCP�S:J? N=?MQ=:=AD9jCfehgML\FaL (qi, xi)|=TUHjQ�?B:JL�F@x�TU:JLXAD<�:=HjgML\FaL^Z]F@<X��:=g

⇒ s ∈ Lm(Si,et/Gi,et)�

Page 132: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~�� I � ����������� � � 5����� � � �7��� ��� ��� � ������

! � � � �PV ?�Z[TSN��BCE? Gi?M9;L�F@IMLXAE>Ug�9X:=AnL\? ��CfehTSIBIB:J<X<X?MH=IB?�N=?�C evgm>UgBHJ?BZ[?BHdL�N=?�IBTUZ[Z�:JL\FaL\AETUH αj,i

�� ?�ZBZ[?�9;TUAEL s ∈ L(Si,et/Gi,et)

L\?BC���:=? s 6= ε |�F@CDT@<X9O9XTUAnL s = αj,iTU: s = αj,iu

|RF¢>U?BI

u ∈ Σ∗j�

A A s = αj,iFaCDTU<;9 δi,et × ξi,et((qi,in, xi,in), s) = (qi, xi) ∈ Qi × Xi

?mL�IMTUZ[Z]? L(Si/Gi)?B9 L�HJTUHbk¦xJCDTS�S:=F@HdL¢|wF@CETU<X9iAEC8?��JAE9;LX?�:JH=?P9XgB��:=?MH=IB?�N�ehgM>UgMH=?BZ[?BHdLX9 v′ |JLX?BC���:=?PN=?BQJ:=AD9^CfehgML\FaL

(qi, xi)|wTUHjF@x�TU:JL\AnL �W:=HjgMLcF¡L�Z]F@<;�S:Jg (qi,m, xi,m) �

C F@<KIMTUH=9;gB��:=?BHdL δi,et × ξi,et((qi,in, xi,in), sv′) = (qi,m, xi,m) � � CETU<X9 sv′(Lm(Si,et/Gi,et))|

IB?MCGF�?MH�LX<\Fa�DH=?O�S:J? s ∈ Lm(Si,et/Gi,et)� V ?�Z�MZ]?O<\FaAD9XT@H=H=?BZ[?BHdL�QR?M:JL�mL\<;?�F@N=T@QJL\ga|b9;ARTUH

9X:=QJQRTU9;?���:=? s = αj,iu�

� �� � �)(�*�� 9�#�,-�O(

� FaH=9�CE?oI s F@Q=AnL\<X?oQ=<;gBIMgBN=?MH�LB|�CDFyIMTUH=9;ADN=gM<\FaLXADTUH N=?M9�N=A �8gM<X?BHdLX9�Z[TbNJ?B9PN=?o_pTUH=IMLXADTUHJH=?BZ[?BHdLADZ[QRTU9XF@AEL�CDF�Q=<;AD9X?�?BH�IMTUZ]QbL\?�NJ?�N=A �8gM<X?BHdLX?B9i9;LX<X:=ImL\:=<;?B9�NJ?�Q=<XTSIBgMN=g�?mLiN=TUH=I�N=?�N=A �8gM<X?MH�LX9�Z[TakN��BCE?B9 �`:=H�Z[TbN��MCD?¤N=?}Q=<;TbIMgBN=g�F@9;9XTSIBAEg �OI s Fa�S:J?�Z[TbNJ? ��� V ?M9�9XQ�gBIBA�wI¢F¡L\ADT@H=9�N=?�Z]TSN=?¥IMTUH=N=:=AE9X?MH�LgB�dF@CE?BZ[?BHdL �oN=g�wHJAD<i:=HjZ]TSN��MCD?�N=?PIMTUHdL\<��@CD?B:J<iQwF@<^Z]TSN=? �

V evF@Q=Q�TU<;LPN=?oIM?[I s F@Q=AELX<X?o?B9 L�NJTU:=x=CE?�� C <X?MZ]A��B<;?BZ[?BHdLPADC¥NJgBZ[TUHdL\<X?o��:=?[��:=?BCECD?W��:=?[9XTUAnLKCGFNJ�SHwF@Z[AD��:=?�N=:�QJ<XTSIBgBNJg@|�CE?�9X:JQR?M<;>SAD9;?B:=<KQwFa<�Z]TSN=?�<X?B9 L\?�:JH=AD��:=? � � ?M:b�bA �BZ[?BZ[?BHdLPAEC�<XF@Q=Q�?BCDCE?�S:J?�9XA£CGFPIBT@Z]Z�:bLcFaLXADTUHoN=?�Z]TSN=?B9}AEH � :=?O9X:=<�CfevF@IMLXAE>aFaLXADTUHWTU:]CGFPN=gB9XF@IMLXAE>aFaLXADTUH[N�eh:=HuZ[TbN��MCD?^N=?Q=<XTSIBgMN=g@|UAECb?MHW>@F�NJ?�Z�MZ]?�QRT@:=<¥CD?�Z]TSN��MCD?rNJ?B9¤9XQ�gBIMA�wIBFaL\AETUH=9�� V ?B9¥Z[TSN��BCE?B9�NJ?B9¤9XQ�gBIMA�wIBFaL\AETUH=9TUHdL�FaADH=9;A�gMLXgogML\?MH=N=:=9�?BH Q=<;gBIMAD9\FaH�L�CE?B9KgML\FaL\9KNJ?[NJgBQwF@< LP?MLPN=?o<;?ML\T@:=<K?BH{IBTUZ[QwFaLXADx=AECDAnL\g�F¢>U?BICfe s AD9 L\TUAE<X?�N=:jQ=<;TbIMgBN=g �@ TU:=9KF¢>UT@H=9�Z[TUHdL\<Xg���:=?WNwF@H=9�CD?�IMTUHdL\?��bLX?WN=?�CDF]9;�SHdL s �B9X?oN=?�IBTUHdL\< �UCD?M:=<X9M|RCE?�IMTUH=IB?MQJLPN=?

IBTUHdL\< �UCGFax=ADCEAEL\gP?M9;LKAEH=9X:�%[9XF@HdLPQRTU:J<�Q=<;TU:J>U?M<KCfeh?m�bAD9 L\?MH=IB?WN�eh:=H�:=HJAD��:=?�9;:=QR?M<;>SAD9;?B:=<KQ=F@<�Z[TbN=? �@ T@LX<X?�NJgBZ[TUH=9;LX<\FaLXADTUHo9;?�xwF@9;?�9;:=<rCDF�H=TaL\ADT@H]N�ehTUx=9;?B< >@Fax=ADCEAEL\g � � Hu? �R?MLr:=H�9;:=Q�?B<;>SAE9X?B:J< S F@9;9XTakIBADg�F@:�Q=<;TbIMgBN=g G H�ehTUx=9;?B<;>@?WQwF@9�CE?B9�gm>UgMH=?BZ[?BHdL\9KNJ?�IBTUZ[Z�:JL\FaL\AETUH � � H�<X?m>@FaH=I s ?@|8ADC�TUx=9;?B<;>@?L\TU:=9�CD?M9�gm>UgMH=?BZ[?BHdL\9rN=?�C e�Fa:JL\TUZ]FaLX?iH=TUH�gmL\?MH=N=: G � � H=9X:=AnL\?a|SHJTU:=9�Fz>@TUH=9�N=g�wHJARN=?M9�9;QRgMIBA�wI¢F¡kL\ADT@H=9^N=?�IMTUHdL\< �UCD?KQ�TU:=<^I s F@��:=?�Z]TSN=?KN=?P_pTUH=ImL\AETUH=H=?MZ]?MH�L��FL�<^CD?B9^Z[TbNJ?B9^N=?P_pTUH=IMLXADTUHJH=?BZ[?BHdLIBTUH=9;ADN=gM<XgM9�Q�?B:J>@?BHdL�ML\<;?oN=A��RgB<;?BHdL\9M|�QwF@<KIBT@H=9XgM�S:J?BHdL�CE?B9P9XQ�gBIMA�wIBFaL\AETUH=9K<X?M9XQ�?BImL\AE>@?B9�9XTUHdL�N=AE9 kL\ADHJIML\?M9�� � F@HJ9�CE?OI s F@Q=AELX<X?OQ=<XgMIBgMN=?BHdL¢|SH=TU:J9rF¢>UT@H=9�LX<\F@AnL\giCD?^Z[gBIBF@H=AD9;Z]?iNJ?�IMTUZ]Z�:JLcFaLXADTUHW?MHdL\<X?CD?B9�N=A �8gM<X?BHdLX9rZ[TbN��MCD?M9�NJ?B9rQJ<XTSIBgBNJgB9r?MH�gmL\?BHJNwF@HdL�IM?B9rNJ?B<XHJAD?B<;9r?mLr?MH�N=gmL\?B<;Z]AEHwF@HdL�CD?B9}gmLcFaLX9rN=?N=gBQwFa<;L�?ML�N=?o<X?mL\TU:J<�Q�TU:=<PI s Fa�S:J?]Z[TbN �BCD? � V ?B9�9XQ�gBIMA�wIBFaL\AETUH=9KN=T@AE>U?MHdL�9;:=AE>S<;?[?��bQ=CDAEIBAELX?BZ[?BHdLCfehgM>UT@CD:JLXADTUHoN=:[Q=<XTSIBgMN=g@|d?MCDCE?B9}9XTUHdL�gB�UF@CD?MZ]?MH�L}9;TU:=Z[AD9;?B9�F@:[Z]gMI¢F@H=AE9XZ[?iN=?^IBTUZ[Z�:JL\FaL\AETUHWQ�TU:=<CGF�NJgML\?M<XZ[ADHwF¡L\ADT@H]N=?M9igML\FaL\9�N=?�N=gMQwF@<;LrTU:uN=?�<X?MLXTU:=<�QRTU:J<rI s F@��:=?�Z]TSN��BCE?�NJ?�CGF�9XQ�gBIBA�wI¢F¡L\ADT@H �

Page 133: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ��� � ��� � � � � � � � ~��J~

−{d ,f ,f }2 31−{d ,f ,f }2 31 −{d ,r }3 1

−{d ,r }3 1

d2

xx0 1

Σ −{f }Σ 3f3

d3x x0 1

x x0 1

p1

r1

f 1 , f3

spécification 1, 2 spécification 3

spécification 4

ΣΣ Σ −{r }1Σ

������� � � ~���� � ��3��%+,"29 35"29�9 ��1���� ) � �$ "����� 9

Page 134: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~��d7 � ����������� � � 5����� � � �7��� ��� ��� � ������

Page 135: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~�� �

� ��������� � �

� ������������� ����� ��� ����� � � ���

"!$# %'&)(�*,+.-�/�01(324+5&

687:9 x �<;$=4>@?BADCFE<?HGF=I?HCKJMLONF;8=I;8=QPKJOCF?R>@ES;8;IT<>UNF;8V 9 GW>@E<;$E�L 7 JOCXCFLH?B=YJ@xF?BLH?R>@Z�NF;8LHJ[V]\FLB>S?R^_V 9 NFZ$LB?HTSJM>@? 9 G;4>[NF;`LHJaTcbdGW>SP��$T<;eNX;`= 9 GW>SE��fLB;$\FE<TgNKJOGXT[LH;h=YJONFE<;`NF;`LHJaif;IT<>S? 9 GjNX;$T[V 9 NX;$TgNX;kA 9 GF=4>@? 9 GFGF;$Vl;$GW>��687 ;4md;$VlCFLH;aES;4>@;$Gn\o= 9 ESES;ITSC 9 GFN �p\XGqT<bDT<>��$Vl;]CFE 9 C 9 T<Z]CKJOEhLH;aifE 9 \XC';]NX;a>@ESJYrOJM?HLtsvuewdxzy�NX;4^rO;$Gn\|{~}ksvu�wqNX\���E 9 \FC';5NF;l��;I=QPF;$E<=QPF;j����svw ��{�LtT 7 JOiO?B>�N 7 \FGo=YJMT�N 7 Z4>@\FNX;l= 9 VlV]\FG ��CFLH\D^T<?H;$\XEST�?BGnrO;$Tc>@?HifJM>@? 9 GFTtN 9 GW>�LH;$TtESZ$T<\FLB>@JM>@T 9 GW>8ZI>SZvCFESZITS;$GW>SZ$TzL 9 E<TtNF\)= 9 GFifE �$Tz��wX� 7:� �t�1� ���z� � ���� �8���asv� � �M�z� �h��� � ���z� �eJMA � ��� �

6 JkCFE 9 =QPKJM?HGF;1TS;$=4>@? 9 G];$Tc>8= 9 GFT@JO=IESZI;�kL�J�CFESZITS;IGn>@JM>@? 9 G]NF\)TcbDT<> �IV.;gZI>@\XNF?HZ1NKJOGFT�=I;g=QPKJMCF?B>SES;;4>hNX;aLHJlNFZIVpJMES=QPF;eN 7 ZI>@\XNF;5CFE 9 C 9 TSZI;�� 6 ;$T�TS;$=4>@? 9 GFT�TS\F?RrOJMGn>S;$Th= 9 E<ES;$T<C 9 GFNF;$GW>`JO\dm�NF? ��ZIES;$GW>S;$TZ4>QJOC;$T�NF;"=I;I>S>S;"NFZ$V.JOES=QPX;���} 9 \FT�= 9 GX=$LH\XE 9 GFT�;IG KG�TS\FE�L 7 JOCXCFLH?B=YJ@xF?BLH?R>@Z�NF;)G 9 >@ES;)CXE 9 C 9 TS?R>@? 9 G��� �z} �O�O� �

"!@� ��*t�¡ �¢¡&)(U£�(324+5& -�¢¥¤n¦_¢g§j¢¡¨ ©�¤4¢

ª[«­¬v«c® ¯±°�²d³´Fµ�¶h·dµ~¸�¹»ºh¼½²n¾v²W·X¿3À�°6 ;`T<bDTc>@Á$Vl;�Â5Z4>@\FNX?H;$Eg;$T<>[\FG�CFESZIPF;$GXTS;$\XEvCFGF;$\XVpJM>S?HÃn\F;`NXZ$CFLHJOÄYJOGW>g\FG�CFE 9 NF\F?R>gN 7 \FG�C 9 Tc>@;

NF;aCFES?BTS;5Âp\FG�C 9 T<>S;]NF;aNFZ$C 9 TS;5TS\F?RrOJMGn>k\FGq=IbD=ILH;5;IG�ÅpÆ�ÇfÈ{�Lt;IT<>`= 9 VlC 9 T<Z5NF;a>@E 9 ?HT�=QPKJMÉ�GX;$TA 9 GX=I>@? 9 GFGF;ILHLB;$TeÃD\X?vJOTST<\FES;IGW>"LH;pV 9 \XrO;$Vl;$GW>]rO;$E<>S?H=$JOLf|UP 9 E<?HÊ 9 Gn>@JOLg;4>)L 7 JOT<CF?HESJM>@? 9 G�È 6 ;$T]NXZ$CFLHJ�^=I;$Vl;$GW>@T"P 9 E<?HÊ 9 GW>QJO\dmË;I>"rf;IE<>S?H=YJM\dmÌT 9 Gn>.JOT<TS\FE<Z$TlCKJOE)NF;I\dmÍrOZ$ES?BGFT Å�N 9 \=xFLB;�;IÎ';I>pÇÍCF?HL 9 >@ZITE<;$TSC;$=4>@?Rrf;$Vl;$GW>hCKJOE¡\FG�NF?HTc>@E<?DxF\X>S;$\FEhÏfÐOÑWxX?HT<>@J@xFLB;�;I>h\FG NX?HT<>SES?ExF\X>@;I\FE�ÏfÐfÑ)V 9 G 9 Tc>QJ@xFLB;OÈÒsgPFJ�^=I\FG|N 7 ;IGn>SES;l;$\dm�;IT<>eZ$Ãn\F?BC'Z"NF;"=$JOCX>@;I\FESTeNF;)ÓKG�NF;"= 9 \XESTS;lV.JOifGFZ4>@?HÃn\F;IT$È 6 J�CFE<Z$PF;IGFTS? 9 G�;IT<>JOT<TS\FE<Z$;eCKJOEv\FG�T<bDTc>@Á$Vl;�Ô�;$GW>@\FE<?­ÈÕ4ÖQ×eØÚÙ]ÛDÜg×�ÝÚÞÚß<à:áãâ­äQåæáçÝ4è`ÞÚéSâ3ØYêÚâëå­ìcí[é<â3Ù3ß<ä4î~åæá:ïRâ3ð

Page 136: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~��O� ���������� �������������������������� �"!#���%$&���'$(��)

yk;I\dm"V 9 NX;$T�NF;1A 9 GF=I>S? 9 GXGF;$Vl;$GW> 9 GW>�Z4>@ZvES;4>@;IGD\XT8C 9 \XE8=$;[TcbdTc>@ÁIV.;�*WLB;[V 9 NF;gG 9 Vl?HGKJOLn;4>�LH;V 9 NF;kNXZ$ifESJONFZOÈXy`JOGFTgLH;kV 9 NF;hG 9 V.?BGKJOLÒLH;�T<bDTc>@Á$Vl;�ES;IV.CXLH?B>zLHJeA 9 GF=4>@? 9 GFGKJOLB?B>SZ�C 9 \FE1L�JOÃn\F;ILHLB;�?BLJ5ZI>SZ`= 9 GXÄ$\&+ër 9 ?HE1CKJOESJOifE@JMCFPF;kT<\F?BrMJOGW>-,4ÈD�k\�= 9 \FEST[NX\pA 9 GF=4>@? 9 GFGF;$Vl;$GW>gG 9 Vl?HGKJOL |WL 7�9 =I=$\FE<ES;IGF=$;N 7 \XG�Z4rfZIGF;$Vl;$GW>.N 7 ; md=$;$Cd>@? 9 G.+ë?H=I?gNF;�NFZ4A JO?HLBL�JOGX=$;�,�;$GXiWJOif;IE@J�LH;pT<bDT<>SÁ$Vl;�;IGÍA 9 GF=I>S? 9 GXGF;$Vl;$GW>NFZ$ifESJONFZ�NKJMGFT]LH;IÃn\F;$L1?HLzC';I\X>"JO=I= 9 VlCFLH?BE�\FGF;jCKJME<>@?B;pNF;pT@J�>-/M=QPF;j;$GÍNXZ$CF?R>)NF;jLHJ NFZ4A JO?HLBL�JOGF=I;= 9 GFT<?HNFZIESZI;OÈ

Poste de déposePoste de prise

Sans aspiration

Avec aspiration

02143�5 ÏdÈ ~�687�9;:�<>=@?A=�BDCFE>G�=H=�IJ?A=K?ALMBON�G�=

{�GF?R>@?HJOLH;IV.;IGn>,LH;gT<bDT<>SÁ$Vl;�;IT<>zNKJOGXT8LH;[V 9 NX;[G 9 Vl?HGKJML­È 6 ;vCFESZIPF;$GFT<;$\FEz;$Tc>z;$G"C 9 TS?B>S? 9 G5PKJO\X>S;@|Â�ifJO\F=QPF;P+ C 9 T<?B>@? 9 G�N 7 JM><>@;$GW>S;�,`;I>�?BLtG 7 boJ�CKJOT�N 7 JOT<CF?HESJM>@? 9 G�È 6 ;)=4bd=ILH;";$G Å�Æ Ç�+ëÓKiO\FES;.ÏdÈ ~ ,= 9 E<ES;$T<C 9 GFN�T<Z$Ãn\F;$GW>S?H;$LBLH;IV.;IGn>�Â"L 7 JO=4>@?BrMJM>S? 9 G.NF;$ThJO=4>@? 9 GFTvTS\F?RrMJOGW>@;$TQ*6 NF;$T<=$;IGFNFES;aLH;`rOZ$ES?BG�rO;$Ec>@?H=$JOLf|6 T@JO?BTS?BEvL�J]CF?BÁ$=$;eÂ)CKJOEc>@?BE[NF\�C 9 Tc>@;�NF;�CFE<?HTS;R+ëCKJOE¡JOT<CF?HESJM>@? 9 GS,m|6 V 9 Gn>S;$E¡L�J]CX?HÁ$=I;@|6 JYrOJMGF=$;IE�LHJ)CF?HÁI=$;eJO\d^_NF;$T<TS\FT�NF\�C 9 Tc>@;�NF;�NFZIC 9 T<;@|6 NF;$T<=$;IGFNFES;aL�J)CF?BÁ$=$;a|6 NFZ$C 9 T<;$E�L�J]CF?BÁ$=$;R+ ÓKG N 7 JOT<CF?HESJM>@? 9 GS,�|6 V 9 Gn>S;$E¡LH;hrfZ$E<?HG�rf;IE<>@?B=YJOL |6 ES;I=$\FLB;$E¡LH;`rOZ$ES?BG P 9 ES?BÊ 9 GW>QJML­Èy`JMGFT5=I;I>a;4md;$VlCFLH;a|,LB;"V 9 NF;lG 9 Vl?HGKJOLtGFZ$=I;$TST<?B>S;jLH;)A 9 GF=4>@? 9 GFGF;IV.;IGn>aT@JMGFTaA JO\d>@;lNF;$Te>@E 9 ?HT

=QPKJMÉ�GX;$T5A 9 GX=I>@? 9 GFGF;ILHLB;$TaJOTST<\FE@JOGW>)LB;pV 9 \XrO;$Vl;$GW>5rO;$E<>S?H=$JOLf|ULH;lV 9 \Xrf;IV.;IGn>]P 9 ES?BÊ 9 GW>@JOL�;I>]L 7 JMTc^CF?HESJM>@? 9 G�È 6 ;jV 9 NF;.NFZ$ifESJONFZ�;IT<>)=$JOE@JO=4>@ZIES?HT<ZjCKJOE5LH;pNdbdTcA 9 GF=4>@? 9 GFGF;$Vl;$GW>"N 7 \FGF;pES;$T<T 9 \XES=$;�NF\T<bDT<>SÁ$Vl;OÈD{�LKTS;$ESJa;IGF=$LB;$GF=QPFZ�TS\X?B>@;�Â�L�J�NFZ4A JO?HLBL�JOGF=I;[NF;�L�J�=QPKJMÉHGF;vA 9 GF=4>@? 9 GFGF;$LBLH;vJMTSTS\XE@JOGW>1LH;¡V 9 \d^rf;$Vl;$GW>lP 9 E<?HÊ 9 GW>QJOL�+ NFZ4A JO?HLBL�JOGX=$;lNF\ÍrfZ$E<?HG 9 \ÍNX\�NX?HT<>SES?ExF\X>@;I\FE5CFJOE];4md;IV.CFLB;�, È 6�9 EST]NX;j=$;4>S>@;ZI>@\XNF;@|'G 9 \FThTS\FCFC 9 T<;$E 9 GFT�Ãn\F;5T<;$\FLB;5=$;4>S>S;]=QPKJMÉHGF;5C;$\X>h> 9 V�x';IEh;IG�CKJOGFGX;@|'JO?HGFT<?3LH;eV 9 NF;eNFZ4^ifE@JONXZlGX;)TS;$ESJ�CXLH\FT�JOT<TS\FE<Z.Ãn\F;"CKJME�NF;$\dm�E<;$T<T 9 \FE<=$;ITT+ë=QPKJMÉ�GX;"rO;$Ec>@?H=$JOLH;5;I>aJOTSCX?HE@J�>@? 9 GS,4È'y`JOGFT=$;l=YJOT�L 7 ;$GXTS;$V�xFLH;)NF;ITa?BGFNF?B=$;$T�NX;lV 9 NF;$T�NF;)A 9 GX=I>@? 9 GFGF;IV.;IGW>a;IT<> {n, d} | 9VU n ES;ICFESZITS;$GW>S;pLH;V 9 NF;lG 9 Vl?HGKJOL�;4> d LB;.V 9 NX;.NFZIifE@JMNFZ@|,;I>]L 7 JMLHCFPKJax';4>aNX;$T5Z4rfZIGF;$Vl;$GW>@T"NF;.= 9 VlV]\X>@JM>@? 9 G�;$T<>Σ′ = {r, p} + r ;IT<>�L 7 ZIrOZ$GF;IV.;IGW>hNX;aE<Z$CKJOESJM>@? 9 G�| p L 7 Z4rfZIGF;$Vl;$GW>hNF;�CKJOGFGF;W,4È

Page 137: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�����(� �� ��2$(��� �(�������� )�� ��� ���%�� ��� � ~�� Ï

ª[«­¬v«­¬ ¯�3À �8´F³ � °�º����·d¼kºk°6 JkNFZIVpJOE<=QPF;gN 7 Z4>@\FNF;vNX\]T<bDT<>SÁ$Vl;v= 9 VlVl;$GF=I;1CKJMEtL 7 ZI>S\FNF;[NX\]V 9 NF;zG 9 Vl?HGKJMLQ+ëTS;I=I>@? 9 G"ÏdÈ � , È

y`JMGFT1=I;kV 9 NX;�LB;vA 9 GF=I>S? 9 GXGF;$Vl;$GW>1NF\pTcbdTc>@ÁIV.;h;$T<>1=YJME@JO=4>@Z$E<?HT<ZhCKJME1\FG.V 9 NFÁILH;¡NF\pCXE 9 =$Z$NXZ GnJO\XÃD\X;$L3;$Tc>`JOT<T 9 =$?BZe\XG V 9 NXÁ$LH;�NX;eT<C'ZI=$?RÓK=YJM>S? 9 GXT EnÈ 6 ;�A 9 GF=4>@? 9 GFGF;IV.;IGn>�NFZIifE@JMNFZ�;$T<>hL 7�9 x��<;4>

NF;5L�J.T<;$=4>@? 9 GoÏdÈ � ;I>�;IT<>�V 9 NFZ$LB?HTSZ�CKJMEkLH;IT`V 9 NFÁILH;IT GdNF\qCFE 9 =$ZINFZ];4> Ed

NX;$T�TSCZ$=I?BÓK=$JM>@? 9 GFTIÈ6 J�TS;I=I>@? 9 GpÏdÈãÏ`;IT<>zNFZ$NX?HZ$;�Â�L�J�= 9 GFT<>SES\F=4>@? 9 G"NF;$TzV 9 NFÁILH;$T8NX;$T�CFE 9 =$ZINFZ$TzZI>S;$GFNX\FT Gn,et

;I> Gd,etÈ

6 ;$TgV 9 NFÁ$LB;$T1ZI>@;IGFNF\FTvNX;$TvTSCZ$=I?BÓK=$JM>@? 9 GFT En,et;I> Ed,et

|XJO?HGXTS?ÃD\X;�L�JaTcbDGn>SPFÁ$T<;aNX;$T[= 9 GW>@E��OLH;$\XESTZ4>@;$GXNF\FT Cn,et

;4> Cd,etT 9 GW>�CFESZITS;$GW>SZ$TkNFJOGFT�L�J]TS;I=I>S? 9 G ÏdÈ��XÈ

(G )n ,et(G )d ,et

En Edn ,et(E ) (E )d ,et

(C )n ,et étendu

Controleur nominal���� ������������

d ,et(C ) étendu

Controleur dégradé

����������������������������������������

������ !!!!""""

##$%�%%�%%�%&�&&�&&�& '�''�'(�()�))�)

)�)*�**�**�*

+++,,, -------.......

Cn ( )

/�/0�0 1�123�33�3445566

77777778888888

9999999:::::::

;;;<<< ==>>

?????@@@@@AABBC�CC�CC�C

C�CC�CD�DD�DD�DD�DD�DE�EE�EE�EFFF

Modèle nominal

Système physique à commander

du procédé G

Modèle nominal

du procédé G

Spécificatin nominale

dn

Modèle dégradé Modèle dégradéétendu

étendue

étendu

étendue

Mode nominal

(n)

Mode dégradé(d)

panne (p)

Spécification dégradéeSpécification nominale Spécification dégradée

Synthèseréparation(r)Synthèse Synthèse

Controleur nominal^ ^ ^

02143�5 ÏdÈçÑ 6HGKLJILK C-:NMO=JBDC-N-BON�G�L-=

sg;I><>@;�NFZIVpJOE<=QPF;@|�CFE<Z$T<;$GW>@ZI;�ÓKiO\FES; ÏdÈçÑ�;$T<>lNFZ4>QJO?BLHLBZ$;jZ4>QJOC;�CKJOE)ZI>@JOC;�NFJOGFT"LH;IT)TS;$=4>@? 9 GFTT<\F?BrMJOGW>@;IT *6�O�PRQTSVUXW�Y[Z]\_^`Uba`\cZXdea`Qgfhai\cakjlPRU�am^inpo�qrU�stPud�\cakvxwzy|{

6 V 9 NFZ$LB?HTSJM>@? 9 GpNF\�CFE 9 =IZ$NFZ Gn*FTS;I=I>S? 9 G�ÏdÈ � È ~

6 V 9 NFZ$LB?HTSJM>@? 9 GpNF;IThT<C'ZI=$?RÓK=YJM>S? 9 GXT En*XTS;$=4>@? 9 G�ÏDÈ � ÈçÑ

6 rfZ$E<?BÓK=$JM>@? 9 G�NF;�L�J]= 9 GW>@E��OL�J@xF?BLH?R>@Z�*DTS;I=I>@? 9 G�ÏdÈ � È �6�O�PRQTSVU~}�Y[Z]\_^`Ub^`j��c�uQg^`j�a`\|akjlPRU�ai^mnpo�qrU�stPud�\ca�v_w��x{

6 V 9 NFZ$LB?HTSJM>@? 9 GpNF\�CFE 9 =IZ$NFZ Gd*KT<;$=I>S? 9 G ÏdÈ � È ~

6 V 9 NFZ$LB?HTSJM>@? 9 GpNF;IThT<C'ZI=$?RÓK=YJM>S? 9 GXT Ed*KTS;I=I>@? 9 G ÏdÈ � ÈãÑ

Page 138: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~�� � ���������� �������������������������� �"!#���%$&���'$(��)

6 rfZIES?BÓF=YJM>S? 9 G�NF;�L�J]= 9 GW>@E��fL�J@xX?HLH?R>@Z�*DTS;I=I>S? 9 G ÏdÈ � È �6kO PRQTSVU~y Y�Si� \xs j ^`j�qLjlPRU�ai^mniqHo�qrU�stPud�\|a�vxw v|{6 JOLB>S;$E<GKJOGF=I;�NF\ V 9 NF;�G 9 Vl?HGKJML'rf;IEST�LH;�V 9 NX;�NFZ$ifESJONFZ πn,d

*KT<;$=I>S? 9 G ÏdÈçÏdÈ ~6 = 9 GXT<>@E<\F=I>S? 9 G�NF\�V 9 NFÁILH;�Z4>@;$GXNF\ NX\ CFE 9 =IZ$NFZ Gd,et

*KTS;I=I>@? 9 G ÏdÈçÏdÈãÑ6 JOLB>S;$E<GKJOGF=I;�NF\ V 9 NF;�NFZ$iOE@JONFZ�rO;$EST�LH;�V 9 NF;�G 9 Vl?HGKJML πd,n

*KT<;$=I>S? 9 G ÏdÈçÏdÈ �6 = 9 GXT<>@E<\F=I>S? 9 G�NF\�V 9 NFÁILH;�Z4>@;$GXNF\ NX\ CFE 9 =IZ$NFZ Gn,et

*KTS;$=4>@? 9 G�ÏDÈãÏdÈ �6kO PRQTSVU ��YVqrSVj�sld � s Q PRd�\caiq UlP s \ca|PR���cf�U�n`� q�j�P U ai^inmqHo�qrU�stPud�\cakvxw�� {6 = 9 GXT<>@E<\F=I>S? 9 G�NF\�V 9 NFÁILH;�Z4>@;$GXNF\ NX;$T�TSCZ$=$?RÓK=YJ�>@? 9 GFT Ed,et

*KT<;$=4>@? 9 G�ÏDÈ �XÈ ~6 T<bDGW>@PFÁITS;aNF\ = 9 GW>@E��fLH;I\FEvZI>S;$GFNF\ ;$G�V 9 NF;�NFZIifE@JMNFZ Cd,et

*KTS;I=I>@? 9 G ÏdÈ��XÈãÑ6 = 9 GXT<>@E<\F=I>S? 9 G�NF\�V 9 NFÁILH;�Z4>@;$GXNF\ NX;$T�TSCZ$=$?RÓK=YJ�>@? 9 GFT En,et

*KT<;$=I>S? 9 G�ÏdÈ��XÈ �6 T<bDGW>@PFÁITS;aNF\ = 9 GW>@E��fLH;I\FEvZI>S;$GFNF\ ;$G�V 9 NF;�G 9 V.?BGKJOL Cn,et

*KT<;$=4>@? 9 G�ÏdÈ��XÈ �

�l!�� (U£e©q¢ #� ¨ +l-�¢¥&�+a¨ 2I&�£�¤�&�+5& �[(3¢¡&�-�/

ªv« �¡«<® ��´X¸v³ �º º ��¹k²��~° À�¸vºh° ¹k¸zÀ�µ~¹ ���Gn

6 J¡V 9 NFZ$LB?HTSJM>@? 9 G�NF\5CXE 9 =$Z$NXZ1= 9 GFTS?BT<>S;gN 7 J@x 9 ESNaÂhNFZI= 9 VlC 9 TS;IE,LB;zTcbDT<>@ÁIV.;1;$GaT 9 \FT~^�TcbdTc>@ÁIV.;IT9 \ E<;$T<T 9 \FE<=$;ITk= 9 GFTS?BNFZ$E<Z$;$T�= 9 V.Vl;�Z$LBZ$Vl;$GW>QJO?BES;ITB|F= 7 ;IT<><^�Â�^�NX?HES;�NF;IT¡ES;$T<T 9 \XES=$;ITkN 9 Gn>�LB;e= 9 GF=I;$Cd^>@;$\XET+ëG 9 \FT ,�= 9 GFT<>SES\F?R>5NX?HES;I=I>S;$Vl;$GW>eLH;"V 9 NFÁILH;OÈ�{�L�T 7 JOiO?B>�?H=I?8NF;$Te>@E 9 ?HT�=QPKJMÉHGF;$T�A 9 GF=4>@? 9 GFGF;ILHLH;ITCFESZITS;$GW>SZ$;$T�CFE<Z$=IZ$NF;IV.Vl;$GW>��ÚÈ 6 ;aV 9 NF;eG 9 Vl?HGKJMLUNX\�T<bDT<>SÁ$Vl;]TS;IE@Jp;IGFTS\X?B>@;5NFZ$=IES?B>hCKJOEh\FG�T<;$\FLV 9 NFÁ$LB;kJM\X> 9 V.JM>S; Gn

9 xX>@;IGD\pCKJOEgLHJa= 9 V.C 9 T<?B>@? 9 G"CKJOESJOLHLBÁ$LH;¡NF;IT[V 9 NFÁILH;IT1NF;h=QPKJO=I\FG�NF;$T1>@E 9 ?HTES;$T<T 9 \XES=$;IT$È

6 ;$TlV 9 NFÁILH;IT.JM\X> 9 V.JM>S;$T"= 9 E<ES;ITSC 9 GFNKJOGW>.ES;ITSC;$=I>S?BrO;$Vl;$GW>�JO\�rfZIES?HGÌrf;IE<>S?H=YJMLK+ ÔkÔ%,m|8rfZIES?HGP 9 ES?BÊ 9 GW>@JOL + Ô���,l;I>�Â�LHJ|rf;IGW> 9 \FT<; +ëÔ ,lT 9 GW>�N 9 GXGFZ$T�CKJMEjL�JoÓKif\FE<;�ÏdÈ � È1{�LBTj= 9 GXT<>@?R>@\F;IGW>�L�JT<>@E<\F=I>S\FES; 9 C'ZIE@JM>S? 9 GXGF;$LBLH;¡G 9 Vl?HGKJMLH;¡ÂaLHJOÃn\F;$LBLH;¡TS;IE 9 GW>¡JMTST 9 =$?BZ$;ITgNF;IT[TSCZ$=I?BÓK=$JM>@? 9 GFTzG 9 Vl?HGKJOLB;$TIÈ} 9 \FT�E<;$V.JOESÃn\ 9 GXT�ÃD\X;)LH;$T�Z4rfZIGF;$Vl;$GW>@TeNF;)= 9 V.V5\X>QJM>S? 9 G p ;I> r G 7 JOCXCKJOE@JM?HTST<;$GW>�CKJOT�NKJMGFT�LH;V 9 NFÁ$LB;�NF\�rfZ$E<?HG�P 9 E<?HÊ 9 GW>QJOL�;4>�N 9 GF=�NKJOGXT�LB;�V 9 NFÁILH; Gn

È6 ;eV 9 NFÁ$LB;�NF\�CFE 9 =IZ$NFZa;$G�V 9 NF;�G 9 Vl?HGKJOL Gn

= 9 VlC 9 E<>S; 64 Z4>QJM>STh;4> 192 >SE@JOGXTS?B>S? 9 GXT$ÈFÔ�\LH;�G 9 V�xFES;�?HVlC 9 E<>@JOGW>[N 7 ZI>@JM>@T�;I>¡NF;�>SE@JOGFT<?B>S? 9 GFTM|F=$;�V 9 NXÁ$LH;kGF;�TS;$ESJlCFJOT¡ES;$CXESZ$T<;$GW>@Za?H=I?­È

ªv« �¡«_¬ �g¶��³'µ��k³ ��·dµ~¸z¹h² ºh¼»À�¸vºh° ¹h¸zÀ�µc¹����En

� >QJMGn>]N 9 GFGFZpL�J T<?HVlCFLH?B=$?R>@Z)NF\Í=4bd=ILH;jNXZ$TS?BESZ.C 9 \XE5=$;pV 9 NF; +ë=IbD=$LB;j;$G Å Æ Ç|NFZI=$ES?R>]CFE<Z4^=$Z$NX;$VlV.;IGn>-,m|3G 9 \XTeC 9 \FE<ES? 9 GFT�G 9 \XTa= 9 GW>@;$GW>S;$EeN 7 ZI=$E<?HES;"L 7 JO\d> 9 V.JM>@;5NFZ$=IES?BrMJOGW>e=$;"=4bd=ILH;l;I>eNF;

�ÚÖ��Fä��'ä��� �âÞ�é3àçä4è�!Iä�!4é�è�Ý" �â$#�ä��æàçé��­Ý4èMâÒÞ�ä èMâKàçäzâ �á:åæétÞÚéUîcéUî&%�ä'#�á�å(�æé3ÞÚé*)4ß+�æáçè,%�Ý��­á.-<Ý4è$å­ä4à�/IÞÚé0)4ß+�æáçè1)4é+� å­áçî<ä àécåhÞÚé�)Iécè$åæÝ" �â é2#�à3 Úå544å768 �é�ÞÚé�î&%�ä:9ãè�é<âgï Ý4èMî�åæáçÝ4è�è�écàçà:éSâvä4â­â ;�­ä4èIå[àçé�ígÝ" �)4é<í[écè$å<%�Ý��­á3-cÝ4è$å_ä à=/Xàçé�í[Ý� �)Iécí[écè$å)Ié��æåæáãîcä4àWé~å3à=> äIâ #�á3�_äQåæáçÝ4èDÖ

Page 139: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�����A� ��� ���2������ ��)�� �H� �P ����� �H���p��������) ! ~����

0 1

3 2

modèle du vérin vertical

0 1

23

modèle du vérin horizontal

0 1

23

flib

dasp

fasp

dlib

fav

dav

drec

frec

dmont

fdes

ddes

fmont

modèle de la ventouse02143�5 ÏdÈ �@6�&N�?��<>=-GK?A=-G C =-G-G�N �AC-:-=-G ?lK��(G <>= I N�?A=��QN I E��cK <

O��cj�a`U Z U acPuq s \|acPR���|f�Q��mf�U�q O��cj�aiU�Z]U�a|Puq d�ams \ca|P �;�cf�Q��mf�U�qNKJYr yk;IVpJMGFNF;�N 7 JÚrMJOGX=$; A JYr �t?BG�N 7 JYrMJOGF=I;NFE<;$= yk;IVpJMGFNF;�NF;�ES;I=$\FL AëES;I= �t?BG�NF;�ES;$=I\FLNFNF;IT yk;IVpJMGFNF;�NF;�NF;$T<=$;IGn>S; AëNF;$T �t?BG�NF;�NF;$T<=$;$GW>S;NFV 9 GW> yk;IVpJMGFNF;�NF;�V 9 Gn>SZ$; AëV 9 Gn> �t?BG�NF;�V 9 GW>SZ$;NKJOT<C yk;IVpJMGFNF;�N 7 JOTSCF?BE@JM>S? 9 G A JOTSC �t?BG�N 7 JMTSCF?BE@JM>S? 9 GNFLB?Dx yk;IVpJMGFNF;�NF;�LH?Ex'ZIE@JM>S? 9 G �K?Dx �t?BG�NF;�LH?DxZ$ESJM>@? 9 G

������5 ÏdÈ ~�6���E>G�IM=@?A=-G L�� L��Q=JI =��OI4GK:-N �OI C! < K�"�<>=-GK=�I E��Q:-N �OI C# < K�"�<>=-G

rOZ$ES?RÓK;$E8Ãn\F;vLB;[L�JMGFiWJOif;1= 9 E<ES;ITSC 9 GFNKJOGW>�;IT<>�= 9 Gn>SE��fLHJ@xFLB;OÈOsg;$L�J�JM\FE@JO?R>�LB;[V.ZIES?R>@;gNX;vL�J`TS?BV.CXLH?H=I?B>SZOÈsg;IC';IGFNKJOGW>¢|OJMÓKG]NX;[V 9 Gn>SES;IEU> 9 \X>@;IT�LH;ITtZ4>QJOC;$T,C 9 T<TS?ExFLH;ITtNF;1G 9 >@E<;gNFZIVpJMES=QPF;a|OG 9 \XT�JOLBL 9 GFT3> 9 \X>NF;�V%$$Vl;�Z$=IES?BES;�NF;IT�T<C'ZI=$?RÓK=YJM>S? 9 GXT$ÈÒsg;I=$?3G 9 \FTvC;$E<V.;4>S>SE@J);$G 9 \X>SES;�NF;�rfZIES?RÓK;$EvL 7 \FGX?H=$?R>@Z`NX;eLHJT 9 LH\X>S? 9 G�ÈKsg;$T¡T<C'ZI=$?BÓF=YJM>S? 9 GFT¡G 9 V.?BGKJOLH;IT[NF;�= 9 V.V.JOGFNF;kC';I\Xrf;IGn>�$I>SES;�LH;ITvTS\F?RrOJMGn>S;$T *

~ È 687 JYrOJMGF=$; GF;�C;$\X>pTS;�A JM?HES;�Ãn\F;�T<?hLB; rOZ$ES?BG rf;IE<>S?H=YJMLh;IT<>j;IG PKJO\d>j;I>pTS?�\FGF;�CX?HÁ$=I;�;IT<>JMTSCF?BESZ$;�&

ÑDÈ 6 ;�ES;I=$\FLÒGF;hC';I\X>gT<;�A JM?HES;¡Ãn\F;hTS?ÒLH;¡rfZIES?HGlrf;IE<>@?B=YJOLÒ;IT<>1;$GjC 9 TS?R>@? 9 G"PKJO\X>S;h;4>gÃn\ 7 \FGF;hCF?HÁI=$;J)Z4>@Z�LH?Ex'ZIESZ$;�&

� ÈhÆ�GF;`CF?BÁ$=I;�GF;�C';I\X>'$4>@ES;�TSJO?HT<?H;hÃD\X;�TS?�LB;krfZIES?HGjrO;$Ec>@?H=$JOL�;IT<>¡;$G�C 9 T<?B>@? 9 GuxKJMTSTS;�;4>¡LH;�rfZ$E<?HGP 9 ES?BÊ 9 GW>QJML�;$G�C 9 TS?R>@? 9 G�ES;$GW>SESZ$;�&

� ÈhÆ�GF;¡CF?HÁI=$;¡GF;�C';I\X>�$I>SES;¡LH?Ex'ZIESZ$;vÃn\F;�TS?ÒLB;[rfZ$E<?HG"rf;IE<>@?B=YJOLK;IT<>1;$GlC 9 TS?B>S? 9 GoxKJMTSTS;�;I>zLB;[rfZ$E<?HG

Page 140: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~���� ���������� �������������������������� �"!#���%$&���'$(��)

P 9 E<?HÊ 9 Gn>@JOL�;IT<>�= 9 VlCFLBÁI>@;IV.;IGW>¡T 9 Ec>@? &ÏdÈ 6 ;�rOZ$E<?HG�rf;$Ec>@?B=YJOL�GF;�V 9 GW>@;�Ãn\F;eTS?�\FGX;eCX?HÁ$=I;�;$T<>hJOT<CF?HE<Z$; 9 \�LH?Ex'ZIESZI; &�XÈv�kCFE<Á$T $4>@ES;)V 9 GW>@Za|'LB;5rfZIES?BG�rf;$Ec>@?B=YJOL,GF;]C;$\X>�NX;$TS=I;$GFNXES;lÃD\X;]TS?�LB;arOZ$ES?BGqP 9 E<?HÊ 9 Gn>@JOLt;IT<>= 9 VlCFLBÁI>@;IV.;IGW>¡T 9 Ec>@?­È

6 ;$T5V 9 NFÁ$LB;$T)JM\X> 9 V.JM>S;$T5= 9 ESE<;$T<C 9 GXNKJOGW>"ES;ITSC;$=I>S?BrO;$Vl;$GW>lÂ�=$;IT 6 = 9 GW>SE@JO?BGn>S;$T]G 9 V.?BGKJOLB;$TT 9 GW>hN 9 GFGFZIT¡TS\FE¡L�J]ÓKiO\FES;aÏdÈ � È

Σ − {dav, ddes, fasp} Σ − {ddes, dlib}

Σ − {dav, fmont, fasp} Σ − {dav, fmont, dlib}

Σ − {drec, ddes, flib}

Σ − {drec, fdes, flib}

Σ − {drec, fdes, dlib}

Σ − {fav, fdes, dlib}

Σ − {dav, fdes, dasp}

Σ − {frec, fdes, dasp}

Σ − {dmont, fasp, flib} Σ − {fmont}

Σ − {drec, fmont, dasp}

Σ − {ddes, dasp}

Σ − {dmont} Σ − {fav, ddes}

Σ − {fav, dmont, dlib}

Σ − {drec, dmont}Σ − {frec, dmont, dasp}

Σ − {dav, dmont}

1

2

0

3

fmont

dlib

dlib

fasp

fmontddes ddes

0 1

2 3

fdes

fdes

dmont

dmont

fdes

0 1

2 3

fasp

dasp

ddes ddes fmont

dasp

flib

flib

dmont

fdes

dmont

spécification 1 spécification 2

spécification 3 spécification 4

spécification 5 spécification 6

S

S

S

S

S

S

1

2

3

4

5

6

:

:

:

:

:

: 0 10 1,

fmont

faspflib

0

2 3

1

fmont

fav

dmont

fav drecdrec favdavfrec dav frec

0 143�5 ÏdÈ �K6 � N�?��<>=-G �QN � L�IM=��D?��;G@?A=-G%GMBOL-:�E � :�K I E N �(G �QN I E��cK <>=-G

ªv« �¡«5� � �´Xµ �`³ ��·dµ~¸�¹ ºk° � � ³'¸�¹1·D´���� ���kµ��cµ_· ��JM?HGW>@;IGKJOGW>�Ãn\F;)G 9 \XT�JÚr 9 GFT�N 7 \FGF;)CFJOE<>kNFZIÓKGX?�LH;IT`V 9 NFÁILH;$ThG 9 GqZ4>@;$GXNF\FT�NF;$T�E<;$T<T 9 \FE<=$;IT

= 9 GFTc>@?R>@\KJOGW>�LB;]V 9 NFÁILH;5NX\�CXE 9 =$Z$NXZlNFJOGFT�LH;5V 9 NF;]G 9 V.?BGKJOLU;I>�N 7 JO\X>SES;)CKJOEc>�LH;IT�V 9 NFÁILH;$ThNF;$TTSCZ$=$?RÓK=YJ�>@? 9 GFT G 9 V.?BGKJOLB;$TB|1G 9 \FT�;IÎ';$=4>@\ 9 GFT�LB;�=$JOLH=I\FL�NF\ = 9 GW>SE��fLB;$\FE�G 9 G ZI>S;$GFNF\ ;$G V 9 NF;G 9 Vl?HGKJOLæÈ 6 ;jV 9 NFÁ$LB;jNF\ÌCFE 9 =$ZINFZ�T 9 \FT"= 9 GW>@E��fLH; +ëÓKif\XES;�ÏdÈçÏV,a;IT<> 9 xX>S;$Gn\�CKJOE]LB;jCFE 9 NF\F?R>)NF;

Page 141: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�����A� ��� ���2��� �� ��)�� )����� '��)�� �K��� ��������) ! ~����

Gn;I>¡NX; En

ÈF{�L�= 9 V.C 9 E<>S; 16 Z4>QJM>ST¡;I> 16 >SE@JOGXTS?B>S? 9 GXTB|X;4>¡T@J)= 9 GFT<>SES\F=4>@? 9 G Â)L 7 JO?BNF;`NF\�L 9 if?H=I?H;ILÅ]��sg� Ç�G 9 \FT¡C;$E<V.;4>¡NF;�rfZ$E<?BÓK;IE¡ÃD\X;a=I;eV 9 NFÁ$LB;`;$Tc>h= 9 GW>@E��fL�J@xXLH;OÈddes fdes dasp fasp dmont fmont

0 1 2 3 4 5 6 7

8911121415 1013

dav

fav

ddesfdesdlibflibdmontfmont

frec

drec

0 143�5 ÏdÈãÏ 6 7 N �OI C# <>=��AC ?��HI N�?A= �QN I E��cK <

�"!�� ±(U£�©q¢ � �¨ +l-�¢ -����*�£e-�� &�+5& �[(3¢¡&�-�/

�hÓFG NX;�CFES;IGFNFE<;�;IG = 9 GXTS?HNXZ$E@J�>@? 9 G LH;�V 9 NF;�NF;�A 9 GX=I>@? 9 GFGF;IV.;IGW>jNFZIifE@JONXZq;I>�CFLB\FTp>QJMESNL 7 JOLR>@;IESGKJOGX=$;)NF\|V 9 NF;"G 9 Vl?HGKJMLtrf;IEST5LB;"V 9 NF;"NFZ$iOE@JONFZa|3LH;"V 9 NFÁILH;)NF\�rfZ$E<?HG|P 9 ES?BÊ 9 GW>@JOL8N 9 ?R>$4>@ES;eJO\XifV.;IGW>@Z�CKJOE¡NF;IT¡ZIrfZIGF;$Vl;$GW>STkNF;�NFZ4A JO?HLBL�JOGF=I;`;I>¡NX;aE<Z$CKJOESJM>@? 9 G&+ p ;4> r ,%+ ÓKif\FE<;5ÏDÈ �;, È

0 1

3 2

p

p

drec

fav

dav

frec

r

0 143�5 ÏDÈ � 6 � N�?��<>= L�IM=��D?��P?��� L�CFE�� MON CFE� N �OI K <

ª[« �h«c® ��´F¸v³|�º �º���¹k²��~° À�¸vºk° º ��8´T��º�Gd

6 ;"V 9 NF;]NFZIifE@JMNFZ";$T<>e;IGF=$LB;$GF=QPFZlTS\X?B>@;"Â�LHJjC';IE<>@;)A 9 GX=I>@? 9 GFGF;ILHLB;5NF\orfZIES?HGoP 9 ES?HÊ 9 GW>QJOLæÈ 6 JG 9 \Xrf;ILHLH;h= 9 GdÓKif\FESJM>@? 9 G.A 9 GX=I>@? 9 GFGF;ILHLB;�NX\�T<bDT<>SÁ$Vl;`;$Tc>vESZINF\F?B>S;�JOL 9 EST1Â5L�J�rf;IGn> 9 \FT<;e;4>vJO\.rfZ$E<?HGrO;$E<>S?H=$JOL­È

wd\FEeG 9 >SES;l;4md;$VlCFLB;@|�LH;lV 9 NF;)NXZ$ifESJONFZp;IT<>a;$GF=ILH;IGF=QPFZpT<?�L 7 ZIrfZIGF;$Vl;$GW>5NF;.NXZIA JO?BLHL�JMGF=$; p TS;CFE 9 NX\F?B>zÂeCKJOE<>S?HE�NF;IT1Z4>QJM>ST 09 \ 2 NF\pV 9 NFÁ$LB;vNF\prfZIES?BGpP 9 E<?HÊ 9 GW>QJOL�+ ÓKif\FE<;`ÏdÈ��;, ÈW{�L'GF;�C;$\X>1CKJOT

$4>@ES;a;$GF=ILH;IGF=QPFZ)ÂpCFJOE<>S?HE�NF;$ThZI>QJ�>@T 1 ;I> 3 *'=I;$T`Z4>QJM>STk=YJME@JO=4>@Z$E<?HT<;$GW>�NF;IT`TS?R>@\KJM>S? 9 GXT 9 U LH;�rfZIES?HGP 9 ES?HÊ 9 GW>QJOL'TS;�>@E 9 \Xrf;�NKJMGFT¡\FGF;eC 9 T<?B>S? 9 GjGX?�= 9 VlCFLHÁ4>@;IV.;IGn>¡T 9 E<>S?�GF?�= 9 V.CXLHÁI>S;$Vl;$GW>¡ES;IGW>@ESZMÈ

Page 142: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~Y�W� ���������� �������������������������� �"!#���%$&���'$(��)

6 ;]V 9 NXÁ$LH;eNF\qCFE 9 =IZ$NFZ Gd;$GqV 9 NX;]NFZ$iOE@JONFZ5;$T<> 9 xX>@;IGn\�CFJOE`= 9 V.C 9 TS?R>@? 9 G CFJOE@JOLBLHÁILH;�NF;$T

NF;$\dmjTS;I\FLHTvJM\X> 9 V.JM>S;$TgZILHZIV.;IGn>@JO?HE<;$T�+ërf;IGW> 9 \FT<;�;I>[rOZ$ES?BGjrf;IE<>@?B=YJOL ,4ÈD{�L�= 9 V.C 9 Ec>@; 17 ZI>@JM>@Tg;I> 38>@E@JMGFTS?R>@? 9 GFT +ëÓKiO\FES;aÏdÈ � ,4È

1 2 3

4 5 6 7

13 14 15

111098

12

0

fmont

dasp

dilb

flib

ddes fdes

dlib

dasp

fmont

dmont

fasp faspfasp fasp

daspdasp

dilb dilb

ddes

ddes

dmont

dmont

flib

fdes

fdesddes dmont

flibflib

0 143�5 ÏdÈ �@6����AI N ILK IM= Gd

?��HI N�?A=@?AL�� C�K;?AL

ªv« ��«_¬ �g¶��³'µ��k³ ��·dµ~¸z¹h² ºh¼»À�¸vºh° º���8´T��º Ed

} 9 \FTt= 9 GFT<?HNFZIE 9 GFT,Ãn\ 7 ;IG)=YJOTtNF;gNFZ4A JO?HLBL�JOGX=$;�NF\5rOZ$ES?BG]P 9 E<?HÊ 9 GW>QJOL |ÚLH;zT<bDT<>SÁ$Vl;[N 9 ?R>tT<;[V.;4>S>SES;NKJOGFTe\FG�ZI>QJ�>�G 9 G�NKJOGFif;IES;I\dm�C 9 \FE�LH\F? ^�V%$$Vl;@|L�JjCF?BÁ$=I;l;4>eL 7�9 C'ZIE@JM>S;$\FEIÈ 6 J�CX?HÁ$=I;)NF;IrDESJ$I>SES;NFZ$C 9 TSZI;a;IG E<;$T<C';I=I>QJMGn>hLH;IT¡TSCZ$=$?RÓK=YJ�>@? 9 GFTvES;4>@;$Gn\F;ITk;IG V 9 NX;`NFZ$iOE@JONFZ�*

~ ÈvL�J)CF?BÁ$=$;�GX;aC;$\X> $4>@E<;eLB?DxZ$E<Z$;�Ãn\ 7 ;$G�C 9 T<?B>@? 9 GuxKJMTSTS;a|ÑdÈvLH;`rOZ$ES?BG GX;eC;$\d>hV 9 GW>@;IEvÃn\F;aT<?�L�J]CF?BÁ$=I;e;IT<>�LH?Ex'ZIESZI;@|� ÈvL�J)CF?BÁ$=$;�GX;aC;$\X>¡CFJOT $I>@E<;eJOTSCF?BESZI;OÈ

fdes

flib

dmont

dmont

−{dmont, flib}−{fdes, dlib}Σ Σd d

−{dasp}Σd

−{dmont}Σd−{dmont}Σ

d

0 1 0 1

0

02143�5 ÏdÈ �K6�&N�?��<>=-G@?A=-G�GMBOL-:�E � :�K I E N �(G ?�� I N�?A=@?AL�� C�K;?AL

Page 143: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� ��� ��� ���2� � ���� %� ����)��2$H��������) !�$ ~Y�=~

6 ;pV 9 NXÁ$LH;lifL 9 xKJOL8NF;pL�J T<C'ZI=$?RÓK=YJM>S? 9 G|;$GËV 9 NF;.NXZ$ifESJONFZ + ÓKif\FE<;�ÏdÈ � ,�;$T<> 9 xX>@;IGn\ÍCKJOE5LHJ= 9 V.C 9 T<?B>@? 9 GjCKJME@JOLBLHÁ$LB;kNF;IT 3 JM\X> 9 V.JM>S;$TvZ$LBZ$Vl;$GW>QJM?HES;IT Ei

+ i ∈ {1,2,3} ,gNF;�L�J5ÓFif\FES;aÏdÈ � ÈΣ d −{flib, dlib, dmont, dasp, fdes}

Σ d −{fmont, fdes, dasp, dlib} Σ d −{fmont, dasp, ddes}

Σ d −{dmont, dasp, flib, ddes}

S :d xd,0xd,1

xd,2 xd,3

flib

ddes

fmont fmont

fdes

ddes

flib

fdes

0 143�5 ÏdÈ �H6��VBOL-:�E � :�K I E N ��� <>N�"NK <>=@?�� I N�?A=@?AL�� C�K;?AL

ª[« �h« � � �´Xµ��k³ ��·dµ~¸z¹»ºk°�� � ³�¸�¹1·D´ � � � �`µ��~µ_· yk;ICF\F?HTk=QPKJOÃn\F;]Z4>QJM>kNF\qV 9 NFÁILH;eNF;5LHJ.TSCZ$=I?BÓK=$JM>@? 9 G�;IGqV 9 NF;eNFZ$iOE@JONFZ]JO\F=$\XGqZIrfZIGF;$Vl;$GW>

?BGF= 9 GW>SE��fLHJ@xFLH;hG 7 ;$T<>�?BGn>S;$E<NF?B>$ÈK�tJOEv= 9 GFT<Z$Ãn\F;$GW>kL�J]= 9 Gn>SE��fLHJ@xF?BLH?B>SZhNX\ = 9 GW>@E��OLH;$\XEvG 9 G�ZI>@;IGFNF\�;$GV 9 NX;]NFZ$iOE@JONFZ);IT<>eiWJOESJOGW>@?B;OÈ�} 9 \FT�G 7 JYr 9 GXTeCFJOT�=YJOLB=$\FLBZ]LH;)CXE 9 NF\F?B>kNF; Gd

JYrf;I= EdCX\F?HT<ÃD\ 7 ?BL

T<;jC';I\X>)Ãn\F;�L 7 Z4>QJM>a?HGF?R>@?HJOL8NF\ÍCFE 9 =IZ$NFZ GdGF;jT 9 ?B> �SJMVpJO?BTaL 7 Z4>QJM>aNF;�NFZICKJOEc>)NKJOGFT5LH;pV 9 NFÁ$LB;

Z4>@;$GXNF\�È

�"! � ±(U£�©q¢ � �©�*t+l0g�¡-��¡  �[(3¢¡&�-�/� 

} 9 \FT)JOLBL 9 GFTeV.JO?HGW>@;IGKJOGW>)= 9 GFT<>SES\F?BES;.LH;$T5CFE 9 =$ZINFZ$T)Z4>@;$GXNF\FT";$GÍ\X>S?HLB?HT@JMGn>aL�J NFZ$V.JOES=QPX;jNF;= 9 GFT<>SES\F=4>@? 9 G�CFE 9 C 9 TSZ$;5NKJOGFT`LB;a=QPFJOCF?B>SES; � *CFE 9 C 9 TS?B>S? 9 G � È � CKJOiO; �O� È'sg;I><>@;)NFZIVpJMES=QPF;aT 7 JOCd^CFLB?HÃn\F;]T<\FE`> 9 \FT�LH;IT�L�JOGFifJOif;$TkNF\oCFE 9 =$ZINFZ"ifL 9 xFJOLf|Ò;I>e;IG�CFJOE<>S?H=$\XLH?H;IEk;ILHLH;aC';I\X>�$I>SES;lJOCFCXLH?HÃn\FZI;T<\FE1> 9 \FTgLB;$T1L�JOGFifJOif;$TzNF\�CFE 9 =IZ$NFZhT 9 \XT[= 9 GW>SE��fLB; + CX\F?HT<ÃD\X; L(S/G) ⊆ L(G) ,4ÈXsg;$L�JeC';IESVl;I>gNF;GF;l= 9 GFTS?BNFZ$E<;$EeÃD\X;.LB;$T�ZI>@JM>@TeÃn\F?�C';I\Xrf;IGn> $I>@E<;.\d>@?HLB?HT<Z$T�;$G x 9 \F=$LB;"Aë;IESVlZ$;MÈ3} 9 \FTaJOLBL 9 GFT�JM?HGFT<?JOCXCFLH?BÃD\X;$E3G 9 >SES;gCXE 9 C 9 TS?R>@? 9 G�TS\FEU> 9 \FT,LH;IT,LHJOGFiWJOiO;$TB|�Ãn\F?DCKJOEc>@;$GW>tNF;gL 7 Z4>QJM>,?HGF?R>@?HJOLO;4>�Ãn\F?DV.ÁIGF;$GW>Âp\XGqZI>QJ�> 9VU L 7 Z4rfZ$GX;$Vl;$GW>�NF;]CKJMGFGF;]C;$\X>`TS;]CFE 9 NX\F?HE<;@|NF\qifE@JMCFPF;"ÏdÈçÏdÈ�hÓKGqN 7 $4>@ES;)= 9 VlCFLH;4>G 9 \FT¡E@JOCFC;$L 9 GFTvLB;$TvCFE<?HGF=I?HC;$Tv\X>S?HLH?BTSZIT$È

ª[«­ªv«c® � �_·d°�´F¹��z¹h³�° ºh¼»À�¸vºh° ¹k¸zÀ�µ~¹ ������°�´X² �~° À�¸vºh° º����´ ��º ��JOCFC;$L 9 GFTaÃn\F;pLH;lV 9 NFÁ$LB;"NF\ËCFE 9 =IZ$NFZ.;$GËV 9 NX;.NFZIifE@JMNFZ Gd

;$Tc>]= 9 V.C 9 TSZp CKJME<>@?BEaNX;$TV 9 NXÁ$LH;IT�NF;$T]NX;$\dm�TS;I\FLH;IT5ES;ITST 9 \FES=I;$TM|trfZIES?HG|rf;$Ec>@?B=YJOLz;I>arf;$GW> 9 \FTS;MÈ�w 9 G�ZI>QJ�>5?BGF?B>S?�JOL�;IT<>]JOL 9 E<TLB;�CFE 9 NF\F?R>h=$JOE<>SZ$T<?H;$G�NF;IThNF;I\dm ZI>@JM>@T¡?HGX?B>@?HJO\dmpNF;�rfZ$E<?HG�rf;$Ec>@?B=YJOL�;4>kNF;�rO;$GW> 9 \XTS;OÈ�} 9 \XThTSJÚr 9 GFT

Page 144: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~Y� Ñ ���������� �������������������������� �"!#���%$&���'$(��)

VpJO?BGW>@;$GFJOGW>�ÃD\X;l=I;I>�Z4>QJM>R+ëZI>QJ�>�?HGF?R>@?�JMLUNX\|CFE 9 =IZ$NFZ Gd,kC';I\X>�GF;)CKJMT $4>@E<;)\X>@?BLH?HT<Z5=$JOE�LH;)CFE 9 ^

=$Z$NXZp;$G�V 9 NF;)G 9 Vl?HGFJOL�J�Z4r 9 LB\FZl;I>aL 7 ZI>QJ�>5Â�CKJOEc>@?BEeNX\FÃn\F;$LzL 7 ZIrOZ$GF;IV.;IGn>5NF;lCKJOGFGF;lTS\XE<rD?H;IGn>GF;�= 9 E<ES;$T<C 9 GFN CXLH\FT"ÂqL 7 ZI>@JM>)?BGF?B>S?�JOL�NF\�V 9 NF;jG 9 V.?BGKJOLæÈ,��ÓKGÌNF;�=YJOESJO=I>SZ$ES?BTS;IE)= 9 E<ES;$=4>@;IV.;IGn>L 7 JOLB>S;$ESGFJOGF=$;�;I>1L�J�= 9 PFZ$E<;$GF=I;`NF\pV 9 NF;hG 9 V.?BGKJOLXrO;$E<T[LH;¡V 9 NF;¡NFZIifE@JMNFZ@|DG 9 \FTgJYr 9 GFT�x';IT 9 ?BGpNF\=YJOGKJML�N 7 ?BGXA 9 E<VpJM>S? 9 G πn,d

?HGW>@;IES=YJMLHZ�;$GW>SES;eLH;$TvNX;$\dm�V 9 NXÁ$LH;ITvNF;$T¡CFE 9 =IZ$NFZITH+ ÓKif\FE<;aÏdÈ ~Y� ,4È

ππ (s)

Modèle Gn

(vv, vh, v)

Gd

Modèle

(vv, v)

n,d

n,ds

0 143�5 ÏdÈ ~Ú�@6�7 K��cK < ?�� E����WN C ILK I E N � πn,d

ªv«­ª[«_¬ � ¸vºh¿ �c° �·d°�¹kºk¼Gd,et

��JOCFC;$L 9 GFT)Ãn\F;�LH;�=YJMGKJOLvN 7 ?HGXA 9 ESV.JM>@? 9 G πn,d;$GW>@E<;�LH;$T"NF;I\dm�V 9 NF;IT)NF;�A 9 GF=I>S? 9 GXGF;$Vl;$GW>

G 9 Vl?HGKJOL;I>¡NXZ$ifESJONFZ�G 7 ;$Tc>¡ÃD\ 7 \FGX;�A 9 GF=I>S? 9 G�NF;�CXE 9 �<;I=I>@? 9 G�NFZ4ÓKGF?H;`A 9 ESVl;$LHLB;$Vl;$GW>1= 9 VlV.;hTS\F?R>�*w 9 ?B> πn,d : Σ∗

n −→ Σ∗d

>@;$LBLH;`Ãn\F; ∀σ ∈ Σn;I> ∀s ∈ Σ∗

n :

πn,d(ε) = ε

πn,d(sσ) =

{

πn,d(s)σTS? σ ∈ Σn ∩ Σd

πn,d(s)TS? σ ∈ Σn \ Σd

} 9 \FTeE@JOCFC;$L 9 GFT�Ãn\F;pLB;"V 9 NFÁ$LB;)NF;lCFE 9 =$ZINFZ Gd;IG�V 9 NF;"[email protected] 9 ?B> $I>SES;lZI>S;$GFNF\8|U>S;$L

ÃD\X;�*Gd,et = (Qd,et, Σd,et, δd,et, qd,0,et, Qd,m,et)

JYrO;$=�*6

Qd,et = Qd ∪ {qd,in}&

6Σd,et = Σd ∪ {p,r} &6qd,0,et = qd,in

&6

Qd,m,et = Qd,m&

6δd,et

;$Tc>kNXZIÓKGF?B;�= 9 VlVl;�TS\F?R>�*~ È ∀ σ ∈ Σd

;I> ∀ q ∈ Qd>@;$LBTvÃn\F; δd(q, σ) ; md?HT<>S;eJOL 9 E<T * δd,et(q, σ) := δd(q, σ) &

ÑdÈ ∀q ∈ QdÂ.CKJOEc>@?BE�NX\FÃn\F;$LU\FGF; 9 =I=$\FE<ES;$GX=$;5NX;5L 7 ZIrOZ$GF;IV.;IGW>`NF;a= 9 VlV]\X>@JM>@? 9 G r ;IT<>C 9 TSTS?ExFLH;�JML 9 E<T δd,et(q, r) := qd,in

&� È¡L�J)>@ESJOGFTS?R>@? 9 G C;$E<V.;4>S>@JOGW>`NF;aNFZI>S;$ESVl?HGX;$E�L 7 ZI>QJ�>kNF;aNFZ$CFJOE<>B| δd,et(qd,in, p) ;IT<>�ÂlNFZ4^>@;IESVl?HGF;IE$È

Page 145: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

��� ��� ��� ���2� � ���� %� ����)��2$H��������) !�$ ~Y�;�

6 ;[V 9 NFÁILH;z?HGF?R>@?HJOLH;IV.;IGn>UJM=I>@?RAK;$Tc> GnN 9 GX=gL 7 JO\X> 9 V.JM>@;1JOTST 9 =I?HZ1TS;g>SE 9 \XrO;vNKJOGFTtL 7 ZI>QJ�>t?BGF?B>S?�JOL

qn,0È'��ZI=$?BCFE 9 Ãn\F;$Vl;$GW>`LB;5V 9 NXÁ$LH; Gd

;$T<>`?HGKJO=4>@?RA~Èw 9 GqJO\d> 9 V.JM>@;e;$Tc>�NKJOGXT`L 7 ZI>@JM>k?BGKJO=4>@?BA qd,inÈ

687 JO=I>S?BrMJM>@? 9 GÒÐMNXZ$T@JM=I>@?RrMJM>@? 9 Gp;IT<>�NF\F;eÂ"L 7�9 =I=$\FE<ES;$GX=$;�N 7 \FG Z4rfZIGF;$Vl;$GW>hNF;�= 9 VlV]\X>@JM>@? 9 G�È687 Z4rfZIGF;$Vl;$GW> p +ëES;$T<C�È r ,�C;$E<V.;4>�NF;]NFZIT@JO=4>@?Rrf;$E�LB;5V 9 NXÁ$LH; Gn

+ E<;$TSC�È Gd,�;I>�N 7 JO=4>@?BrO;$E`LB;

V 9 NXÁ$LH; Gd+ E<;$T<C�È Gn

,4È 6�7 JO\X> 9 V.JM>@; GdC 9 T<TSÁINF;5CFLB\FTS?B;$\FE<TkZ4>QJM>SThNF;aNFZ$CFJOE<>kCF\F?HT<Ãn\F;5L 7 Z4rfZ$GX;4^

Vl;$GW>¡NF;�= 9 V.V]\d>QJM>S? 9 G�C;$\X>¡T<\FE<rO;$GF?BEhNFJOGFT¡CFLH\XTS?H;I\FESTvZ4>QJM>ST¡NF;�L 7 JO\X> 9 VpJM>S; GnÈ

6 J5CKJOGXGF;`TS\XE<rf;IGKJOGW>�NKJOGFT1L 7 ZI>@JM> 29 \jL 7 ZI>@JM> 0 NF\�= 9 VlC 9 T@JOGW>1rfZ$E<?HG�P 9 ES?HÊ 9 GW>QJOLÒC;$\X>[N 9 GF=T<\FE<rO;$GF?BEl;IGW>@ES;�LH;IT"ZI>QJ�>@T 0 ;I> 6

9 \ ;IGW>@ES;�LH;IT)ZI>@JM>@T 8 ;I> 14 + ?BGF=$LB\FT-,5NX\ CFE 9 =IZ$NFZ�T<\FC';IE<rD?HT<Z+ ÓKif\FE<;jÏdÈçÏV, È�wd\XCFC 9 T 9 GFTaÃn\F;j=$;4>S>S;pCKJOGXGF;jJOE<ES?Rrf;lNKJOGFTaL 7 ZI>QJ�> 8 NF\ËifESJOCFPF;.NF;pLHJ�ÓFif\FES;jÏdÈçÏdÈ� 9 \FE3NFZI>S;$E<V.?BGF;$E�L 7 Z4>QJM>�NX;zNXZ$CKJOEc>UNF\aCXE 9 =$Z$NXZ Gd

;IGaV 9 NF;�NFZIifE@JONXZzG 9 \FT3=QPF;$E<=QP 9 GFT,LH;8LHJOGFiWJOiO;Kn,8

Ãn\F?�CKJME<>¡NF;ICF\F?HTvL 7 Z4>QJM>[?HGF?R>@?�JML;4>¡V.ÁIGF;krO;$EST¡L 7 Z4>QJM> 8 ÈKy 7 JOCFE<Á$T¡LH;`V 9 NFÁ$LB;`JO\X> 9 V.JM>@;`NX;�L�JÓKiO\FES;aÏdÈçÏ]G 9 \FT�J@x 9 \X>S?HTST 9 GFT¡JO\Dm�T<bDT<>SÁ$Vl;$T�N 7 Z$Ãn\KJM>S? 9 GFT¡T<\F?BrMJOGW>@TQ*

qn,0 = ddes qn,1

qn,1 = fdes qn,2

qn,2 = dasp qn,3

qn,3 = fasp qn,4

qn,4 = dmont qn,5

qn,5 = fmont qn,6

qn,6 = dav qn,7

qn,7 = fav qn,8

qn,8 = ddes qn,9 + ε

qn,9 = fdes qn,10

qn,10 = dlib qn,11

qn,11 = flib qn,12

qn,12 = dmont qn,13

qn,13 = fmont qn,14

qn,14 = drec qn,15

qn,15 = frec qn,0

(qn,i)E<;$CFE<Z$TS;IGW>@;�L 7 Z4>QJM> i NX\ CFE 9 =IZ$NFZ TS\FC;$Ecrd?BTSZMÈvsg;$T.T<bDT<>SÁ$Vl;$TjN 7 ZIÃD\FJM>@? 9 GFT.JONFVl;I>S>S;$GW>L 7 \FGX?HÃn\F;�T 9 LH\X>S? 9 G%* Kn,8 = (ddes.fdes.dasp.fasp.dmont.fmont.dav.fav.ddes.fdes.dlib

.f lib.dmont.fmont.drec.frec)∗.(ddes.fdes.dasp.fasp.dmont.fmont.dav.fav) È 687 JMCFCFLH?B=YJM>S? 9 GNF;8LHJ1A 9 GF=4>@? 9 G�NF;8CFE 9 �<;$=4>@? 9 GeT<\FE�=$;8LHJOGFiWJMif;�N 9 GXGF;�* πn,d(Kn,8) = (ddes.fdes.dasp.fasp.dmont

.fmont.ddes.fdes.dlib.f lib.dmont.fmont)∗.(ddes.fdes.dasp.fasp.dmont.fmont) Èy 9 GF=�L 7 ZI>QJ�>¡NF;�NFZ$CKJME<>¡TS\X?B>@;e Kn,8;IT<> δd,et(qd,in, p) = δd(qd,0, πn,d(Kn,8)) = qd,8

È687 ; md;$VlCFLH;]N 9 GFGFZ]CXESZ$=IZ$NF;IV.Vl;$GW>�= 9 ESE<;$TSC 9 GFNFJO?B>`Âj\FGF;]CKJMGFGF;"JOE<ES?BrMJOGW>hNKJOGFT�L 7 Z4>QJM> 8 NF\CFE 9 =IZ$NFZMÈ�� JO?HGW>@;IGKJOGW>hTS?UL�J)CKJOGFGX;5TS;aCFE 9 NF\F?R>�NF;$CF\X?HT�L 7 ZI>QJ�> 0 NF\�CXE 9 =$Z$NXZ5TS\XC';IE<rD?HT<Z@|'JOL 9 E<T¡LH;LHJOGFiWJOiO;`CKJOEc>QJOGW>¡NF;ICF\F?HT¡L 7 Z4>QJM> 0 ;4>hVl;$GFJOGW>vrf;$E<Th=I;I>hZI>@JM>¡;$Tc> Kn,0 = (ddes.fdes.dasp.fasp

.dmont.fmont.dav.fav.ddes.fdes.dlib.f lib.dmont.fmont.drec.frec.ddes.fdes.dasp

.fasp.dmont.fmont.dav.fav)∗ È 687 JOCFCFLB?H=YJ�>@? 9 G NF;5L�J.A 9 GX=I>@? 9 G�NF;)CXE 9 �<;I=I>@? 9 GqTS\XE`=$;)LHJOGFiWJOiO;N 9 GFGF;�* πn,d(Kn,0) = (ddes.fdes.dasp.fasp.dmont.fmont.ddes.fdes.dlib.f lib.dmont.fmont

.ddes.fdes.dasp.fasp.dmont.fmont) ÈMy 9 GF=gL 7 ZI>QJ�>tNF;gNFZ$CKJME<>8T<\F?B>S;[Â Kn,0;$Tc> δd,et(qd,in, p) =

δd(qd,0, πn,d(Kn,0)) = qd,0È

6 ;"V $IV.;]ESJO?HT 9 GFGF;IV.;IGW>aC;$\d>�$I>@E<;lJON 9 CX>SZ"TS?8=$;4>S>S;lCFJOGFGF;lTS\FEcrD?H;$GW>eNKJOGXTe\XG�JO\d>@ES;)Z4>QJM>$È

Page 146: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~Y�f� ���������� �������������������������� �"!#���%$&���'$(��)

� 9 \FEe= 9 GFT<>SES\F?BES;"LH;"CFE 9 =IZ$NFZlZI>S;$GFNF\|NF\�V 9 NF;)NFZ$iOE@JONFZa|3G 9 \FTeJOCFCXLH?HÃn\ 9 GFT�G 9 >@E<;"CFE 9 C 9 T<?B>@? 9 GTS\FE�> 9 \FT8LH;IT�L�JMGFiWJOif;IT K NF\"CFE 9 =IZ$NFZvT<\FC';IE<rD?HT<ZvNF\"V 9 NF;1G 9 Vl?HGKJOLnÃn\F?FVlÁ$GX;$GW>8rf;IEST�\FG)ZI>@JM> 9VUL 7 ZIrfZIGF;$Vl;$GW>,NF;�CKJOGFGX;zC;$\d>,T<;�CFE 9 NF\F?BES;�;4>,G 9 \FT 9 xX>S;$G 9 GXTULB;8V 9 NFÁILH;�Z4>@;$GXNF\aNX\aV 9 NX;8NFZ$ifESJONFZNF;¡L�JkÓKif\XES;�ÏdÈ ~U~ È 687 ZIrOZ$GF;IV.;IGn>1NF;vCKJMGFGF;¡TS;IE@J�ES;ICFESZITS;$GW>SZhCKJME8NF;$T�ZIrOZ$GF;IV.;IGW>@TgT<?HifGX?BÓK=$JM>@?RAëTtNF;>�bdC; pi

* p = piT<? δd,et(qd,in, p) = qd,i

È 6 J`V $IV.;zNFZ$V.JOE<=QPF;vN 9 ?R>�$4>@ES;[JOCFCFLB?HÃn\FZ$;[ÂkL 7 ZIrOZ$GF;IV.;IGn>NF;�ESZ$CFJOE@JM>S? 9 G�È

1 2 3

4 5 6 7

13 14 15

111098

12

0

fmont

dilb

ddes fdes

dlib

dasp

fmont

dmont

q

p

p

3

9

ddes

fdes

fdes dmont

daspdasp

flibflib

p14

p

p0

1

p2

p

p10

p8

11p

dasp

fasp fasp fasp fasp

fdes dmontddes

ddes dmont

6

d,in

02143�5 ÏdÈ ~U~�6���=MBDC L-G�=��OI K I E N �"B K C�I E =�<4<>=@?�� I N�?��<>=HL�IM=��D?�� ?�� I N�?A=@?AL�� C�K;?AL

6 ;kV 9 NFÁ$LB;hNF;hL�J�ÓKif\FE<;�ÏdÈ ~U~ G 7 ;$Tc>vCKJOTg= 9 VlCFLH;4>YÈDx8Gj;IÎ';I>B|XL 7:9 x��<;$=I>S?BA�NX;`=$;4>S>@;hÓKif\FE<;k;$Tc>vNF;V.;4>S>@E<;�L 7 JO=$=I;$GW>UTS\FE3LH;IT�ZI>@JM>@TUNF;�NFZ$CFJOE<>UNF\eV 9 NFÁILH;8ÂvCKJOEc>@?BE�NF;�L 7 ZI>QJ�>3?HGKJO=4>@?RA qd,in

È 6�7 ZIrOZ$GF;IV.;IGW>NF;pE<Z$CKJOESJM>@? 9 G r G 7 JMCFCKJOESJMÉH>�N 9 GF=pCKJMTaNKJMGFTaLB;"V 9 NFÁ$LB;@|�CF\X?HTSÃn\F;.=$;4>5Z4rfZ$GX;$Vl;$GW>)GF;"A JO?B>�Ãn\F;= 9 GFNX\F?HE<;eLB;�V 9 NFÁILH;krO;$EST�L 7 ZI>@JM>¡?HGFJO=I>S?BA qd,in

È

ªv«­ª[«5� � �_·d°�´F¹���¹k³�° ºh¼»À�¸vºh° º����´ ��º ��°�´X² �c° À�¸vºh° ¹h¸zÀ�µc¹����wd?tG 9 \FT�= 9 GFTS?BNFZ$E 9 GFT�L 7 JOLR>@;$E<GKJOGF=I;]NF\oV 9 NF;5NFZ$ifESJONFZ]rO;$ESTeLH;5V 9 NF;]G 9 V.?BGKJOLf|JOCXESÁ$TeJYr 9 ?HE

ZI>@;IGFNF\�LH;IT]V 9 NFÁILH;$TaNF\ÌCFE 9 =$ZINFZj;4>"TSCZ$=$?RÓK=YJ�>@? 9 GËNF\ÌV 9 NF;.NFZ$ifESJONFZa|�?HLzG 9 \FT]A JM\X>)NFZ4>@;$E<V.? ^GF;$EeLH;ITaZ4>QJM>STaNF;lES;4> 9 \XEa;IG�V 9 NF;"G 9 V.?BGKJOL­È��hJMCFC';IL 9 GXTeÃn\F;lLH;ITaZ4>QJM>STaNX;.E<;I> 9 \FEaNX\|CFE 9 =IZ$NFZNF\ÍV 9 NF;lG 9 Vl?HGKJML8NFZ$C;$GFNX;$GW>"NF;$Ta>@E@JM=$;$T5;$GFE<;$if?BT<>@E<Z$;IT]NKJOGFT5LH;lV 9 NF;lNFZ$ifESJONFZj;4>]=I;jNF;$CX\F?HTL 7 ?HGFTc>QJOGW>[NX;�L�J5T<Z$LH;I=I>S? 9 GjNX\�V 9 NF;kNFZIifE@JMNFZh�<\FTSÃn\ 7 Â]L 7 ?HGXT<>QJMGn>gNF;�L 7�9 =$=$\XESES;IGF=$;�NX;`L 7 ZIrOZ$GF;IV.;IGn>NF;�= 9 VlV]\X>@JM>@? 9 G r È 687 JOLR>@;IESGKJOGX=$;`NF\�V 9 NF;kG 9 Vl?HGKJOLÒrf;IEST�LH;`V 9 NF;�NFZ$iOE@JONFZ�;IT<>hJOT<TS\FE<Z$;�=$;4>S>@;A 9 ?HT~^�=$?tCKJOE�LH;)=$JOGKJOLtN 7 ?BGXA 9 E<VpJM>S? 9 G πd,n

?HGW>@;IES=YJMLHZ];IGn>SES;lLH;IT�V 9 NFÁ$LB;$T`NX;$TeCFE 9 =$ZINFZ$T Gd;I> Gn+ëÓKif\XES;aÏdÈ ~ ÑV,4È

Page 147: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�����;� ��� ���2� � �2$(� �������������������$P���#����� �� ���� � !� �$H��������) !�$ ~Y� Ï

π

s’π (s’)

Modèle Gn

(vv, vh, v)

Gd

Modèle

(vv, v)

d,n

d,n

0 143�5 ÏdÈ ~ Ñ 6 7 N I I � I K I E N �&?�� I N�?A=��QN I E��cK < � =�C-G%<>= I N�?A=@?AL�� C�K;?AL

ª[«­ªv« � � ¸vºk¿ �~° ºk¼ ¶k´F¸v³|�º �·d°�¹hºk¼Gn,et

�tJME�JOGKJML 9 if?B;�JO\]=$JOTtN 7 ZI>S\FNF;[CXESZ$=IZ$NF;IGW>8TS\FEtL�J¡= 9 GFTc>@E<\F=I>S? 9 G]NX\]V 9 NFÁILH;�ZI>S;$GFNF\)NX\]CFE 9 =$ZINFZ;IG V 9 NX;`NFZ$iOE@JONFZa|ÒLH;�V 9 NFÁILH;`Z4>@;IGFNF\�NF\ CXE 9 =$Z$NXZa;IG V 9 NX;`G 9 Vl?HGKJML�;$Tc>kN 9 GFGFZ�= 9 V.Vl;`TS\X?B>�*

Gn,et = (Qn,et, Σn,et, δn,et, qn,0,et, Qn,m,et)JYrf;I=�*

6Qn,et = Qn ∪ {qn,in}

&6

Σn,et = Σn ∪ {p,r} &6

qn,0,et = qn,0&

6Qn,m,et = Qn,m

&6

δn,et;IT<>�NFZ4ÓKGF?H;�= 9 V.Vl;�TS\X?B>�*

~ È ∀σ ∈ Σn;4> ∀q ∈ Qn

>S;$LBLH;`Ãn\F; δn(q, σ) ; md?HT<>S;eJOL 9 E<T δn,et(q, σ) := δn(q, σ) &

ÑDÈ ∀q ∈ QnÂoCKJOE<>S?HE)NF\XÃD\X;$L�L 7�9 =I=$\FE<ES;$GX=$;�NF;�L 7 ZIrfZIGF;$Vl;$GW>pNF; = 9 VlV]\X>QJ�>@? 9 G p ;IT<>

C 9 T<TS?ExFLH;�JOL 9 ESTQ* δn,et(q, p) := qn,in&

� È δn,et(qn,in, r) ;$Tc>hÂ"NXZI>@;IESVl?HGF;IE�3rf;$=hL�J�V%$$Vl;vNFZ$V.JOES=QPX;hÃn\F;�C 9 \FE�L 7 JOLB>S;$ESGFJOGF=$;vNX\pV 9 NF;vG 9 V.?BGKJOLDrf;$E<TgLB;�V 9 NF;vNFZ$iOE@JONFZa|

L 7 ;IGFTS;IV�xFLH;eNF;IT`ZI>@JM>@ThNF;5E<;I> 9 \FEhNFJOGFT`LB;aV 9 NXÁ$LH;�NF\�CFE 9 =$ZINFZ5;IGqV 9 NF;�G 9 Vl?HGKJML�;$T<> Qn,retour|

>S;$L�Ãn\F;�*Qn,retour = {(vv0, vh0, v0), (vv1, vh0, v0), (vv2, vh0 v1), (vv2, vh0 v1), (vv2, vh0 v2),

(vv3, vh0 v2), (vv0, vh0 v2), (vv1, vh0 v2), (vv2, vh0 v3), (vv2, vh0 v0), (vv3, vh0 v0),}|KJYrf;$=�*

vviL 7 Z4>QJM> i NF\�rfZIES?BG�rO;$E<>S?H=$JOLf| vhi

L 7 ZI>@JM> i NF\�rfZIES?HG�P 9 E<?HÊ 9 GW>QJOL�;4> viL 7 ZI>@JM> i NF;�rf;IGW> 9 \FT<;OÈ

�"!�� ±(U£�©q¢ � � �©q�¡0g2��0g£�(324+5&�  ¢[( 0g+5&)(�*�a¤4¢¡/j*� ��[(3¢¡&�-�/� 

ª[« ��«c® �[¶ �³�µ �k³ ��·dµc¸�¹ �·X°�¹hºk¼h°�°�¹ À�¸vºk° º���8´T��º Ed,et

6 ;$TaTSCZ$=$?RÓK=YJ�>@? 9 GFTaNX;IrMJOGW>]T<\F?BrDES;.;4mdCFLB?H=$?R>@;IV.;IGn>eL 7 Z4r 9 LB\X>@? 9 G|NX\ËCFE 9 =$ZINFZ@|U;$LBLH;ITaT 9 GW>]T 9 \d^Vl?HT<;$Tv= 9 V.Vl;`LH;�CXE 9 =$Z$NXZ5JO\�VlZ$=$JOGF?HT<V.;�NX;e= 9 VlV]\X>QJ�>@? 9 G�È

Page 148: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~Y� � ���������� �������������������������� �"!#���%$&���'$(��)

} 9 \FT�T@JYr 9 GXT`Ãn\ 7 JM\�NFZ$CFJOE<>B|LB;aV 9 NFÁ$LB;�NF\�CFE 9 =IZ$NFZa;$G�V 9 NF;�NFZ$ifESJONFZa;$T<>k?HGKJM=I>@?RA�+ëL 7 JO\X> 9 ^VpJM>S;)JOT<T 9 =$?HZ5TS;5>SE 9 \XrO;)NKJOGFT�L 7 Z4>QJM>k?HGKJM=I>@?RA qd,in

,4È 6 ;]V 9 NFÁILH;5NX;)L�J.T<C'ZI=$?RÓK=YJM>S? 9 G EdJOTST 9 =I?HZ

N 9 ?B>)JO\FTST<?'$I>SES;�?HGFJO=I>S?BA +ëT 9 G�JO\X> 9 V.JM>@;jN 9 ?B> $4>@E<;�NKJOGFT)L 7 Z4>QJM>)?BGKJO=4>@?BA xd,in,4Èt} 7�9 \=xFLB? 9 GXT]CKJOT

ÃD\X;5G 9 \XThNF;4r 9 GXT`JO=4>@?BrO;$E�LH;�V 9 NXÁ$LH;�NF;�T<C'ZI=$?BÓF=YJM>S? 9 G EdNF;$CF\X?HT�\FG�Z4>QJM> x ∈ Xd

C;$ESVl;I><>QJOGW>N 7 JR�<\FT<>S;$EkLB;$T�JO=4>@? 9 GFThNX;a= 9 GW>@E��OLH;�;$G = 9 VlCKJM>S?DxF?BLH?B>SZkJYrO;$=5LHJlG 9 \Xrf;ILHLB;eNdbdGFJOV.?BÃn\F;aNX\ CFE 9 =IZ$NFZGdÈ��ÓKGÍNF;�CFE<;$GFNFE<;�;$GÍ= 9 GFTS?BNFZ$ESJM>@? 9 GËL 7 JOLR>@;IESGKJOGX=$;p;IGW>@ES;�LB;$TaV 9 NF;$T5;I>)CKJME]= 9 GXTSZ$Ãn\F;IGW>.LB;$T

ZIrfZIGF;$Vl;$GW>STeNX;)= 9 VlV]\X>@JM>@? 9 G�|KG 9 \XT`NF;Ir 9 GFT�Z4>@;$GXNFES;)LB;5V 9 NFÁILH;aNF;]L�JlTSCZ$=I?BÓK=$JM>@? 9 G EdNX;]L�J

VpJOGX?HÁ$E<;�TS\F?RrMJOGW>@;�* Ed,et = (Xd,et, Σd,et, ξd,et, xd,0,et, Xd,m,et)JYrO;$=�*

6Xd,et = Xd ∪ {xd,in}

&6

Σd,et = Σd ∪ {p,r} &6xd,0,et = xd,in

&6

Xm,d,et = Xm,d&

6ξd,et

;$Tc>�NFZIÓKGX?H;�= 9 VlVl;`TS\F?R> &~ È ∀σ ∈ Σd

;I> ∀x ∈ Xd>@;ILHLH;kÃD\X; ξd(x, σ) ;4md?HTc>@;eJOL 9 EST ξd,et(x, σ) := ξd(x, σ) &

ÑdÈ ∀x ∈ XdÂoCKJOEc>@?BE)NF\FÃn\F;$L¡L 7:9 =$=I\FESE<;$GF=I; NF;�L 7 ZIrOZ$GF;IV.;IGW>pNF;�= 9 V.V5\X>QJM>S? 9 G r ;IT<>

C 9 TSTS?ExFLH;a|KJOL 9 EST ξd,et(x, r) := xd,in&

� È¡L�J5A 9 GX=I>@? 9 G�NF;�>@ESJOGFTS?R>@? 9 G ξd,et(xd,in, p) T<;$E@J"NFZ4ÓKGF?H;�\FLR>@ZIES?H;I\FES;IV.;IGW>YÈ� 9 \FE�ZI>@J@xFLB?HE�LH;qV 9 NFÁ$LB;qZI>@;IGFNF\�NX;�LHJ�T<C'ZI=$?RÓK=YJM>S? 9 G±NF\ V 9 NF;qNFZIifE@JMNFZ@|¡?HLhA JO\X>�=YJOESJO=I>SZ$E<?R^TS;$E"LHJ A 9 GF=4>@? 9 GËNF;j>@ESJOGFT<?B>@? 9 G ξd,et(xd,in, p) È�sg;I=$?[C;$E<V.;4>S>@ESJ�NF;�NFZ4>@;$E<V.?BGF;$E5L 7 ;$GFT<;$V�xFLB;jNF;ITZI>QJ�>@T)NF;�NFZICKJOEc>"NF;�L�J�T<C'ZI=$?RÓK=YJM>S? 9 G Ed

È 687 ZI>QJ�>)NF;�NFZICKJOE<>"NX;�L�J�T<C'ZI=$?BÓF=YJM>S? 9 GÍ;IT<>"ES;IL�JM>S?BA�ÂL 7 ZI>QJ�>gNF;hNFZ$CFJOE<>gNF\jCFE 9 =IZ$NFZ Gd

ÈXwd\FCFC 9 T 9 GFT[CKJOEz;4md;IV.CFLB;kÃn\ 7 JOCFE<Á$T[LHJeifZIGFZ$ESJM>@? 9 GpNX;kL�J�>@ESJO=$;s = ddes.fdes.dasp.fasp.dmont.fmont.dav.fav |tL 7 ZIrfZIGF;$Vl;$GW>.NF;�CKJOGFGX; p T 7 ;$Tc>pCXE 9 NF\F?B>B|NKJOGFT�=I;)=YJOT�L 7 Z4>QJM>kNF;)NFZ$CFJOE<>�NX\�CXE 9 =$Z$NXZ)NFZ$ifESJONFZ);IT<> qd,8

+ëCKJOE@JMifE@JOCXPF;]CFE<Z$=$ZINF;$GW>-,4ÈUyk;$CX\F?HT=$;I>]ZI>QJ�>5LB;.TcbdTc>@ÁIV.;jT<;.>SE 9 \XrO;jJO\D^�NF;ITSTS\XT]NF\ËC 9 T<>S;pNF;.NFZ$C 9 T<;jJYrf;I=j\FGF;jCX?HÁ$=I;.TSJO?HT<?H;lCKJOEeL�Jrf;$GW> 9 \FTS;l;I>`ÃD\X;)LH;arOZ$E<?HG�rf;IE<>S?H=YJMLt;$Tc>�;$GqC 9 TS?R>@? 9 G�PKJM\X>@;MÈ 6 ;]L�JOGXiWJOif;eNFZ$T<?HE<Z)NF;$CF\X?HT`=I;I>�Z4>QJM>;$T<> Kd,8 = {ddes, ddesfdes, ddesfdesdlib, ddesfdesdlibf lib, ddesfdesdlibf libdmont,...} È� 9 \FEvNXZI>@;IESVl?HGF;IEgL 7 Z4>QJM>gNF;�NFZ$CFJOE<>vNX;`L�J5T<C'ZI=$?RÓK=YJM>S? 9 G Ed

|XG 9 \FT[ESJOCFC;$L 9 GFT[L�JaCFE 9 C 9 T<?B>@? 9 G � È ~CKJOif; ~ Ñ � ÈKy`JOGFT¡=I;I>�;4md;$VlCFLB; H = {xd,0, xd,1, xd,2, xd,3}

;4> Σ(qd,8) = {ddes, dlib} È� 9 \FE¡=QPKJMÃD\X; x ∈ H *

~ È Σa(xd,0) = {ddes, fdes, fmont, fasp, f lib}

⇒ Σa(xd,0) ∩ Σ(qd,8) = Σ(qd,8) ∩ Kd,8

⇒ H = H &

ÑdÈ Σa(xd,1) = {fdes, fmont, fasp dlib, f lib}

⇒ Σa(xd,1) ∩ Σ(qd,8) 6= Σ(qd,8) ∩ Kd,8

Page 149: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�����;� ��� ���2� � �2$(� �������������������$P���#����� �� ���� � !� �$H��������) !�$ ~Y� �

⇒ H = H − {xd,1}

⇒ H = {xd,0, xd,2, xd,3}&

� È Σa(xd,2) = {ddes, fdes, dmont, fmont, fasp, f lib}

⇒ Σa(xd,2) ∩ Σ(qd,8) 6= Σ(qd,8) ∩ Kd,8

⇒ H = H − {xd,2}

⇒ H = {xd,0, xd,3}&

� È Σa(xd,3) = {fdes, dmont, fmont, fasp, dlib, f lib}

⇒ Σa(xd,3) ∩ Σ(qd,8) 6= Σ(qd,8) ∩ Kd,8

⇒ H = H − {xd,3}

⇒ H = {xd,0}È

�,JOE = 9 GFT<Z$Ãn\F;$GW>oL 7 Z4>QJM> NF;�NFZ$CKJME<>�NX;�L�JÌTSCZ$=I?BÓK=$JM>@? 9 G EdÃn\F?e= 9 E<ES;$T<C 9 GFN Â L(Gd,qd,8) ∩

L(Ed,xj) = Kd,8;$Tc> xd,0

È 6 ;jV%$$Vl;pESJO?HT 9 GFGF;IV.;IGn>5C';I\X> $4>@ES;jJON 9 CX>SZjC 9 \FE5NXZI>@;IESVl?HGF;IE]LH;ITJO\d>@ES;ITgZ4>QJM>ST[NF;kNXZ$CKJOEc>YÈ 6 ;`V 9 NFÁILH;¡ZI>S;$GFNF\�NX;`TSCZ$=I?BÓK=$JM>@? 9 GpNF\�V 9 NF;hNXZ$ifESJONFZk;IT<>vN 9 GFGFZ`CFJOELHJ5ÓKif\FE<;5ÏDÈ ~�� È

Σ d −{flib, dlib, dmont, dasp, fdes} Σ d −{dmont, dasp, flib, ddes}

Σ d −{fmont, fdes, dasp, dlib} Σ d −{fmont, dasp, ddes}

xd,0 xd,1

xd,2 xd,3

p8

ddes

fmont

fdes

ddes

flib

fdes p p p

ppp

1 23

0 6 10 p14

flib fmont d,inx

p9

p11

0 143�5 ÏdÈ ~��@6 �VBOL-:�E � :�K I E N �&L�IM=��D?��O= =��bI N�?A=@?AL�� C�K;?AL

ª[« ��«­¬ ��¸�¹1·D´����~°�¼h´��·X°�¹hºk¼ °�¹»À�¸vºh° º���8´T��º Cd,et

6 J5= 9 Gn>SE��fLHJ@xF?BLH?B>SZv;I>gLH;�G 9 Gd^lxFL 9 =YJOiO;hNF\p= 9 GW>@E��fLH;I\FEgE<Z$T<\FLB>@JOGW>[ZI>S;$GFNX\�T 9 GW>[rOZ$ES?RÓKZ$T[Â5L 7 JO?HNX;NF;�Åk��sg� ÇfÈ 6 ;1= 9 GW>@E��fLH;I\FE�E<Z$TS\XLB>QJMGn>�NKJOGFT�LB;gV 9 NX;gNFZIifE@JONXZvJONFVl;I> 11 Z4>QJM>ST8;I> 16 >@ESJOGFTS?R>@? 9 GFT+ ÓKif\FE<;�ÏdÈ ~Y� ,)L 7 ZIrOZ$GF;IV.;IGW>jNF; ESZ$CFJOE@JM>S? 9 G�C 9 \FESESJO?B>.JOCXCKJOE@J�ÉH>@E<;�NKJOGFT.=$;�V 9 NFÁ$LB;@|8?HL¡= 9 GFNF\F?R>L 7 JO\d> 9 V.JM>@;�rf;IEST�L 7 ZI>QJ�>¡?HGKJO=4>@?RA qd,in

ª[« ��« � �[¶ �³�µ �k³ ��·dµc¸�¹ �·X°�¹hºk¼h°En,et

� 9 \FE`ZI>@J@xFLB?HE�LH;5V 9 NFÁ$LB;aZ4>@;$GXNF\oNF;]TSCZ$=I?BÓK=$JM>@? 9 G Sn;$GqV 9 NX;5G 9 Vl?HGFJOLf|KG 9 \FT`NF;4r 9 GFT�NXZ4^

>S;$ESVl?HGX;$EzL 7 ;$GFT<;$V�xFLB;kNF;IT[ZI>@JM>@TgNF;kE<;I> 9 \FE[NF;h=$;I><>@;`T<C'ZI=$?RÓK=YJM>S? 9 G�ÈFsg;ITvZI>QJ�>@TgN 9 ?BrO;$GW>'$I>SES;`= 9 V)^

Page 150: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~Y� � ���������� �������������������������� �"!#���%$&���'$(��)

0 1 2 4 5

6 7 8 9

fdes

dmont

fasp

fdes

fmont

fmont

p2

p p

flibp3

dlib

p

p0

ddes

p9

p

18

10 11p

14

q

3

p6

d,in

0 143�5 ÏdÈ ~Y�K6��'=MBDC L-G�=��OI K I E N �RB K CFI E =�<4<>=@?�� :-N �OI C# <>=��AC L�IM=��D?�� ?��HI N�?A=@?AL�� C�K;?AL

CKJM>@?ExFLH;ITkJYrO;$=)L�J"G 9 \drf;$LBLH;aNXbDGKJOVl?HÃn\F;5NX\�CFE 9 =$ZINFZOÈ{�LHThT 9 GW> 9 xX>@;IGn\FT`;$GqE<Z$T 9 LBrMJOGW>hL 7 Z$Ãn\KJM>S? 9 GTS\F?RrOJMGn>S;�*

L(Gn,q) ∩ L(En,xj) = Kn,q| 9VU Kn,q

ES;ICFESZITS;$GW>S;�LH;lL�JOGFifJOif;"NFZ$T<?HE<Zp= 9 V.CKJ�>@?DxXLH;"JYrf;I=jL�JG 9 \XrO;$LHLB;�NXbDGKJOVl?HÃn\F;�NF\�CFE 9 =$ZINFZ�;$G�V 9 NF;`G 9 V.?BGKJOL L(Gn,q) ÈK�k?BGFTS? |XLH;�V 9 NFÁ$LB;`ZI>S;$GFNF\ NF;�L�JTSCZ$=$?RÓK=YJ�>@? 9 G�;IG V 9 NF;�G 9 Vl?HGKJML�;$Tc>�N 9 GFGFZ�= 9 V.Vl;�TS\X?B>�*

En,et = (Xn,et, Σn,et, ξn,et, xn,0,et, Xm,n,et)JYrf;$=�*

6Xn,et = Xn ∪ {xn,in}

&6

Σn,et = Σn ∪ {p,r} &6

xn,0,et = xn,0&

6Xm,n,et = Xm,n

&6

ξn,et;$Tc>hNXZIÓKGF?B;�= 9 VlV.;�T<\F?B> *

~ È ∀σ ∈ Σn;I> ∀x ∈ Xn

>S;$L�Ãn\F; ξn(x, σ) ;4md?HTc>@;eJOL 9 EST ξn,et(x, σ) := ξn(x, σ) &

ÑdÈ ∀x ∈ XnÂoCFJOE<>S?HE]NF\XÃD\X;$L¡L 7�9 =I=$\FE<ES;IGF=$;�NF;�L 7 ZIrOZ$GF;IV.;IGW>.NX;�= 9 VlV]\X>QJ�>@? 9 G p ;$T<>

C 9 TSTS?ExFLH;a|KJOL 9 EST ξn,et(x, p) := qn,in&

� È ξn,et(xn,in, r) = xjJYrO;$= xj

;IT<>¡NFZ4>@;$E<V.?BGFZkA 9 E<V.;ILHLB;$Vl;$GW>g= 9 VlV.;`Z4>QJOGW>¡LHJ5T 9 LB\X>@? 9 GNF;�L 7 Z$Ãn\KJM>S? 9 G%* L(Gn,q) ∩ L(En,xj) = Kn,q

Èu�GlC;$\X>zJON 9 CX>@;IE8L�J�V%$$Vl;[NFZ$V.JOE<=QPF;¡C 9 \XE8NFZI>S;$ESVl?HGX;$E�LB;$T�ZI>@JM>@T8NF;¡E<;I> 9 \FE8NF;¡L�J`T<C'ZI=$?BÓF=YJM>S? 9 GEnÈ

ªv« �¡« � ��¸�¹1·D´����~°�¼h´��·d°�¹kºk¼ °�¹ À�¸vºk° ¹k¸zÀ�µ~¹ ���Cn,et

6 ;`= 9 GW>@E��OLH;$\XEvZI>@;IGFNF\�;$G�V 9 NX;`G 9 Vl?HGKJML';IT<> 9 xX>S;$Gn\�CKJOE[LB;`CFE 9 NF\X?B>vNF;ITvV 9 NFÁILH;$TgZI>@;IGFNF\FTNF;�CFE 9 =$ZINFZ Gn,et

;I>�NF;�TSCZ$=I?BÓK=$JM>@? 9 G En,et|F?BL�;$Tc>�N 9 GFGFZ�CKJME�LHJ5ÓKif\FE<;aÏdÈ ~ Ï

Page 151: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

������� �����H����!�$ ���� ~Y� �

0 1 2 3 4 5 6 7

89101112131415dmont flib dlib ddesfdesfmont

frec fav

drec

p

pp p10

p p8

p p2

p p p

ddes fdes dasp fasp dmont fmont dav

r r r r1 24 5

r3

p6

6r

p89101430

2111

p0

0rq

n,in

0 143�5 ÏdÈ ~ Ï 687 N �OI C# <>=�� CHL�IM=��D?�� ?�� I N�?A=��QN I E��cK <

�"!�� ��+a&�0g¤I/� �24+5&

y`JOGXT`=$;)=QPKJMCF?B>SES;5G 9 \FT�JYr 9 GXT`CFESZITS;IGn>SZ"L 7 JOCFCFLB?H=YJaxF?HLB?B>@ZkNF;]G 9 >SES;]CXE 9 C 9 TS?R>@? 9 G N 7 ; md>S;$GFT<? 9 GNF;"LHJ�>SPFZ 9 ES?H;"NF;l��JOV.JONFif;);4>�� 9 GFPFJOV C 9 \FE�L�J�CFE<?HTS;";IG|= 9 V.Cd>@;"NF;lNF;$\dm�V 9 NF;$T�NF;"A 9 GF= ^>S? 9 GFGX;$Vl;$GW>YÈ�� CKJOE<>S?HE"N 7 \FG ; mX;IV.CXLH;�T<?HVlCFLH;a|8LH;IT.NF;I\dm V 9 NF;$TlNF;�A 9 GF=I>S? 9 GXGF;$Vl;$GW>.ES;I>S;$Gn\FTT 9 GW>]LH;lV 9 NF;.G 9 Vl?HGKJML8;I>]LB;.V 9 NF;.NXZ$ifESJONFZOÈ 6 ;.A 9 GF=4>@? 9 GFGF;IV.;IGn>a;$GÍV 9 NF;.G 9 V.?BGKJOL8;IT<>"JOT~^T<\FESZhCKJOE1>SE 9 ?BT1ZILHZIV.;IGn>STgNF\pT<bDT<>SÁ$Vl;OÈX�h\j= 9 \FEST[NX\pA 9 GF=4>@? 9 GFGF;$Vl;$GW>1G 9 Vl?HGKJMLf|WL 7�9 =$=$\XESES;IGF=$;hNF;L 7 Z4rfZ$GX;$Vl;$GW>8NF;1NFZIA JO?BLHLHJOGF=$; p ;$GFiWJMif;gLB;1TcbdTc>@ÁIV.;[NFJOGFT�\FG5V 9 NF;zNFZ$ifESJONFZMÈM� =QPKJOÃn\F;vV 9 NF;z= 9 Ec^E<;$TSC 9 GFN�\XGjV 9 NFÁILH;�NF\�CFE 9 =$ZINFZ`;4>[\FG�V 9 NXÁ$LH;�NF;IT[TSCZ$=I?BÓK=$JM>@? 9 GFT$ÈD�k\pNFZ$CKJME<>vLB;$TgZ4rfZIGF;$Vl;$GW>@TNF;5NFZIA JO?BLHLHJOGF=$; p ;4>�NF;]E<Z$CKJME@JM>S? 9 G r + Z4rfZIGF;$Vl;$GW>@T�NF;5= 9 VlV]\X>@JM>@? 9 GS,[GF;]T 9 GW>�CKJOT`= 9 GFT<?HNFZIESZ$TNKJMGFT�LH;IT�V 9 NFÁ$LB;$T`NX;$T�CFE 9 =$ZINFZ$T�;4>�NF;$T�TSCZ$=I?BÓK=$JM>@? 9 GFT`NX\oA 9 GF=I>S? 9 GFGX;$Vl;$GW>�G 9 Vl?HGKJML­È'sg;$\dmn^_=$?T 9 GW>v= 9 GXTS?HNXZ$ESZITvNKJOGFTv\XGF;�TS;I= 9 GFNX;�ZI>QJMC'; 9 U T 9 GW>¡NFZ4ÓKGF?HTgLH;$TgV 9 NFÁ$LB;$T1ZI>@;IGFNF\FT¡NF\�CXE 9 =$Z$NXZ�;I>NF;ITvTSCZ$=I?BÓK=$JM>@? 9 GFTg;IG�V 9 NF;kNXZ$ifESJONFZOÈKsg;$TvV 9 NFÁILH;ITgT 9 Gn>¡= 9 GFTc>@ES\X?B>@T[Â5CKJOEc>@?HE1NF\�CFES;IV.?B;$Ez>�bdC;N 7 JOLR>@;$E<GKJOGF=I;vÃn\F?K;$Tc>1=$JOE@JM=I>@ZIES?BTSZvCKJOE8LB;v=YJOGFJOLFN 7 ?HGXA 9 ESV.JM>@? 9 G πn,d

Èfx�GdÓKG.;IGl>SE 9 ?BTS?BÁ$Vl;[ZI>@JOC';vLB;NF;I\dmd?HÁIV.;k>�bDC;�N 7 JOLB>S;$ESGFJOGF=$; + NFZIifE@JONXZkrf;IEST¡LH;hG 9 Vl?HGKJOL ,m|W=$JOE@JO=4>@ZIES?HT<Z�CKJOE1LH;`=$JOGKJOL'N 7 ?BGXA 9 E<VpJ�^>S? 9 G πd,n

|�C;$E<V.;4>`NF;5NFZI>S;$ESVl?HGX;$EkLB;$ThZI>QJ�>@T�ÂpCFJOE<>S?HE�NF;$T<ÃD\X;$LHT 9 GqES;$CXES;$GXNqLH;aA 9 GF=I>S? 9 GFGX;$Vl;$GW>;IG�V 9 NF;�G 9 Vl?HGFJOL�;I>kN 9 GF=aNF;5= 9 GFT<>SES\F?BES;e;$G�= 9 VlCKJM>@?ExF?HLB?B>SZ`LH;IThV 9 NXÁ$LH;IThZ4>@;IGFNF\FT`NX\�CFE 9 =$ZINFZ;4>¡NF;�TSCZ$=$?RÓK=YJ�>@? 9 G�È

6 JeTcbDGn>SPFÁ$T<;kNF;IT1= 9 GW>@E��fLH;I\FESTz;$GlV 9 NF;vG 9 V.?BGKJOLF;4>1;IGpNFZIifE@JMNFZ¡;$T<>�xKJOT<Z$;�TS\FEz=$;IT1NX?BÎ'Z$ES;IGW>@TV 9 NXÁ$LH;IT�ZI>@;IGFNF\FTT+ CFE 9 =IZ$NFZIT];I>aTSCZ$=I?BÓK=$JM>@? 9 GFT ,4È 6 ;$T5= 9 GW>@E��fLH;I\FESTeZI>S;$GFNF\XT]NF\�V 9 NF;"G 9 Vl?HGKJOL;4>¡NFZ$ifESJONFZ�T 9 Gn>h= 9 Gn>SE��fLHJ@xFLB;$TB|dG 9 Gd^lxFL 9 Ãn\KJOGW>@T¡;4>¡TS?HVlCFLB;$T$È

6 JËTS?BV.CFLB?H=I?B>@Z�NF;qL 7 ; md;$VlCFLH; G 9 \FT�JOVlÁ$GX;oÂËLH?HVl?B>S;$ElÂËNF;I\dm V 9 NX;$TjNF;�A 9 GF=I>S? 9 GFGX;$Vl;$GW>;4> N 9 GF=oNF;�= 9 GFT<?HNFZIES;IE�T<;$\FLB;$Vl;$GW> NF;$\dm V 9 NFÁ$LB;$T�NF;IT CFE 9 =IZ$NFZIT ;4>�NF;$T�TSCZ$=I?BÓK=$JM>@? 9 GFT$È�u`G

Page 152: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ Ï � ���������� �������������������������� �"!#���%$&���'$(��)

C';I\X>�?HV.JOif?BGF;$E¡Ãn\F;)G 9 >@ES;aCFE 9 C 9 T<?B>S? 9 G C';I\X> $I>SES;)JMCFCFLH?BÃn\FZ$;a;��l=YJO=I;$Vl;$GW>�C 9 \FEkNX;$T�T<bDTc>@Á$Vl;$TNF;�>QJO?BLHLH;.?HGFNX\FT<>SES?H;ILHLB;pZIr 9 LH\FJOGW>.NFJOGFT"CFLH\XTS?H;I\FEST)V 9 NF;$T)NF;�A 9 GX=I>@? 9 GFGF;IV.;IGW>YÈ�sg;�=YJMTlN 7 Z4>@\FNF;CFESZITS;$GW>S;�\FGF;jNFZI= 9 VlC 9 TS?R>@? 9 G�\d>@?HLB?HTSJ@xFLH;)C 9 \FEe> 9 \d>5CFE 9 xFLBÁ$Vl;.= 9 V.CXLH;4md; + \FG�V 9 NFÁ$LB;.\XGF?HÃn\F;NFZ$=IES?BrMJOGW>lLH;p= 9 VlC 9 E<>@;IV.;IGW>)NF\�T<bDT<>SÁ$Vl;�NXZ$= 9 V.C 9 TSZ�;IG CXLH\FT<?H;$\XEST)V 9 NFÁILH;IT]TS?BV.CFLB;$T ,4È�� 9 \FE=QPKJOÃn\F;jV 9 NXÁ$LH;"NF\|CFE 9 =$ZINFZpNFJOGFT5\XG�V 9 NF;lNF;"A 9 GF=4>@? 9 GFGF;$Vl;$GW>aN 9 GFGXZpG 9 \XTaZI=$ES?Rr 9 GXT]JO\FT<TS?>@ESÁITtT<?HVlCFLH;IV.;IGn>3NX;$TtT<C'ZI=$?RÓK=YJM>S? 9 GXTtJOT<T 9 =$?BZ$;$T,;I>,G 9 \FTU;$Ga;IÎ';$=4>@\ 9 GXT�L�J¡T<bDGW>@PFÁITS;[NX;1= 9 GW>@E��OLH;$\XE$È

Page 153: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� ����������������

Page 154: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 155: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�����H����!�$ ���� ~ Ï �

6 ;8>@E@JYrMJO?BLOCFE<Z$TS;IGW>@ZgNFJOGFT3=$;4>S>@;8>SPFÁ$T<;1= 9 GFT<>S?B>S\F;�\FGF;�;4mD>@;IGFTS? 9 G5NX;zLHJg>@PFZ 9 ES?B;8NF;�= 9 GW>SE��fLB;zCFJOET<\FC';IE<rD?HT<? 9 G�C 9 \XEhLHJ.if;IT<>@? 9 G�NF;IT`V 9 NF;ITkNF;eA 9 GF=4>@? 9 GFGF;$Vl;$GW>$È 6 ;$TkV 9 NF;$T�NF;5A 9 GF=I>S? 9 GFGX;$Vl;$GW>E<;$CFE<Z$TS;IGW>@;$GW>8L 7 ;IGFTS;IV�xFLB;zNX;$Tt= 9 VlC 9 Ec>@;IV.;IGn>STUJONFVl?HTST<?DxFLB;$T�NF\aT<bDT<>SÁ$Vl;gC 9 \FE3\FGF;z= 9 GXÓKif\FESJM>@? 9 GN 9 GFGFZ$;gNF;$T8E<;$TST 9 \FE<=$;$TIÈ 6 ;[CFE 9 xFLHÁIV.;1ÃD\X?FTS;[C 9 T<;[;$Tc>zJOL 9 E<TtN 7�9 xX>S;$GF?BEt\FG)= 9 GW>@E��fLH;I\FE�CKJOE,V 9 NF;MÈ{�L`T 7 JMif?B>�NFJOGFT�\FG±CFE<;$Vl?H;$E.>@;$VlCFT�NF;q=$JOE@JM=I>@ZIES?BTS;$E�;4>�NF;oES;ICFESZITS;$GW>S;$E�LH;$TpNF?BÎ'Z$E<;$GW>@T�V 9 NF;ITC 9 TST<?DxFLB;$T¡N 7 \FG�TcbDT<>@ÁIV.;e;I>hNKJOGXTh\FG�TS;I= 9 GXN�>@;IV.CFT¡NF;eifZIES;$E�= 9 ESES;I=I>S;$Vl;$GW>kL 7 JMLB>@;IESGKJMGF=$;�;IGn>SES;=I;$T8V 9 NF;IT$È 6 ;IT8ESZ$T<\FLB>@JM>@T8NX;vG 9 T�>@ESJYrOJM\dm)T 9 GW>�CFESZITS;$GW>SZ$Tz;$G"NF;$\Dm"CKJOEc>@?H;IT *fLHJkCFES;IV.?BÁ$E<;[;4mdC 9 TS;LB;�= 9 GW>@; mD>@;e;I>¡L�J)CFE 9 xFLBZ$V.JM>@?BÃD\X;@|XLHJ]TS;I= 9 GFNX;5CFE<Z$TS;IGW>@;eG 9 T¡CFE 9 C 9 T<?B>S? 9 GFTIÈ

y`JOGXThLHJ"CXES;$Vl?HÁIES;�CKJOEc>@?B;@|KG 9 \XTkJYr 9 GFT�A JM?B>¡\FG ZI>QJ�>hNX;aL 7 JOEc>¡Ãn\F?3G 9 \FThJlC;$E<V.?BTvNF;eES;I>S;$GF?BEÃn\F;�*6 6 J�T<bDGW>@PFÁITS;jNF;.= 9 GW>SE��fLB;$\FEe;$Tc>]\FGF;pJOCFCFE 9 =QPX;.A 9 E<V.;ILHLH;)V.Ju�<;I\FES;.C 9 \XEaL 7 JO\d> 9 V.JM>@?BÃn\F;OÈ� ?H;$G±Ãn\ 7 PKJOGFNX?H=YJMC'ZI;|CKJME�NX;$T�CXE 9 xFLBÁ$Vl;$T�NF;o>QJM?HLHLB;�NF;�V 9 NFÁILH;ITB|vG 9 \XT JYr 9 GFT�V 9 GW>@E<ZÃn\ 7 ;$LBLH;eC';I\X> $4>@E<;5\X>S?HLH?BTSZI;eNX;5V.JOGF?HÁIES;eT@JM>S?HTcA JO?HTSJOGW>@;@|ÒT 9 ?B>hifE /M=$;]ÂlNF;$TkT<>@E<\F=I>S\FES;IT`CKJOEc>@? ^=I\FLH?BÁ$E<;$TB|XT 9 ?R>¡ifE /O=I;�ÂlL 7 \d>@?HLB?HTSJM>@? 9 G.NX;�A 9 ESV.JOLH?BTSVl;$T[JM\X>@E<;$T¡Ãn\F;�LH;$T�JO\d> 9 V.JM>@;IT¡Â)ZI>QJ�>@T &6 6 Jp= 9 GFTc>@ES\X=I>@? 9 GqNF\q= 9 GW>@E��OLH;$\XE`CKJOEhL 7 JOCFCFE 9 =QPF;5NXbDGKJOVl?HÃn\F;]C;$E<V.;4>`N 7 \X>@?BLH?BTS;$EhL�J">@E@JM=$;NX;$TzZIrfZIGF;$Vl;$GW>ST[CKJOT<TSZ$TIÈFsg;4>S>S;h>@ESJO=$;¡A 9 \FE<GF?H;¡\FGX;h?BGXA 9 ESV.JM>S? 9 G�x;YJM\F= 9 \XCpCFLB\FT1E<?H=QPF;�Ãn\F;L 7 Z4>QJM>B|XÃn\F?3;$Tc>�L�J]TS;I\FLH;�?BGXA 9 ESV.JM>S? 9 G.\X>@?BLH?HT<Z$;`NFJOGFT�L 7 JOCFCFE 9 =QPF;�Tc>QJM>S?HÃn\F; &6 6 J¡if;$Tc>@? 9 GaNX;$TtV 9 NF;$TU;$Tc>t\FGerfZIES?B>@J@xFLB;1CFE 9 xFLBÁ$Vl;8?HGFNF\XT<>@E<?H;ILD;IG5=I;1Ãn\F?D= 9 GX=$;$E<GF;gLB;$Ttwd�`�UÈsg;IC';IGFNKJOGW>B|t;$LBLH;.J�TS\XE<> 9 \X>)ZI>SZpZ4>@\FNF?BZ$;pA 9 ESVl;$LHLB;$Vl;$GW>eNKJOGFTaLH;.N 9 V.JO?HGF;lNF;IT]T<bDT<>SÁ$Vl;$T= 9 GW>@?BGD\XT�;4>�NF;$ThwXy � ;IG�>@JOGW>hÃn\F;�CF?BL 9 >@JOif;`NX;eCXPKJOTS;IThNX;�A 9 GF=I>S? 9 GFGX;$Vl;$GW>YÈ

sg;$T"NF?RÎ�ZIES;IGn>ST)C 9 ?HGW>@T]G 9 \FT 9 GW>lJOVl;$GFZIT)Âq=QP 9 ?BTS?HEaL 7 JOCFCFE 9 =QPX;�NXbDGKJOVl?HÃn\F;j=$JOE);$LBLH;pG 9 \FTC;$E<V.;4>"N 7 JM=$=$ZINF;$E.Âq\FGF;�?HGdA 9 ESV.JM>@? 9 GËE<?H=QPF;a|�L�J�>@ESJO=$;a|8;I>"CKJMES=$;�Ãn\F;�G 9 T)>@ESJYrOJM\dmÌC 9 \FESE 9 GW>$4>@ES;5ZI>@;IGFNF\FT�;IGq\X>@?BLH?HTSJOGW>kNX;$T�T<>SES\F=4>@\FE<;$T�PF?BZ$E@JMES=QPF?BÃD\X;$T 9 \qV 9 NX\FL�JO?BES;IT$È 6 ;$T`>@ESJYrOJM\dm�T<\FE�LH;ITTcbdTc>@ÁIV.;ITa= 9 GW>@?HGn\FT�;4>aLB;$TewXy2� G 9 \FT 9 GW>�V 9 GW>SESZ)Ãn\ 7 \FGF;"r 9 ?B;l?BGW>@Z$E<;$T<T@JOGW>@;lN 7 ZI>S\FNF;"NF;$TeNF?RA�^AëZIES;$GW>S;$T�CFPKJOT<;$TeNF;)A 9 GF=4>@? 9 GFGF;$Vl;$GW>�N 7 \FG�T<bDTc>@Á$Vl;l= 9 GFT<?HTc>@;"Â�= 9 GXT<>@E<\F?HE<;"NF?BÎ'Z$E<;$GW>@T�V 9 NXÁ$LH;ITJO\DmXÃn\F;ILHT�T 9 GW>kJOTST 9 =I?HZIT�NX;$T�V.ZI=YJOGF?BTSVl;$T¡NF;eT@JO\d>hN 7 \FG V 9 NFÁILH;�Â"L 7 JO\X>@E<;�;I>�NF;eE@JO=I= 9 E<NF;$Vl;$GW>N 7 ZI>@JM>@T + ZI>@JM>`NX;)NFZ$CKJME<>�N 7 \FGF;5CFPKJOT<;"Âp\FGqG 9 \drf;$LtZI>QJ�>�?HGF?R>@?HJOL�NKJOGXT�L�J.G 9 \Xrf;ILHLB;5CFPKJMTS;"ÂjJM>c^>S;$?HGXNFES;W,4È3x8G 9 \X>SES;a|UC 9 \FE�E<;$GFNFE<;pG 9 TaCFE 9 C 9 TS?R>@? 9 GFT�JOCFCFLB?H=$J@xFLH;ITB|�G 9 \FT]JYr 9 GFTeN���E<Z$C 9 GFNFE<;jÂNF;I\dm�= 9 GW>@E@JM?HGW>@;IT *

~ ÈhJYr 9 ?HEv\FGX;eE<;$CFE<Z$T<;$GW>QJM>S? 9 G�T<bDGW>@PXZI>@?BÃn\F;aNX;$T�V 9 NF;$Tv;4>�NF;$T�JOLR>@;$E<GKJOGF=I;$TM|ÑDÈ�V.JMÉB>@ES?BTS;IEgL�J5>@JO?HLBLH;hNF;$T�V 9 NFÁILH;$TIÈ

Page 156: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ Ï � �����H����!�$A��'�

} 9 \FTaJÚr 9 GFTaESZ$C 9 GFNX\ÍÂ�=I;$T]= 9 GW>@ESJO?HGW>@;ITa;IG�CFE 9 C 9 T@JOGW>5\FGF;.JOCFCFE 9 =QPF;.V]\FLR>@?R^_V 9 NFÁILH;OÈ'ÆhGV 9 NFÁ$LB;5NF\oCFE 9 =IZ$NFZ);4>�\FGqV 9 NFÁILH;aNF;$T�T<C'ZI=$?BÓF=YJM>S? 9 GFTkT 9 GW>eJOT<T 9 =$?HZIT�Âj=QPKJO=I\FG|NX;$T�V 9 NF;IT`NF;A 9 GF=I>S? 9 GXGF;$Vl;$GW>zES;4>@;$Gn\�È 6 ;¡V 9 NFÁILH;[NF\.CFE 9 =$ZINFZ¡ES;ICFESZITS;$GW>S;kL�J�= 9 GXÓKif\XE@JM>S? 9 G"NF;ITzZILHZIV.;IGn>STgJMTc^TS\FESJOGW>tLHJvA 9 GF=I>S? 9 GFGFJOLH?R>@Z�J�>S>@;IGFNF\F;zNKJOGXT,LB;8V 9 NF;OÈ 6 ;IT,T<C'ZI=$?RÓK=YJM>S? 9 GXTU; mdCFES?BV.;IGn>ULB;$T3= 9 GW>SE@JO?BGn>S;$TNF;lA 9 GF=I>S? 9 GFGX;$Vl;$GW>e?HVlC 9 T<Z$;ITaÂ�=QPKJO=I\FGËNF;ITaV 9 NFÁ$LB;$T�NF;IT5CFE 9 =IZ$NFZIT$È 6 J�= 9 V.V5\X>QJM>S? 9 Gq;IGW>@ES;V 9 NF;$T"?BGn>S;$Ecrd?B;$GW>lTS\F?R>@;�ÂoL 7�9 =I=$\FE<ES;IGF=$;�N 7 ZIrOZ$GF;IV.;IGn>STjCKJOEc>@?B=$\FLB?H;$E<TB|tJOCFC;$LHZIT"ZIrfZIGF;$Vl;$GW>STpNF;= 9 VlV]\X>@JM>@? 9 G�Èv} 9 \FT�JYr 9 GFT�= 9 GFT<?HNFZIESZ�\XGF;�>�bDC 9 L 9 if?H;�>S;$LHLB;oÃD\ 7 ?BLe; md?HT<>S;|> 9 \ � 9 \FE<T \XG T 9 \FTc^;$GFT<;$V�xFLB;kNF;�ES;ITST 9 \FES=I;$T1= 9 VlV]\FGF;IT1;IGW>@ES;hNF;$\DmlV 9 NF;$TIÈdsg;$=$??HVlC 9 TS;vNF;�TS\X?BrDES;�L 7 ZIr 9 LH\X>S? 9 G"NF\CFE 9 =$ZINFZ¡C 9 \XE�NFZI>S;$E<V.?BGF;$E�= 9 ESE<;$=4>@;$Vl;$GW>zLH;IT�ZI>@JM>@T8NX;vNFZ$CKJME<>�NF\"CFE 9 =IZ$NFZ¡;I>�NF;vL�J`T<C'ZI=$?BÓF=YJM>S? 9 GNF\|G 9 \Xrf;$JO\�V 9 NF;OÈ�� 9 \FE�E<Z$C 9 GFNFE<;lÂ�=I;"CFE 9 xXLHÁ$Vl;]G 9 \FT�JYr 9 GFTe?HGW>SE 9 NF\F?B>k\FG�V.ZI=YJOGF?BTSVl;]NF;TS\F?Rrd?æÈÒsg;�V.ZI=YJOGX?HTSVl;�;$Tc>hJOTST<\FESZ�CKJOE¡NF;IT¡=YJOGKJM\dm�N 7 ?HGXA 9 ESV.JM>@? 9 Gp?BGn>S;$E<=YJOLBZ$Tv;$GW>SES;eLH;$TvV 9 NFÁ$LB;$TNF;$T]CXE 9 =$Z$NXZ$T$È 6 ;pE��OLH;"NF;p=I;$T]=$JOGKJO\Dm�= 9 GFT<?HT<>S;jÂ�;IGFES;Iif?HTc>@E<;$E�> 9 \X>S;$TaLH;$TaTSZIÃD\X;$GF=I;$T"N 7 ZIrfZIGF;4^V.;IGn>ST[ifZIGFZ$E<Z$;$T¡CKJMEgLH;hCFE 9 =$ZINFZ`N 7 \FG�V 9 NF;�NF;ICF\F?HTgL 7 ?HGFTc>QJOGW>[NX;`T@J]T<Z$LH;I=I>S? 9 G �<\XTSÃn\ 7 Â]L 7 ?HGFTc>QJOGW>9VU \XG Z4rfZ$GX;$Vl;$GW>kC;$E<V.?BTvNF;�= 9 VlV]\X>@JM>@? 9 GjT 7 ;IT<>hCFE 9 NF\F?R>YÈ

sg;4>S>@;5NFZ$V.JOES=QPX;]C';IESVl;I>kNF;]NFZ4>@;$E<V.?BGF;$EhLH;ITkZI>@JM>@TkNF;]E@JM=$= 9 ESNF;IV.;IGn>B|�= 7 ;IT<><^�Â�^�NX?HES;a\FG�Z4>QJM>JONFZ$Ãn\KJ�>�JYrf;I=]L 7 ZI>@JM>`ÂlCKJOEc>@?HE¡NF\XÃD\X;$LtL 7 Z4rfZIGF;$Vl;$GW>�NF;a= 9 VlV]\X>@JM>@? 9 G�J.;I\�LH?B;$\�ÈK��ÓKG�N 7 JOCFCFE<Z4^PF;$GFNX;$EvL�J�C 9 E<>SZ$;kNX;`G 9 >SES;kCXE 9 C 9 TS?R>@? 9 G�|WG 9 \XTvJYr 9 GFTg= 9 GFT<?HNFZIESZhNKJOGFT[\XGjCFES;IV.?B;$E�>@;IV.CFT1LH;h=YJOTLH?HVl?B>SZ¡ÂaNF;I\dm.V 9 NF;IT1NF;�A 9 GF=4>@? 9 GFGF;$Vl;$GW>$È 6 JeifZ$GFZIE@JOLB?HTSJM>@? 9 GlÂaCFLB\FTS?B;$\FE<T1V 9 NX;$T1Ja;$GXTS\F?R>@;kZ4>@ZCFESZITS;$GW>SZ$;OÈt} 9 \XTaE<;I>@?B;$GFNXE 9 GFTeÃn\F;l=$;I><>@;lifZ$GXZ$E@JMLH?HTSJM>@? 9 GqGF;lTS;lLH?BV.?R>@;5CFJOTaT<;$\FLB;$Vl;$GW>5Â�L 7 JO\XiM^V.;IGn>@JM>@? 9 G�NX\�G 9 V�xFES;aNF;5V 9 NX;$T�VpJO?BT¡GFZ$=I;$TST<?B>S;]L�J"V.?BTS;e;$G�CXL�JO=I;aN 7 \FGF;aNFZ$V.JOE<=QPF;5NF;aCFES?BTS;;$G�= 9 VlCX>@;�NF;IT¡NF?BÎ'Z$E<;$GW>@T¡= 9 V�xF?HGFJO?HT 9 GFTvC 9 TST<?DxFLB;$TvNF;�= 9 V.V]\d>QJM>S? 9 GFTg;$GW>@E<;eV 9 NF;$TIÈ

x8Go=$;"Ãn\F?8= 9 GF=$;IESGF;"NF;ITaJMCFC 9 E<>@T�;IG|= 9 VlVpJOGXNF;]G 9 \XT�JÚr 9 GFTeNFZ$V 9 GW>@E<Z)Ãn\ 7 ?BL�;4md?BT<>@;WxX?H;$G\FG�T<;$\FL�TS\XC';IE<rD?HT<;$\FEeCKJOE�V 9 NF;";4>aG 9 \FTaJÚr 9 GFTaJOTST 9 =I?HZlÂ�=QPKJO=$\XGËNF;$TeV 9 NFÁILH;IT�NF;$TeCFE 9 =$ZINFZ$T\FG V 9 NFÁ$LB;�NF;oTSCZ$=I?BÓK=$JM>@? 9 G±JONFZIÃn\KJM>YÈ[x�G ;IÎ';I>�T<?�LH;�V 9 NFÁ$LB;�NF;oTSCZ$=I?BÓK=$JM>@? 9 G N 9 ?R>�TS\X?BrDES;L 7 ZIr 9 LH\X>S? 9 G NF\ CFE 9 =IZ$NFZoC 9 \FE�Ju�<\FTc>@;IE�LB;$T�JO=4>@? 9 GFTjNF;o= 9 Gn>SE��fLB;$T�ÂÍV.;IGF;$E�JYrO;$=�L�JÍG 9 \XrO;$LBLH;NXbDGKJOVl?HÃn\F;�NF\pCFE 9 =IZ$NFZa|d?BLKN 9 ?R>1= 9 VlV.;¡LH;¡V 9 NXÁ$LH;vNX\jCFE 9 =$ZINFZ $I>@E<;kV]\XGF?KN 7 \FGjVlZ$=YJMGF?HT<V.;¡NF;= 9 VlV]\X>@JM>@? 9 G�È�} 9 \FTeES;I>S?H;IGFNFE 9 GFT5JM\FTST<?1Ãn\F;lL�J�>@PFZ 9 ES?B;"NF;.= 9 GW>@E��fLH;lCKJOE�TS\XC';IE<rD?HT<? 9 G|C';IESVl;I>NF; rOZ$ES?RÓK;$E"A JO=I?HLH;IV.;IGW>"LH;$TlCFE 9 CFES?BZI>SZ$T"NF;�= 9 GW>@E��fL�J@xX?HLH?R>@Z.;I>.NF; G 9 Gd^¦xXL 9 =YJOif;�NX;$Tp= 9 GW>@E��fLH;I\FESTZI>@;IGFNF\FThNF;�=QPKJO=I\FG NX;$T�V 9 NF;$TvNX;�A 9 GF=I>S? 9 GFGX;$Vl;$GW>YÈ

} 9 >@E<;¡JOCFCFE 9 =QPF;�C;$ESVl;I>B|WJO\lNF;$LHÂ�NF;¡L�J`if;IT<>@? 9 G"NF;�L 7 JOLB>S;$ESGFJOGF=$;gNF;$TzV 9 NF;ITB|fNF;¡= 9 GW> 9 \FE<GF;$E;I>[NX;hV.JMÉH>SES?BTS;$E8L 7 ; mdCFL 9 T<? 9 G"= 9 V�xF?BGKJM> 9 ?HES;vNX;hL 7 ;ITSCKJO=I;kN 7 ZI>@JM>@Tz;$Gp= 9 GFT<?HNFZIE@JOGW>1\FGp;IGFTS;IV�xFLB;kNF;V 9 NFÁ$LB;$ThTS?HVlCFLB;$T�;I>�NF?BT<>S?HGF=4>@T`JM\�LH?B;$\�NX;]TS;5A 9 =YJMLH?HT<;$E¡TS\XE`\FGqV 9 NFÁILH;e\FGF?BÃD\X;5ES;ICFESZITS;IGn>@JOGW>eLH;T<bDT<>SÁ$Vl;OÈ3y`JOGXT�LH;5=$JONFE<;)NF;]L 7 JOCFCXE 9 =QPF;]V]\FLR>@? ^�V 9 NFÁILH;�G 9 \FT�C 9 \Xr 9 GXT�JO\FTST<?tA JO=I?HLH;IV.;IGW>kZI=$ES?BES;NF;$T�T<C'ZI=$?RÓK=YJM>S? 9 GXT,NF;z>QJO?BLHLB;$T�= 9 GF=$?BTS;$TtC 9 \XE,=QPKJM=$\FG)NF;ITtV 9 NXÁ$LH;IT,NX;$TtCXE 9 =$Z$NXZ$T$È 6 ;$Tt= 9 GW>@E��fLH;I\FEST9 xX>@;IGn\FT5NKJMGFT�=$;I><>@;.JOCFCFE 9 =QPX;$TeT 9 GW>aTS?HVlCFLB;$TB|';4mdCFL 9 ?B>@J@xFLH;IT�CKJOE�LH;ITeJOLHi 9 ES?B>SPFVl;$TkNX;.TcbdGW>SPFÁ$T<;;I>�=YJOESJO=I>SZ$E<?HTS;IGW>hLB;�T<bDT<>SÁ$Vl;a= 9 VlVpJOGXNFZ�NKJOGFT¡NF?RÎ�ZIES;IGn>ST¡V 9 NF;$TvNX;�A 9 GF=I>S? 9 GFGX;$Vl;$GW>YÈ

y`JMGFTtG 9 T,>@ESJYrOJM\dmaLH;$TUZIrOZ$GF;IV.;IGW>@T8C;$ESVl;I><>QJOGW>tNF;rxKJMTS=$\XLH;$E,N 7 \FG]V 9 NF;zNF;zA 9 GF=I>S? 9 GXGF;$Vl;$GW>

Page 157: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�����H����!�$ ���� ~ ÏfÏ

ÂpL 7 JM\X>@E<;5T 9 Gn>`TS\FCFC 9 T<Z$T 9 xFT<;$E<rMJ@xXLH;$TQ*�Âp\FGq?BGFT<>@JOGW>�N 9 GFGXZ]G 9 \FTk= 9 GFGFJO?HT<T 9 GFT�C;$Ec>@?BGF;$VlV.;IGW>LB;�V 9 NF;�TSZILH;$=4>@? 9 GFGFZMÈ�ÆhGF;�C';IEST<C';I=I>@?Rrf; N 7 ; mD>@;$GXTS? 9 G ?HGW>SZ$ES;ITSTSJOGW>@;�NX; G 9 Tl>SE@JYrMJO\dmÌT<;$E@JM?B>lNF;= 9 GFTS?BNFZ$E<;$E"NF;IT.Z4rfZ$GX;$Vl;$GW>@T.NF;�= 9 VlV]\X>@JM>@? 9 GÍ?HG 9 xFTS;IE<rMJ@xFLB;$T$È�y`JOGFTl=$;�=YJOTM|8G 9 \FT"C 9 \FE<ES? 9 GFTCKJME);4md;$VlCFLH;�JR� 9 \X>@;IE"\FG V 9 NF\FLH;.NF;�NFZI>S;$=4>@? 9 G NF;IT"V 9 NF;$T)NX;�A 9 GF=I>S? 9 GFGX;$Vl;$GW>YÈ8Æ�GF;�JO\X>SES;C;$E<TSC;$=I>S?BrO;qTS;$ESJO?B>pNF;qES;ICFESZITS;IGn>S;$E�LH;ITj=QPKJOGXif;$Vl;$GW>@T�C 9 T<TS?DxXLH;$TpNF;�V 9 NF; CKJOEj\XG JM\X> 9 V.JM>S;= 9 GFT<>SES\F?R>zTS\FE�L 7 JOLBCFPKJ@x;I>�NF;IT1Z4rfZIGF;$Vl;$GW>@T1NF;�= 9 VlV]\X>@JM>@? 9 G�ÈO�±=I;I>gJO\X> 9 VpJM>S;vES;ICFESZITS;$GW>@JOGW>[\FGCFE 9 =IZ$NFZa|WG 9 \FT�C 9 \FE<ES? 9 GFT�JOTST 9 =I?H;IE8NF;$T�TSCZ$=I?BÓK=$JM>@? 9 GFT�;4mdCFE<?HV.JOGW>8NF;IT1= 9 GW>@E@JM?HGW>@;ITzCFJOE<>S?H=$\XLH?HÁIES;ITT<\FE¡LH;$Tv=QPFJOGFif;IV.;IGn>SThNX;eV 9 NF;OÈRÈBÈ

Page 158: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 159: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ Ï �

� ��� ���»� �

� � ����� � ��� � �� � ��� �� ��� � � � ������������� �

sg;I><>@;�JOGFGX;4md;�CFESZITS;$GW>S; Ãn\F;ILHÃn\F;$TlG 9 >S? 9 GXT]NF;yxKJOT<;�TS\FE"LH;IT"JO\X> 9 VpJ�>@;$T5;I>lTS\FE)LHJ�>@PFZ 9 ES?B;NF;IT¡L�JOGFifJOif;$TIÈKy`JOGXT�\XG CFE<;$Vl?H;IE[>@;$VlCFTM|FG 9 \FT�J@x 9 E<NF;$E 9 GFT¡Ãn\F;$LBÃD\X;$T�NFZIÓKGX?B>@? 9 GFTvE<;$L�J�>@?BrO;$T¡JO\DmJO\d> 9 V.JM>@;IT$ÈK} 9 \FT�J@x 9 ESNX;$E 9 GFTv;$GFT<\F?B>S;�LH;$T¡LHJOGFiWJOiO;$T$È

!$# /j(3+a¨ £�(3¢¡ 

ÆhGlJO\d> 9 V.JM>@;¡Â`Z4>QJM>ST8ÓKGF?HT8;IT<>z\FG)A 9 E<VpJOLB?HT<V.;z=YJOESJO=I>SZ$E<?HTSZ¡CKJME8LH;$T8Z4>QJM>ST8;I>zLH;IT8ZIrOZ$GF;IV.;IGn>ST$ÈÆ�G Z4>QJM>�ES;ICFESZITS;IGn>S;]\FGF;aJO=4>@?BrD?R>@Z 9 \�\FG�Z4>QJM>�NF;�A 9 GF=4>@? 9 GFGF;IV.;IGn>�NF\�T<bDTc>@Á$Vl;@|\FG ZIrfZIGF;$Vl;$GW>;IT<>�\FG�TS?HiOGKJOL�C;$E<V.;4>S>QJMGn>¡NX;eCFJOTST<;$E�N 7 \XG Z4>QJM>�Â"\FG�JO\X>SES;OÈ

� «c®�«<® � ¼¡·d¸1À ��·d°�²Íº �·d°�´FÀ�µc¹hµ~²n·d°�² w�Wgw�W w�W � j � amd Pud�\camq� j � aid Pud�\ca weW� � K�� IMN ILK IM=@?AL�I =�C I E��OE>G�IM= =-G�I ?AL � �OE B K C�� �� �� ��BD<>=�I

G = (Q, Σ, δ, q0, Qm)N����

� Q��=��(G�=JI%"�<>= � �OE2?�� L�I K I4G��

� ��=��(G�=JI%"�<>= � �OE?A=�G�9 I%"�N <>=-G��K�B;BO=�<>L K���G-G�EK < BgM K�"�=�I��

� q0

�2L�I K I2E��OE4I E�K <��� δ

�Q×Σ −→ Q

=-G�I�< K �WN �Q:�I E N � ?A='I C�K��(G�E4I E N �@B K CFI E =�<4<>='IM=�<4<>=�� �S=�BON � C'��� L�I K I�?�� K CFCFE�� L-=q′ ∈ Q

=�I ��� L�I K I@?A= ?ALMB K CFIq ∈ Q

N � K G-G�N�:�E = � � L�� L��Q=JI =��OIσ ∈ Σ

�H: � =-G�I������ ? E4C =δ(q, σ) = q′ � 7 =�I I = �WN �Q:�I E N � BO=��AI! �I C-=@L�I =��D?��O= :-N I I =�G��AE4I δ : Q×Σ∗ −→ Q

IM=�<4<>="� �O=BON �ACJIMN �AI =2G�L#� �S=��Q:-= ?�� L�� L��Q=JI =��OI4G

s ∈ Σ∗ =�I(BON � C I N �AI σ ∈ Σ�δ(q, sσ) = δ(δ(q, s), σ)

�� Qm

�2=��(G�=JI%"�<>= ?�� L�I K I4G ILK C$� �SL-G � �

6 ;$TvNF;I\dm�NXZIÓKGF?R>@? 9 GFT[T<\F?BrMJOGW>@;ITvC';IESVl;I><>@;$GW>vL 7 Z4>@\FNX;`NF\yxFL 9 =YJMif;kNF\�CXE 9 =$Z$NXZOÈ 6 J]CFE<;$Vl?HÁ$E<;= 9 GF=$;IESGF;"L 7 ;IGFTS;IV�xFLH;)NX;$T�ZI>@JM>@T�JO=I=$;ITSTS?ExFLH;IT�;I>�L�JjNX;$\dmd?HÁIV.;)=$JOE@JM=I>@ZIES?BTS;)L 7 ;$GXTS;$V�xFLH;)NF;IT�ZI>QJ�>@T

Page 160: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ Ï � ���������%� �H� �"!��J� �P�����2$ ��� ��� ���� � � )��2$ ����� ��� �'� $

= 9 ^�JO=$=I;$TST<?DxFLB;$T¡NF\�CFE 9 =$ZINFZ G È� j � amd Pud�\ca wz}� � L�I K I

q?A= < � K�� IMN ILK I =

G=-G�I�? E4I�KA:-:-=-G-G�E "�<>=@G � E4<2=��VE>G�IM= � �Q=KG�L#� �S=��Q:-= ?�� L�� L��Q=JI =��OI G

sK�B �

B K C�IM=��cK��OI �L(G)

I =�<4<>= � �O=δ(q0,s) = q � � � =��(G�=JI%"�<>=R?A=-G L�I K I4G KA:-:-=-G-G�E "�<>=-G =-G�I�?AN � �QL%B K C �

Qac = {q ∈ Q | ∃s ∈ Σ∗,δ(q0,s) = q} ��� <=�� ?AL-:-N �A<>= � �O=H< � K��AIMN ILK I = G=-G�I'? E4I KA:-:-=-G-G�E "�<>= G�E

Qac := Q � �� j � amd Pud�\ca wzy� � L�I K I

q=-G�IH? E4I":-N�� KA:-:-=-G-G�E "�<>=TG � E4<�=��VE>G�IM=~K�� I N E��(G � �Q= G�L#� �O=��Q:-= ?�� L�� L��Q=JI =��OI GKB K C�I K��OI

?A=MB � E>G :-=�I�L�I K I'=�I I =��cK��OI!� ��� L�I K IhILK C$� �SL � � � =��(G�=JI%"�<>=@?A=-G L�I K I G :-N�� KA:-:-=-G-G�E "�<>=@?A= < � K��AIMN��ILK I =

G=-G�I �

Qco = {q ∈ Q | ∃s ∈ Σ∗,δ(q,s) ∈ Qm}� � � K�� IMN ILK I = G

=-G�I'? E4I�:-N�� KA:-:-=-G-G�E "�<>=%G�EQco := Q � �

weWgw�Wgwz} � �u\_^inid�PLq��_ams��i�u\ca`UbUlP s \cZ]SV\cq d Pud�\ca SiQT�uQgf�f�f�Uw 9 ?H;$GW>¡NF;I\dm JO\X> 9 V.JM>@;IT G1 = (Q1, Σ1, δ1, q0,1, Qm,1)

;4> G2 = (Q2, Σ2, δ2, q0,2, Qm,2)È

� j � amd Pud�\ca w����=�BDC N�?��AE4I ?A=

G1 × G2

=-G�I ��� K�� IMN ILK IM=G = (Q, Σ, δ, q0, Qm)

K�� =-: �� Q = Q1 × Q2

�� Σ = Σ1 ∩ Σ2

�� δ((q1,q2),α)

=-G�I�?AL � �OE TS?3;4>kT<;$\FLB;$Vl;$GW>kT<? δ(q1,α)=�I

δ(q2,α)G�N �OIJIMN �AI =-G@<>=-GK?A=����P?AL � �

�OE =-G � G K��(GH:-= :�K G δ((q1,q2),α) = (δ(q1,α),δ(q2),α))�

� q0 = (q0,1,q0,2)�

� Qm = Qm,1 × Q2,m �

� j � amd Pud�\ca wzv��=�BDC N�?��AE4ISG�9 �Q:NMAC N �Q= � N � :-N I�BON�G�E4I E N �'B K C�K <4< �<>=��

G1||G2

=-G�I � �LK��AI N ILK IM=G = (Q, Σ, δ, q0, Qm)K�� =-: �

� Q = Q1 × Q2

�� Σ = Σ1 ∪ Σ2

�� δ1 × δ2

=-G�IJ?AL � �OE =@?A= < K � K�� N � G�� E�� K��OIM= �� � δ1 × δ2((q1,q2),σ) = (q′1,q2)

G�Eδ1(q1,σ) = q′1

=�Iδ2(q2,σ)

� � =��VE>G�IM= B K G �� � δ1 × δ2((q1,q2),σ) = (q1,q

′2)G�E

δ1(q1,σ)� � =��VE>G�IM=�B K GH=�I

δ2(q2,σ) = q′2�

� � δ1 × δ2((q1,q2),σ) = (q′1,q′2)G�E

δ1(q1,σ) = q′1=�I

δ2(q2,σ) = q′2�

� � � � =-G�I B K G ?AL � �OE =�G�E δ1(q1,σ)=�I

δ2(q2,σ)� � =��VE>G�I =��OI B K G �

� q0 = (q0,1,q0,2)�

� Qm = Qm,1 × Q2,m �

y`JMGFTvLH;`=$JOTvCKJOEc>@?B=$\FLB?H;$E 9VU Σ1 = Σ2=$;$TvNXZIÓKGF?R>@? 9 GFT[T 9 GW>¡Z$Ãn\F?BrMJOLB;$GW>@;IT$ÈÒu`G�CKJOE<LH;kJOL 9 E<T[NF;

= 9 VlC 9 TS?B>S? 9 Gj> 9 >QJMLH;$Vl;$GW>vTcbDGF=QPFE 9 GF; G1||SG2È

Page 161: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�K� �(� ����� ��� �'� $ ���R!�� �� �$ ~ Ï �

� «c®�«_¬ � ¼¡·d¸1À ��·d°�²Í¹k¸�¹ º �·d°�´KÀ�µ~¹hµc²W·d°�²� j � aid Pud�\ca w=�� � K�� IMN ILK IM=��QN �&?AL�I =�C I E��OE>G�IM=H=-G�I2< KT?AN � �QL-=@?�� ��� � � E��OI ��BD<>L

G = (Q, Σ, δ, Q0, Qm)N����

� � Q�Σ=�I

Qm

N �OI�<>=-G�I JI =-G%?AL � �OE4I E N �(G � �O= ?lK��(G�< K"?AL � �OE4I E N � ?A=�< � K��AIMN ILK I =%?AL�I =�C I E ��OE>G�IM= �

� � Q0

=-G�I2< � =��(G�=JI%"�<>= ?A=-GHL�I K I4GKE��OE4I E�K���� �� � δ : Q × Σ −→ 2Q

=-G�I < K �WN �Q:�I E N ��?A= I C�K��(G�E4I E N � B K CFI E =�<4<>= IM=�<4<>= � �S= BON � C ��� L�I K I?A= ?ALMB K CFI �

q ∈ Q� N � K G-G�N�:�E =���� L�� L��Q=JI =��OI

σ ∈ Σ�T: � =-G�I������ ? E4C =

δ(q,σ) ∈ 2Q� �

7 N I I =�BON �ACK< � K��AIMN ILK I =H?AL�IM=�CJI E��OE>G�IM= :-=�I IM= �WN �Q:�I E N �TBO=��AI �I C = L�I =��D?��O=":-N I I = G��AE4I �δ : Q × Σ∗ −→ 2Q

IM=�<4<>= � �O=�BON �ACHIMN � IM=HG�L#� �O=��Q:-= ?�� L�� L��Q=JI =��OI4Gs ∈ Σ∗ =�I�BON �AC I N �AI

σ ∈ Σ�δ(q,sσ) = δ(δ(q,s),σ)

��

x8GqN 7 JO\X>@E<;$Tk>S;$E<V.;IT`\FGqJO\d> 9 V.JM>@;e;$Tc>�NF?B>hG 9 G�NFZI>S;$ESVl?HGX?HT<>S;5T<?tN 7 \FGqV%$$Vl;aZ4>QJM>k?HLU;4md?HTc>@;JO\�V 9 ?HGFTkNF;$\dmo>SE@JOGXTS?B>S? 9 GXT�NF?BÎ'Z$E<;$GW>@;ITaZ4>@?HÃn\F;4>@ZI;$TeCKJOE�LH;)V%$$Vl;"ZIrfZIGF;$Vl;$GW> σ

9 \|T 7 ?BL8;4md?HTc>@;CFLB\FTS?B;$\FE<TvZI>@JM>@T¡?HGX?B>@?HJO\dm'È

!@� � £e& �5£ �a¢¡  *t��a/�¤I24¢[*� 

� «­¬[«<® ¯� �`¹hµ_·Xµ~¸�¹k²� j � aid Pud�\ca w��

� �hLHCFPFJ@x';4>�* � � =��(G�=JI%"�<>= � �OE �QN � ��E ?A= Σ?A=%G�9 I%"�N <>=-G � <>=�I I C-=K?A= � N � BD< �;G�E =�� C GH:�K C�KA: �

I �C =-G�� �� � 9 > 9 \�=QPKJMÉ�GX;�* IMN �AI =%G�L#� �O=��Q:-=-G � �OE =@?�� L�<>LJI =��OI4G@?A= Σ

�� ε * <>= I N I ��E ?A= � � � N�:-:��ACFC-=��Q:-= ?�� � � IM=�<�L�� L��Q=JI =��OI �Q= I N�? E � =KB K G < � L�I K I :-N � C�K��OIK?��G�9�G�I JI =��� Σ+ * < � =��(G�=JI%"�<>= ?A=-G I N I4G��QN � ��E ?A=-G"� �S= < � N � BO=��AI �WN C I =�C�G��AC Σ

�� Σ∗ * < � =��(G�=JI%"�<>=%E�� � �OE :-N �OIM=��cK��OI�I N �;G <>=-G I N I4G BON�G-G�E "�<>=-G�G��AC Σ � E � = � Σ∗ = Σ+ ∪ ε

�� |m| * < K <>N � ���S=��AC@?��HI N I m � E � = � <>=��QN I%"�C =@?A=%G�9 I%"�N <>=-G@?A= Σ

:-N I�BON�GrK��OI2<>= I N I��� Σn * < � =��(G�=JI%"�<>= ?A=-G I N I G ?A= Σ∗ ?A= <>N � ���S=��AC n ��� �RBO=��AI�L-:�C�E4C = �

Σ∗ =+∞∑

n=0

Σn N��(Σ0 = ε)

� �

Õ4Ö2Q é<â å3à=> é<è�â é<í ��àçé8ÞÚé<â�âæÝ� Mâ���écè�âæécí ��àçé<â�ÞÚé Q

Page 162: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

~ � � ���������%� �H� �"!��J� �P�����2$ ��� ��� ���� � � )��2$ ����� ��� �'� $

p � � =JI�BD<>=� N E4I < � K < BgM K�"�=�I

Σ = {a,b} � aaaa,bbbbaaa,ba,εG�N �OI�?A=-G�I N I4G ?A=

Σ?A=K<>N � ���S=��AC GKC-=-GMBO=-: �

I E�� =-G � ��� � � =�I�� �� N E =��OI

u = σ1.σ2...σn

� K�� =-:σi ∈ Σ

�P=�Iu = β1.β2...βm

� K�� =-:βi ∈ Σ

� � K <>N C G < KP:-N �Q:�K IML ��cK I E N �&?A=

u=�I

v=-G�I2<>= I N I

u.v == σ1.σ2...σn.β1.β2...βm� y

687 Z$LHZIV.;IGW> ε ;IT<>�L 7 Z$LBZ$Vl;$GW>¡GF;$\d>@ES;�C 9 \FEvLHJ"= 9 GF=$JM>@ZIGKJM>@? 9 G%* u.ε = ε.u = u È� j � amd Pud�\ca w��� � K�B;BO=�<4<>=%< K�� �lK �A=�G��AC�� � K < BgM K�"�=�I Σ IMN � I�G�N ��G � =��(G�=JI%"�<>= ?A= Σ∗ � �

p � � =JI�BD<>=� N E4I�< � K < BgM K�"�=�I

Σ = {a,b} � � = < K�� �lK �A= L ?AL � �OE G�� C < � K < BgM K�"�=�I Σ =-G�I2<>= < K�� �lK �A= E�� � �OE�I =�<� �S=L = {ε,a,b,ab,ba,aab,anb,bma,anbm...} � y

� «_¬[«­¬ �˶��´ �8·dµ~¸�¹k²Í²D¼h´ �~°�² � ��¹ � � ��°�²� >QJMGn>UN 9 GFGFZ$T3NF;I\dmeL�JMGFiWJOif;IT L1

;4> L2TS\FE3\FGaJOLBCFPKJ@x;I> Σ |ÚG 9 \FTUJOLHL 9 GFT�?BGn>SE 9 NF\F?BES;�Ãn\F;ILHÃn\F;$T9 C'ZIE@JM>S? 9 GXT[A 9 GFNKJOVl;$GW>@JOLH;ITvTS\FE¡LH;ITvL�JOGXiWJOif;IT$È

� j � amd Pud�\ca w��� � � �OE N � � L1 ∪ L2 = {s ∈ Σ∗ | s ∈ L1

N �s ∈ L2}

�� � � �OIM=�C G�=-:�I E N � � L1 ∩ L2 = {s ∈ Σ∗ | s ∈ L1

=�Is ∈ L2}

�� � 7 N �Q:�K I L��cK I E N � �

L1L2 = {s = s1s2 ∈ Σ∗ | s1 ∈ L1

=�Is2 ∈ L2}

�Ln = {s = s1s2...sn ∈ Σ∗ | si ∈ L

BON �AC I N �AIJE∈ {1...n}}

�� � I N E4<>= � L∗ =

n≥0Ln

��

� j � amd Pud�\ca w�W��� � < K�� �lK �A=�C L���� < E =�C

LG��AC ����K < BgM K�"�=�I

Σ=-G�I2?AL � �OE�C-L-:��AC G�E�� =JI =��OI2?A=%< K ILK��OE �C =�G�� E�� K��OIM= �

� � {ε} =-G�I�� � < K�� �lK �A=%C-L����A< E =�C�G��AC Σ�

� � �SE σ ∈ ΣK <>N C G

{σ}=-G�I�� � < K�� �lK �A=�C L���� < E =�C�G��AC

σ�

� � �SE L =-G�I���� < K�� �lK �A=�C L���� < E =�C�G��AC Σ K <>N C-GLn=�I

L∗ G�N �OI2?A=-G�< K�� �lK �A=-G�C-L����A< E =�C G�G��AC Σ �� � �SE L1

=�IL2

G�N �OIJ?A=-G@< K�� �lK �A=-G C L���� < E =�C G G�� C��K <>N C G

L1 ∪ L2

�L1 ∩ L2

=�IL1.L2

G�N �OI?A=-G < K�� �lK �A=-G%C L����A< E =�C-G � �

sg;IT5L�JMGFiWJOif;IT�ESZIif\FLH?B;$E<TeT<;.NXZ$=$E<?BrO;$GW>5>SESÁ$TeA JO=$?BLH;IV.;IGn>�CFJOE�\FGF;p; mdCFES;ITSTS? 9 G�E<Z$if\XLH?HÁIES;"N 9 GW>r 9 ?B=$?�L�J]NXZIÓKGF?R>@? 9 G�È

Page 163: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�K� �(� ����� ��� �'� $ ���R!�� �� �$ ~ � ~

� j � aid Pud�\ca weW W� =-G =�� BDC =-G-G�E N �(G C L����A< E �C =-G � � � � � � G��AC � � K < BgM K�"�=�I

ΣG�N �OI ?AL � �OE =-G C L-:��AC-G�E�� =JI =��OIR?A=&< K

ILK��OE �C =�G��AE�� K��OIM= �� � ε=-G�I ���Q= � � � � � � E2?AL-:�CFE4I2<>= < K�� �lK �A= {ε} �

� � �SE σ ∈ ΣK <>N C-G

σ=-G�I ���Q= � � � � � � E2?AL-:�CFE4I {σ} �

� � �SE w =-G�I�� �Q= � � � � � �AE2?AL-:�C�E4I�<>= < K�� �lK �A= L � K <>N C G w∗ =-G�I � �Q= � � � � ?AL-:�CFE�� K��OI L∗ �� � �SE w =-G�I�� �Q= � � � � � �AE2?AL-:�C�E4I�<>= < K�� �lK �A= L � K <>N C G w+

=-G�I�� �Q= � � � � ?AL-:�CFE�� K��OI L+�

� �SE w1

=�Iw2

G�N �OI�?A=-G � � � � � �AE ?AL-:�C�E�� =��OI C =-GMBO=-:�I E�� =JI =��OI�<>=-G@< K�� �lK �A=-G L1

=�IL2

� K <>N C Gw1/w2

=-G�I � �Q= � � � � ?AL-:�CFE�� K��OI L1.L2

�� � �SE w1

=�Iw2

G�N �OI�?A=-G � � � � � �AE ?AL-:�C�E�� =��OI C =-GMBO=-:�I E�� =JI =��OI�<>=-G@< K�� �lK �A=-G L1

=�IL2

� K <>N C Gw1.w2

=-G�I����Q= � � � � ?AL-:�CFE�� K��OI L ∪ L1� �

� j � aid Pud�\ca weW�}� N E4I

s� �Q=T:NM K����Q="?AL � �OE =HG�� C%��� K < BgM K�"�=�I

Σ � � �Q= :NM K����Q= v=-G�I�? E4I =%BDC L � � = � :�<>N�G ?A=

sG � E4<

=��VE>G�IM=����Q= :NM K����Q=w ∈ Σ∗ IM=�<4<>= � �S= s = vw

� =�I'N � �QN IM= K <>N C Gs = v � �

p � � =JI�BD<>=��K CH=�� =JI�BD<>=��< � =��(G�=JI%"�<>= ?A=-G�BDC L � � =-G � :�<>N�G ?A= < K :NM K����Q=

s = αβ=-G�I �

{ε,α,αβ} � y

sg;I><>@;�NFZ4ÓKGF?B>S? 9 G�C;$\X> $4>@ES;�Z4>@;$GXNF\F;eTS\FE¡LH;ITvL�JOGXiWJOif;IT$È� j � aid Pud�\ca weW�y� =�BDC L � � = � :�<>N�G�?��T< K�� �lK �A=

L� �QN IML

L=-G�I�< � =��(G�=JI%"�<>=�?A=�IMN ��G�<>=-G�BDC L � � =-G � :�<>N�G�?A=-G :NM K����Q=-G�?A=

L � ��K CH=�� =JI�BD<>=��<>=�BDC L � � = � :�<>N�G ?�� < K�� �lK �A= L = {ε,αβ}=-G�IJ?AN � �QL B K C

L = {ε,α,αβ} � �

Page 164: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;
Page 165: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � �

� ��� ���»� �

� � ����� � � � � � �

sg;I><>@;¡JOGXGF;4md;¡?HGW>@E 9 NX\F?B>,TS\F=I=$?BGF=I>S;$Vl;$GW>�LH;[LB;$VlV.;zN 7 �kE<NF;$G";I>�Ãn\F;ILHÃn\F;IT 9 C'ZIE@JM>S? 9 GFT,TS\FE8NX;$TLHJOGFiWJOiO;$T¡ESZIif\FLH?B;$E<T$Èsg;$ThESZITS\FLR>QJM>SThT 9 GW>hA 9 GXNKJOVl;$GW>QJO\Dm�ÃD\FJOGW>�Â.LHJ)=YJOLB=$\FLHJ��F?HLB?B>SZ`NF;$T�L�JMGFiWJOif;ITV.JOESÃn\FZIT�;I>�LHJËESZ$T 9 LH\d>@? 9 G NF;$T�T<bDTc>@Á$Vl;$T�N 7 Z$Ãn\KJM>S? 9 GXT$È¡� 9 \FE�NF;oCFLH\XT�JOV.CXLH;$TpNFZI>@JO?HLBT��gG 9 \FTT<\FififZIE 9 GFT � � 9 G � Ñ � È

U�ZXZ]U� weWXo�U�ZXZ U ^� � ^`U�aV{ I K��OI ?AN � �QL-G@?A=���� < K�� �lK �A=-G C L����A< E =�C G A

=�IB�

� � � � L#� � K I E N � X = AX + BK;?tI =�I�I N ���WN � C G ���Q=�G�N < � I E N �&?AN � �QL-= B K C

X = A∗B�

� � 7 =�I IM=%G�N < � I E N � =-G�I�� �OE�� �O=%G�E =�IG�=�� <>=JI =��OI�G�E ε 6∈ A �

p � � =JI�BD<>=� N E4I2< � K�� IMN ILK I =

G = (Q, Σ, δ, q0, Qm)?A= < K � ��� C =�� � � �hK�� =-: �

� Q = {q0, q1, q2}�

� Σ = {a, b, c}�

δ(q0, a) = q1

δ(q1, b) = q2

δ(q2, c) = q0

� Qm = {q0}

� N ��G K <4<>N �(G :�K <>:��A<>=�C�<>=%< K�� �lK �A= ILK C$� �SL%?A=%< � K��AI N ILK IM=G � � K�B;BO=�<>N �(G � �O=H:-=�< K�� �lK �A= =-G�I

�WN C I L�B K C < � =��(G�=JI%"�<>= ?A=-G@G�L#� �S=��Q:-=-G ?�� L�� L��Q=JI =��OI G'BO=�C I =�I I K��OI�?�� K I I =�E��D? C = ��� L�I K I ILK C$� �SL?A=MB �AE>G < � L�I K I E��OE4I E�K < ��� N CJI =�<4<>=JI =��OI �

Lm(G) := {s ∈ Σ∗ | δ(q0, s) ∈ Qm}

Page 166: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � ��������������� ����'��� ) � �� �)��2�

ca

b

q

q

0

1q 2

0 143�5 � È � 6 ���AIMN ILK I =K?�� BDC N�:-L ?AL G

� =J< K�� �lK �A=ILK C#� �OL�?A=G�Lm(G)

�ABO=��AI �I C-=�:�K <>:��A<>L2G�=�<>N � <>=�G�9�G�I JI =�?�� L#� �TK I E N �(G�G�� E�� K��OI �

q0 = aq1 + ε

q1 = bq2

q2 = cq0

� � C =JILK C$� �S= � �S=H<>= I N I'��E ?A= ε=-G�I�K �WN � IML � < K BDC =JI E �C =RL#� � K I E N � :�K CH< � L�I K I

q0

=-G�I�<>=KG�=��A<L�I K IhILK C#� �OL �

� � C =JI�BD< K��uK��OI q1

B K Cbq2

B �AE>Gq2

B K Ccq0

?lK��(G%< � =�� BDC-=-G-G�E N � ?A=q0

���QN �;GHN�"�IM=��QN �(G �

q0 = abcq0 + ε + � È � ,7 =�I I =%L#� � K I E N � =-G�I�L#� �AE�� K <>=��OI = �

X = AX +BK�� =-:

X = q0

�A = abc

=�IB = ε � � �AE>G � �S=

ε 6∈ A� E4< =��VE>G�IM='���Q=�=�I � �Q= G�=��A<>=JG�N < �AI E N � ?A='< � L#� � K I E N � � � � � IM=�<4<>=�� �S= q0 = A∗B = (abc)∗ε =

(abc)∗ � GHN �Q: <>= < K�� �lK �A= ILK C$� �OLK?A= < � K��AI N ILK IM= G� K�� I

(abc)∗ � y

687 ;4mdCFES;ITST<? 9 G N 7 \FGX;�T 9 LH\X>S? 9 G�N 7 \FG T<bDTc>@Á$Vl;�N 7 ZIÃD\FJM>@? 9 GFTpC;$\d> $4>@ES; TS?BV.CFLB?BÓKZI;�;$G = 9 GFT<?R^NFZ$ESJOGW>]LH;IT 9 C'ZIE@JM>S? 9 GFT�T<\FE5LB;$T�L�JOGXiWJOif;ITeT<\F?BrMJOGW>S;$T$È � >QJOGW>5N 9 GFGFZl\FGË;IGFTS;IV �FLB;.NF;IT5LHJOGFiWJOiO;$TESZ$iO\FLH?B;$EST L � M ;I> N �F>@;$LBT¡ÃD\X;e=QPFJO=$\FG N 7 ;$GW>@E<;a;I\dm�;$Tc>�\FG T 9 \FT~^�;$GXTS;$V �FLH;eNF; Σ∗ �KJOL 9 EST *

� È Lε = εL = L � L + L = L � L + M = M + L &

ÑdÈ (L + M) + N = L + (M + N) &� È (LM)N = L(MN) � (L + M)N = LN + MN &� È L∗ = ε + LL∗ � L∗L∗ = L∗ � (L∗)∗ = L∗ � LL∗ = L∗L &

ÏdÈ (L∗ + M∗)∗ = (L∗M∗)∗ = (L∗M∗)L∗ = (L + M)∗ &

�XÈ (LM)∗L = L(ML)∗ � (L∗M)∗ = ε + (L + M)∗M È

Page 167: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� �WÏ

� ��� ���»� �

� � ���� ���� � � � � � � � �

sg;I><>@;¡JOGXGF;4md;¡CFESZITS;IGn>S;¡L 7 JOLHi 9 ES?B>SPFVl;8NF; � \FVpJME ��� \XV � � � N 9 Gn>�L 7�9 ���<;$=4>@?RAÒ;$T<>�NX;v=YJOLB=$\FLB;$EtLB;LHJOGFiWJOiO;vTS\FCFE $$Vl;h= 9 GW>@E��fL�J��XLH;OÈWsg;kL�JMGFiWJOif;v;IT<>1LH;¡CFLB\FT1iOE@JOGFNlL�JMGFiWJOif;v= 9 GW>@E��fL�J��XLH;vT@J�>@?HTcA JO?HTSJOGW>LB;$Tv= 9 Gn>SE@JO?BGW>@;$T¡?BV.C 9 TSZI;$TvCKJME�LB;�=YJOPX?H;$EvNX;$T¡=QPKJOE<if;$TIÈ

f��c\ � d P �mZ U ^iU��HnmZ QT�� >QJOGW>gN 9 GFGFZh\FGpV 9 NFÁ$LB;hNF\.CFE 9 =$ZINFZ G = (Q, Σ, δ, q0, Qm) JO\FÃn\F;$L';$Tc>vJOT<T 9 =$?HZ�\FGjV 9 NFÁ$LB;NF;IT¡= 9 GW>@ESJO?HGW>S;$T¡NF;�A 9 GF=4>@? 9 GFGF;$Vl;$GW> S = (X, Σ, ξ, x0, Xm) *

O P QTSVUXW�Y s[JOLB=$\FL�NX\ CFE 9 NX\F?B>¡TcbdGX=QPFE 9 GX;5NF; G ;I> S È 687 JM\X> 9 V.JM>S;eE<Z$T<\FLB>@JOGW> (S × G) JONFVl;I>= 9 VlV.;`LHJOGFiWJMif;`ifZIGFZ$E<ZaLB;�L�JOGFifJOif; L(S/G) := L(S) ∩ L(G) ÈO P QTSVU~}�Y ykZ4>@;IESVl?HGKJM>S? 9 GlNF;`L 7 ;IGFTS;IV �FLB; D NF;IT[ZI>@JM>@T (q, x) NF;kL 7 JO\X> 9 VpJM>S; S ×G rOZ$ES?RÓÒJOGW>�*

� Èv{�Lg;4md?BT<>@;p\FGËZIrOZ$GF;IV.;IGW>"?HGF= 9 GW>@E��OL�J��FLB; σ ∈ Σuc>@;ILgÃn\F; δ(q, σ) ;$Tc>)NFZ4ÓKGF?H;pNKJOGFTL 7 JO\X> 9 VpJM>S; G &

ÑDÈ ξ(x, σ) G 7 ; mX?BT<>S;�CKJOT5NFJOGFT)L 7 JO\X> 9 V.JM>@; SE � = � L 7�9 =I=$\FE<ES;IGF=$;�NF;pL 7 ZIrfZIGF;$Vl;$GW> σ ;IT<>

G 9 G JO\X> 9 ES?HT<Z$;�NF;ICF\F?BT�L 7 Z4>QJM> x NF;�L�J]T<C'ZI=$?BÓF=YJM>S? 9 G S Èsg;4>S>S; Z4>QJOC; C;$E<V.;4> ��JOCXESÁ$T.JYr 9 ?BE"ifZ$GFZIESZ�L 7 ;$T<CKJO=$;�N 7 ZI>@JM>@T.NF; L 7 JM\X> 9 V.JM>S; S × G �8NF;=$JOLH=I\FLH;IE�L 7 ;$GFT<;$V �XLH; D ÈUsg;l=YJOLB=$\FLt= 9 GFT<?HTc>@;.Â�Ãn\KJOLB?BÓK;IE�\FG�;$GFT<;$V �FLB;"N 7 Z4>QJM>ST��3NF?R>�ZI>QJ�>@T?BGW>@;$E<NF?B>ST��MC 9 \XE�LH;ITSÃn\F;$LBT 9 G"C';I\X>8>@E 9 \XrO;$E8\FG"ZIrOZ$GF;IV.;IGW>g?BGF= 9 GW>SE��fLHJ��FLH; σ ∈ Σuc

C 9 TST<? �FLB;NX;$CF\F?BTvL 7 ZI>@JM> q NF\�CFE 9 =$ZINFZe;I>¡G 9 G JO\X> 9 ES?BTSZ�NKJMGFT¡L�J)TSCZ$=I?BÓK=$JM>@? 9 G�JOTST 9 =I?HZI;OÈ

O P QTSVU~y�Y ykZ4>@;IESVl?HGKJM>S? 9 G�NX;eL 7 ;IGFTS;IV �FLB; D′ NF;$T�ZI>@JM>@T (q, x) NF; S × G Ãn\F?3GF;�TSJM>@?BT<A 9 GW>¡CKJOTD ;4>aC 9 \FE�LB;$TSÃn\F;ILHT�?HLt;4md?HTc>@;"\FGF;lTSZIÃD\X;$GF=I;pN 7 ZIrOZ$GF;IV.;IGn>ST]?HGX= 9 GW>@E��fL�J �FLH;IT s ∈ Σ∗

ucÃn\F?

= 9 GFNF\X?B>�Â)\FG�ZI>QJ�>¡NF; D Èsg;4>S>S;lZ4>QJOC;)C;$ESVl;I>���JOCFE<Á$T�JYr 9 ?HE�TS\XCFCFES?BV.Za> 9 \FT�LB;$T�ZI>@JM>@T�?BGW>@;$E<NF?B>ST���NX;)=YJOLB=$\FLB;$E`L 7 ;IGd^T<;$V �XLH;�NF;IThZ4>QJM>ST D′ �KNF?R>¡L 7 ;$GFT<;$V �XLH;�NF;IThZ4>QJM>ST[A JO? �FLB;$Vl;$GW>v?BGn>S;$E<NF?B>ST$È

O P QTSVU � Y6 wd\FCFCFE<;$T<TS? 9 GjNF;$CX\F?HTzL 7 JO\X> 9 VpJ�>@; S ×G NF;h> 9 \FTzLH;$TzZI>@JM>@TzNF; D ;4>gNF; D′ +æJO?BGFTS?ÒÃn\F;

Page 168: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � ���������%� � � ��� � �' '������P� )���� ![� ��

LH;IT[>@E@JMGFTS?R>@? 9 GFT¡JOTST 9 =I?HZI;$T�Â)=$;$T�ZI>@JM>@T , &6 wd\FCFCXES;$T<TS? 9 GqNF;$ThZI>@JM>@T (q,x) C 9 \FEkLB;$TSÃn\F;ILHTh?HL3G 7 ;4md?HTc>@;5CFJOTkNF;a=QPF;$Vl?HG�JO=$=IZ$NKJOGW>�Â

(q, x) NF;ICF\F?BT�L 7 Z4>QJM>¡?BGF?B>S?�JOL (q0, x0)È

6 ;|LHJOGFiWJOiO;�NX;|L 7 JO\d> 9 V.JM>@;oJM?HGFT<? 9 �X>@;IGn\�;$Tc>�LB;|LHJOGFiWJOiO;qTS\FCFE $$Vl;�= 9 GW>@E��OL�J��FLB;��[G 9 >@ZSupC(K) È

p � � =JI�BD<>=� � �"?�� E4<4< ��G�I C =�C<>=-G

4L�I K�BO=-G ?�� :�K <>:�� <�?��%G���BDC� JI =�:-N �OI C# < K�"�<>=�� �QN �;G�:-N �(G�E ?AL�C N �(G< � =�� =JI�BD<>=

:�< K G-G�E�� �S=@?A=-GK?A=���� ILKA:NMAE��Q=-G E ?A=��OI E�� �O=-GH=�I ?�� ���PG�IMN�:��"E��OI =�C I L ? E�K E4C =S

� � ���AC =R7 � � � �� = I N�?��<>= � <>N�"NK <�?AL-:�C�E�� K��OI2<>= :-N I�BON CFI =JI =��OI ?A=K< KP:NM K����Q=K?A='BDC N�?��S:�I E N � =-G�IJC =MBDC L-G�=��OI L

B K C < � K��AI N ILK IM=T?A=T< K � ���AC-= 7 � � � � < =-G�I@:-N �(G�I C � E4I � B K CFI E4CT?A=R< K :-N I�BON�G�E4I E N � B K C�K <4< �<>= ?A=-G?A=�� � K��AI N ILK IM=-GK?A=-G ILKA:NMAE��Q=-G

1=�I

2 �� =-G :-N �OI C�K E��OIM=-G@E I�BON�G�L-=-G G�N �OI C =�< K I E�� =-G � < K :�K�B KA:�E4IMLH?��PG�IMN�:�� � 7 =�I IM= ?A=�C �OE �C = =-G�I2G���B �

BON�G�L-='< E I E4I L-= � � �Q=JG�=�� <>=�BDE -:-= � ��= I N�?��<>=�?A=�:-=�I I =�:-N �OI C�K E��OI =�=-G�I�C =MBDC L-G�=��OI L�B K C'< � K�� IMN ILK I =?A= < K � ��� C =R7 � � �O PRQTSVU W�Y ��= BDC N�?�� E4I'G�9 �Q:NMAC N �Q=T?A=

G=�I

S�S × G

� ?AN � �Q="< � K��AIMN ILK I =T?A=R< K � ��� C = 7 � � �� �#L�I K I%?A=P:-=�I K��AIMN ILK I =P=-G�I�<>=@BDC N�?��AE4I@:�K CFI L-G�E =�� ?�� ���#L�I K I ?A= < K�ILKA:NMAE��Q=

1�%?A= < K

ILKA:NMAE��Q=2=�I ?��TG�I N�:��

S � ��=-G@L�I K I4G 0N �

1C =MBDC L-G�=��OI =��OI< � L�I K I ��E ?A=KN �HBD<>=�E�� ?��TG�IMN�:�� �

O PRQTSVU�}�Y GHL�I =�C I E��cK I E N � ?A= < � =��(G�=JI%"�<>=@?A=-GKL�I K I4G E��OI =�C ? E4I4GD �

� < =-G�I :�< K E4C � �O= δ(q1, f1)=-G�I2?AL � �OE =�?lK��(G�< � K�� IMN ILK I = ?��@BDC N�:-L ?AL

G� � ��� C =H7 � � �R=�I � �O=

ξ(x1, f1)� � =��VE>G�I =�B K G ?lK��(G2< � K��AI N ILK IM= ?A=2GMBOL-:�E � :�K I E N �

S� � ��� C =�7 � � � � GHN �Q:2< � =��(G�=JI%"�<>=

?A=-G L�I K I4G E��OIM=�C ? E4I4GH=-G�I{M1A21, M1M21}

�O PRQTSVU�y�Y GHL�I =�C I E��cK I E N � ?A= < � =��(G�=JI%"�<>=@?A=-GKL�I K I4G � K E "�<>=JI =��OI�E��OI =�C ? E4I4G

D′ �� �KG�=2C-L �WL�C�K��OI ��< � K��AI N ILK IM=J?A=2< K � ���AC-=�7 � � �D< � N�:-:��ACFC =��Q:-= ?A=�< � L�� L��Q=JI =��OISE��Q:-N �OI C# < K�"�<>=f2

�2B K CFI E4CJ?A=2< � L�I K IM1M21

:-N �D?��AE4ID< � K�� IMN ILK I =�� =�C G2< � L�I K I E��OIM=�C ? E4IM1A21

� GHN �Q:< � L�I K IM1M21

=-G�I � K E "�<>=JI =��OI�E��OIM=�C ? E4I �O PRQTSVUb� Y

� � � B;BDC =-G-G�E N � ?A=%< � K��AI N ILK IM= S ×G?A=%IMN ��G%<>=-G@L�I K I G ?A=

D=�I ?A=

D′ � K E��(G�E � �O=%<>=-GI C�K��(G�E4I E N �(G K G-G�N�:�E L-=-G � :-=-G L�I K I4G�� �

� � � B;BDC =-G-G�E N � ?A= I N �;G <>=-G L�I K I G (q,x)?A= < � K��AI N ILK IM=

S/G� �AE�G�N �OI E��cKA:-:-=-G-G�E "�<>=-G

?A=MB � E>G%< � L�I K I2E��OE4I E�K <�?A=%< � K�� IMN ILK I =K?A=%< K � ��� C ="7 � �G K��(GK< � =�� =JI�BD<>=���=�I K�BDC#-GLK�� N E4C"L�I K�"�< E4C@<>=-G

4L�I K�BO=-G�� �QN ��GRN�"�I =��QN �(GK< � K��AI N ILK IM="?A=H< K

� ��� C =R7 � � �� = < K�� �lK �A=@?A= < � K��AI N ILK IM=�K E��(G�E N�"�IM=�� � =-G�I

SupC(K) �

y

Page 169: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � �

Machine 2Machine 1 Sf fdd1 1 2 2

0 143�5 skÈ � 6 7mM K����Q=@?A= BDC N�?��S:�I E N �

d

d

dd f

f

f

f

1

1

1

1

22

2 2

q q

q q

0 1

2 3

02143�5 skÈçÑ 6 ���AI N ILK IM= GC =MBDC-L-G�=��OI K��OI2<>=H:-N I�BON CFI =JI =��OI ?�� G�9 G�I JI =

d

f

2

1

Σ − {d , f } Σ− {d , f }1 12 2

x x0 1

0 143�5 skÈ �K6 ��� IMN ILK I = S ?A=%GMBOL-:�E � :�K I E N � ?�� G�IMN�:��

A A 01 2 1 2A 0M 1 2A A 1 1

M2

A 1

1A M 02M

1 2M 0

1 2M M 1

1 2A M 1

d d

dd

d

1 1

1

22

d1

f

f

f

2

2f1

f

f2

1

2

0 143�5 skÈ �H6���� IMN ILK I = :-N CFC =-GMBON �D?lK��OIhK�� BDC N�?��AE4I ?A= G=�I

S

Page 170: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � � ���������%� � � ��� � �' '������P� )���� ![� ��

A A 01 2 1 2A 0M 1 2A A 1

1A M 02

1 2A M 1

1 2M M 0

��������������������

��������������������

������������

������������

d d

dd

d

1 1

1

22

d1

f

f

f

2

2f1

f

f2

1

2

11

M2

A 1

1 2M M 1

0 143�5 skÈãÏ 6 I K I4G E��OI =�C ? E4I4G {M1A21, M1M21}

A A 01 2 1 2A 0M 1 2A A 1

1A M 02M

1 2M 0

1 2A M 1

d

d

d

1

1

2

f

f

2

f1

f

1

2

f 2

0 143�5 skÈ � 6���� IMN ILK IM=�K G-G�N�:�E L K��P< K�� �lK �A= SupC(K)

Page 171: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�J �J� �� �' ������� � � � �

� ��������� ������ �����

� � � y +�f�M� x¡È���� ��� 1� �,u]È� ��� ������� ����È�� ����3 �Uu]È�� ������� ;4>5�aÈ�� � � ���A1 *�x�Î�;I=I>@?Rrf;

T<bDGW>@PF;ITS?HT 9 AhT��¡?R>@=QPF?BGFiq= 9 GW>SE 9 LBLH;$E<T5A 9 E)LB?HGF;$JOE5TcbdTc>@;IV È � C N�:-=-= ? E�� � G N � � � � � ���� * � � � � 6 � � ÑfÏ �XÑ �f�O� È

� �`y`x � � � ��������� *���\F?BNF;�N 7 � >S\FNF;aNF;$T�V 9 NF;IT�NX;aV.JOES=QPX;$T�;I>hN 7 JMESE $4>@TIÈ[��JOCFC 9 E<>¡>@;I=QPd^GF?HÃn\F; �K�`y`x��'� � � ��� � È

� �kGFN � � � sgPKJOESLB;$T�� �� ���! *k��;ICFES;ITS;$GW>@JM>@? 9 GoJOGFNqJMGKJOLBbDT<?HT 9 A�ES;$JO=I>S?Brf; �';IPKJYrd? 9 EST *�J.T<bDGd^=QPFE 9 G 9 \FT[JMCFC 9 JO=QP�È � � � ILKA:-G'� �A< I E :-N ���W=�C =��Q:-=K7 N I�B �AI K I E N �cK < � � � E��Q=-=�CFE�� �KE���S9 G�IM=JIKG � B;BD< E :�K I E N �(G��-7 � � � � �dCKJOif;IT � � 6 Ñ � � 6 ?HLHLB;�� � ��� �dÈ� � sv� ���M� �ÒESJOGF=I;$TS= 9 � � 1��� ��tJMTSÃn\KJOLB;#"%$ 1 �'&'& $ 1 �Ë;4>k�hLH;$T<T@JOGXNFE 9)( 1 � � *[wd\FC;$E<rD?BT 9 Ecb= 9 GW>@E 9 L 9 A�C';4>@ES?UGF;4>@T��KJMTS;$N 9 G�TS\ � 9 CX>S?HV.JOL3V 9 GX?B> 9 E�CXL�JO=I;$T$È � � � �OIM=�C��cK I E N �cK <*"N C���GNMON-B � � G E>G�:�C =�IM= � � =��OI �S9�G�I =JIKG �+* � G � ��� �gCKJOiO;$T � Ï 6 � � �vwXJMESNF?BGF?�J �{_>QJOLRb � � � ��� È

� � ;$E ���M� �tJOT<=YJOL, ����� � ��- * 7 N �OI CFE " �AI E N � K��&C-=-:-N ����C =JI =��OI�?A=-G G�9�G�I JI =-G�.�=��VE "�<>=-G ?A=BDC-N�?��O:�I E N � ILK�� � � KA:�I �AC�E �C = �xK��cK < 9�G�=�?A='< K@IMN <>L�C�K��Q:-=�=�I�C =-:-N � � ���AC�K I E N � ÈK�vPFÁITS;NF; N 9 =4> 9 ESJM> ��Æ�GF?BrO;$EST<?B>SZ NF;IT�wd=I?H;IGF=$;ITp;I>.�U;$=QPFG 9 L 9 if?B;$T"NF; 6 ?BLHLB; � �8NFZI=$;$V �FES;� ����� È

� � � � �M� / È, � �102� ;4>��|È,3 �54�6 �2��� * s 9 Gn>SE 9 L 9 A`NF?HT<=$ES;4>@;�;IrO;$GW>�T<bDTc>@;$VlTjV 9 NX;$LH;INJOT"PF?H;IE@JOE<=QPF?H=$JOLgTc>QJM>S;�VpJO=QPX?HGF;IT$È � � � �87 C�K��(GrKA:�I E N �(G N � ���AI N ILK I E : :-N �OI C N < ���� + � ÑV,�* � �f�V��6 � � � � � � � �V� È

� � ?HL �O�O� �,È' 1��� ���� * �&N�?AL�< E>GrK I E N � ?A=-G�I N�?A=-G ?A=�ILK C :NMO=H?lK��(GK<>=�BDE4<>N I K �A= ?�� ��� G�9 G �I JI =�K��AI N ILK I E>G�LJ?A= BDC-N�?��O:�I E N � Èf�vPFÁ$T<;1NX;zN 9 =4> 9 ESJM> � � = 9 LH;1sg;$GW>SE@JOLB;zNX;1}hJOGW>@;IT��AëZIrDES?B;$E � ���O� È

� �g9 ? � � � w'È9 � 1 �* � �OI L�� C�K I E N � ?A= < K �A=-G�I E N �#?A=-G I N�?A=-G ?A= ILK C :NMO=P?lK��(G <>=KBDE4<>N I K �A=?�� � � G�9�G�I JI =R?A=�BDC N�?��S:�I E N � È]�vPFÁITS;lNF;"N 9 =I> 9 E@JM>���ÆhGF?Rrf;IESTS?R>@Z)NF;IT]wD=$?H;IGF=$;IT�;I>�,;I=QPFG 9 L 9 if?H;IT¡NF; 6 ?BLHLB; � �FG 9 rO;$V �XES; � ��� � È

� s �,: +�f��� � ?H=QPF;IL;"%� 6 � �'& � � �U�tJOT<=YJOL� ����� � �<- � � ES?B=)= ��6 �'> �t�UÈ?"%$ �2� � � ��� � � ;I>

� �NF;$LBPKJA@n?HVCBD$ �5- � � *�wd\XC';IE<rD?HT<? 9 GoJOGXNqV 9 GX?B> 9 ES?HGXi 9 A�CXE 9 NF\F=I>S? 9 G�T<bDT<>S;$VlT$È� � � =-:-N �D?":-N ���W=�C-=��Q:-= N � ��K��cK �A=JI =��OI�K��D? 7 N �OI C N <�N � � C N�?��S:�I E N � K��D? � N � E>G �I E :-G � � 7 � � � ���ES;IG 9 �FLB;�� �<\X?HLHLB;I>vÑ �f�f� È

Page 172: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� �O� �J � ���� �' ����2�� �

� s[y�w �[� � � � ?H=QPX;$L "%� 6 � �'& � � ���|È�� � � 1� 02�S1� � ;4>��5È� ����� ��1� *���E 9 ifG 9 TS?HTkJOGFNqE<;4^= 9 rf;IE<b�;IrMJOLB\KJM>S? 9 Gq?BG �F;4md? �FLB;"VpJOGn\XA JM=I>@\XES?HGXi�T<bDT<>S;$VlT5TS\XC';IE<rD?HT<? 9 G�È � � � �OIM=�C ��cK I E N �cK <�:-N ���W=�C-=��Q:-=KN � � �D?��;G�I CFE�K < � � � E��Q=-=�CFE�� � K��D? � C N�?��S:�I E N ��~K��cK �A=JI =��OI� � � � � � ����\X;��;$=��'s[JOGFJONKJ �ÒJ 9 �X>hÑ �f� � È

� sgPKJ � Ï � �5È<"%$ ��1� ���<- * �JB;BDC N�:NMO= I � < I E � I N�?��<>=-GBON � C�< KR:-N I ILK��D?A=�=�I�< K@G�� C � =�E4<4< K��Q:-==�� IM=JI�BOG@C L-=�<�?A=-G G�9 G�I JI =-G � L�� L��Q=JI =��OI4GH? E>G�:�C =�I G È��vPFÁ$T<;)NF;5N 9 =4> 9 ESJM> �ÆhGX?R^rf;IESTS?R>@Ze�tJM\FL,wXJ��KJM>S?H;IE��X� 9 \FL 9 \FT<;��KNFZI=$;$V �FES; � ��� ÏDÈ

� sgPKJ �f�M� wXJOVl?HE "%$ � � 1�� * �JC N-BON�G�E4I E N �P?�� � �Q='G�I C��O:�I � C =%?A= :-N �OI C# <>=�B K C�G���BO=�C���E>G�E N � MAE L �C�K C-:NMAE�� �O= =�I@? E>G�I C�E " �OL-= ��K�B;BD< E :�K I E N � � < K�:-N�N C ? E��cK I E N � ÈÍ�vPFÁ$T<;�NF;�N 9 =I> 9 E@JM>��{�GFT<>S?B>S\X>�}kJM>S? 9 GFJOL�NF;ITkwD=$?H;IGF=$;ITh�hCFCFLB?HÃn\FZ$;IT¡NF; 6 b 9 G �Ñ �O�f� È

� s 6 ���M� sgPFES?BT<> 9 T��)È�" � �+� ���� �� � ;4>zwD>@ZICFPKJOGX;� � �1� ��- � ��� * � �OI C-N�?��O:�I E N � IMN�G E>G�:�C =�I =� � =��OI �S9�G�I =JIKG È � LB\1�1;$E¡�v=$JONF;$Vl?H=��8\ �XLH?HT<PF;$E<T�� � � ��� È� s 9 V � � � � ?H=QPX;$L�"%� 6 � ��& � �"* 7 N I ILK��D?A=@=�I�G��AC � =�E4<4< K��Q:-= ?A=-G�G�9�G�I JI =-G"� L�� L��Q=JI =��OI G? E>G�:�C =�I G :-N I�BD<>=�� =-G � K�B;BD< E :�K I E N � K����kK IM=�< E =�C GD.'=��VE "�<>=-G È��vPFÁITS;oNF;oN 9 =I> 9 E@JM>��ÆhGF?Rrf;IESTS?R>@Ze�tJM\FLUwXJ��KJ�>@?H;IE��F� 9 \FL 9 \FT<;��FNFZI=$;IV �FES; � ��� � È

� s[�h� � Ñ � �,È9"%$ �2� � � ��� � � �t�gÈ� � -�� � � � ;I>pw'È � ! ��� *Ë�8E 9 =$;ITST 9 C;$E@J�>@?HGXiqV 9 NF;V 9 GF?B> 9 ES?BGFi[CFE 9 =I;$TST *fw1�¡?B>@=QPX?HGFi 9 GFLB?HGF;�>SPF;�ES?BifPW>,= 9 GW>@E 9 LHLB;$E$È � � � � 7 C�K��(GrKA:�I E N �(GN � �S9�G�I =JIKG � � � �ÒÑ �f� ÑDÈ

� sgE<\ � � � y5È " � � �<-'-�� * � L�I MON�?AN <>N � E = ?A=K:-N �Q:-=MBDI E N � ?A=-G�G�9�G�I JI =-G@:-N I�BD<>=�� =-G"� L�� L��Q= �I =��OI�? E>G�:�C =�I4G �VK�B;BD< E :�K I E N ���T< K :-N �Q:-=MBDI E N � =�I � < K � K < E ?lK I E N � MAE L�C�K C-:NMAE>G�L-=K?A=< K :-N I ILK��D?A=@?A= :-=�<4< �A<>=-G�.�=��VE "�<>=-GK?A=�BDC N�?��O:�I E N � ?lK��(G < � E��D?���G�I CFE = ILK�� � � KA:�I � �CFE �C-= Èt�vPFÁ$T<;aNF;�N 9 =4> 9 ESJM> �XÆhGF?Rrf;$E<TS?R>@Z�NF;$T�wD=$?H;IGF=$;ITh;4>¡�,;I=QPFG 9 L 9 if?B;$TvNF; 6 ?HLBLH; � �AëZIrDES?B;$E � � � � È

� y`JMG �f�M� }kJM>SPKJOLB?H;#� ����3 ��� 6 � � * 7 N �OI CFE " � I E N � � < K �A=-G�I E N �8?A=-G I N�?A=-G ?A=-GKG�9�G�I JI =-GK�� IMN ILK I E>G�L-G ?A=HBDC N�?��O:�I E N � ÈË�vPXÁ$TS;�NF;�N 9 =I> 9 E@JM>��8ÆhGX?Brf;IEST<?B>@Z�NX;$T.wd=$?B;$GF=I;$Tl;I>�,;I=QPFG 9 L 9 if?BÃD\X;$T¡NF; 6 ?HLHLB;��d�KE@JOGF=I;��Ñ �O�f� È

� N � �V�M� �5È�NF;, � ����� 0���� * � L-:�K��OE>GJI =-GJ?A=JC =MBDCFE>G�=�?lK��(G <>=-G �S9 G�I JI =-G ?A=%7 N I ILK��D?A= � � L��Q=JI =��OI GVG E>G�:�C =�I4G Èf�vPFÁITS;gNX;1N 9 =I> 9 E@J�> �ÚÆ�GF?BrO;$EST<?B>SZg�,JO\FLdwXJ��KJ�>@?H;IE��Y� 9 \FL 9 \FT<;��TS;ICX>@;IV �FES; � ��� � È

� yk;IL ����� �gÈ�� ��� 6 � -'-�� * ���cK < 9�G�= I �A< I E � I N�?��<>=-G È��vPFÁITS;"NF;"N 9 =I> 9 E@JM>���Æ�GF?BrO;$E<TS?B>SZ)NF;$TTS=I?H;$GX=$;$T�;I>¡>S;$=QPFGF?BÃn\F;$T�NF; 6 ?HLHLB;�� � ����� È

� y 6 ����� �eÈ � � � �2� � ;I>�wD>@ZICFPKJOGF;�� � �1� � - � ��� * u`G�JOG 9 CX>S?HVl?HÊ$JM>@? 9 G CFE 9 �FLH;IV ?HGTS;IGFT 9 E1TS;ILH;$=4>@? 9 G�È � � � � � � 7 N ���W=�C =��Q:-=%N � GH=-:�E>G�E N � K��D? 7 N �OI C N < �nCKJOif;IT �����f� 6� ��� Ï �K�8P 9 ;IGF?Rm �F�hES?BÊ 9 GKJ �FNFZ$=I;$V �XES; � ����� È

� x8?HL �M�O� w'È2� 1����� � ���Q3 * ��� IMN ILK I K��'�_K�� ��� K �A=-G���K��D? �~KA:NMAE��Q=-G��� DN < � � È.}h; � /z9 E @S*�v=YJONX;$Vl?H=�� � ���M� È

Page 173: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�J �J� �� �' ������� � � � �

� �eJ�A �V�M� y`JOGF?B;$L ( � � � ! *,� 9 NXZ$LH?BT@JM>S? 9 Gl;I>1rfZIES?BÓF=YJM>S? 9 G.N 7 \XG�T<bDT<>SÁ$Vl;`V.ZI=YJM>SE 9 GX?HÃn\F;kCFJOET<bDGF=$=QPFJOE<>ST$È � � �&N�?AL�< E>GrK I E N � ?A=-G �S9 G�I JI =-G �'L�KA:�I E � G � ��� � � �8CFJOif;$T � Ï 6 � ��� �� ;I>SÊ���KE@JOGF=I;�� 9 =I> 9 �FES;eÑ �f�V� È

� �eJMT �f�M� � È ( � �+� � * � ?A=��OI E � :�K I E N � ?A=-G�G�9�G�I JI =-G@? 9 �cKtI E�� �O=-G��QN � < E��QL�K E4C =-G �[K�B;BDC N�:NMO=I � < I E � I N�?��<>= È��vPFÁ$T<;"NF;]N 9 =I> 9 E@JM>���sg;IGn>SES;)NF;"�¡;$=QPX;$ES=QPX;l;IGo�k\X> 9 VpJ�>@?HÃn\F;aNF;}kJOGF=4b �Ò{�GFTc>@?B>S\X>�}kJ�>@? 9 GKJOL�� 9 LBbn>S;$=QPFGF?BÃn\F;aNX; 6�9 E<E@JO?BGF;��XNFZ$=I;$V �FE<;aÑ �f�f� È

� � � � Ï � � ?�J 9 bD? ( � ��� ;I> 6 J �¡ES;IGF=$;[x¡È 3 � ��� ��� ��4 *Xyh?HT<>SES? �F\X>@;IN5NF?BTS=IES;I>S;g;4rf;$GW>8= 9 GW>@E 9 LT<>@E<\F=I>S\FES; �¡?R>@P = 9 GW>SE 9 LBLH;$E ?HGW>@;IE@JO=4>@? 9 GFT$È � � � I =�C�E :�K�� 7 N �OI C N < 7 N ���W=�C =��Q:-=� �H7�7 � �FCKJOif;IT � � Ï � 6A� � Ït� �Xwd;4>S>@LB;�� ��JOTSPX?HGFiO> 9 G � � ��� ÏdÈ

� �a� �V�M� � È ( � � �1� ;I>7�h;IE<rfZ�� �2� & $ ���� *zs 9 GW>@E��fLH;�NF;�T<bDTc>@Á$Vl;$TkÂlZ4rfZIGF;$Vl;$GW>@ThNF?HT~^=$ES;4>@T�PF?BZ$E@JMES=QPF?BÃD\X;OÈ � � � N�?AL�< E>GrK I E N � ?A=-G��S9�G�I JI =-G���L�KA:�I E � G � ��� � � �[CKJOiO;$T���O� 6 � ��� �K��;I>@Ê ��ÒESJOGF=I;�� 9 =I> 9 �FES;aÑ �O�V� È

� �e�z� �V�M� y`JYrd?BN ( ��� 4 �������O;YJOGD^~�KE@JOGXÄ 9 ?BT � !�- 1� ;I>��kLB;4md?�J ( ��� 1� *]� 9 NFÁ$LB;$T�NF\oCFE 9 ^=$Z$NXZe;4>vNF;�T<;$T¡TSCZ$=I?BÓK=$JM>@? 9 GFT[C 9 \FE[LHJ]T<bDGW>@PFÁITS;eNF;�L�Ja= 9 VlVpJMGFNF; 6 CXE 9 C 9 TS?R>@? 9 GN 7 \XGF;)NFZ$V.JOE<=QPF;)V 9 NF\FLHJO?HE<;OÈ � � �&N�?AL�< E>GrK I E N � ?A=-G �S9 G�I JI =-G �'L�KA:�I E � G � ��� � � �CKJOif;IT � Ï 6 � � �K� ;I>SÊ��Ò�KE@JOGX=$;�� 9 =I> 9 �FE<;eÑ �f�V� È

� �e� ��� � � �kTSV.J ( $ � � � ��� 1 �t}�?HNFPKJML ����3 ;I> � ?�J 9 LHJOG�� 1� *Ís 9 GF=$;ICX>@? 9 GÌNF\�TS\FC;$Ecrd? ^TS;$\XE 9 Cd>@?HV.JOL3rD?BrMJOGW>aÂ�L 7 JM?HNF;]NX;lLHJj>@PFZ 9 ES?B;)NF;$T�ESZIif? 9 GFT$È � � � N�?AL�< E>GrK I E N �8?A=-G�S9 G�I JI =-G �'L�KA:�I E � G � ��� � � �FCKJOiO;$T �W� 6 Ï � �F� 9 \FL 9 \FTS; �Ò�ÒESJOGF=I;��ÒÑ �O� � È

� �kJOE ����� y`JYrd?BN 3 ����� � *wD>QJ�>@;$=QPFJOE<>ST�*WJkrD?HT<\KJOLDA 9 ESV.JOLH?BTSV A 9 Et= 9 V.CFLB;4m5T<bDT<>S;$VlT$È � :�E =��Q:-=N �"7 N I�B � IM=�C � C-N � C�KtI I E�� � � + � ,F*ãÑ � � 6 Ñ �M� � � ��� � È

� �h;IE � Ñ � x¡È�3 � ��� �2�� 2��� * 7 N �OI C N < N � �@N �O< E��Q=�K CHG�9�G�I =JIKG � G�E�� � � � B �AI�� � � I B � I � ���WN C �ILK I E N � Èv�vPFÁITS;aNF;5N 9 =I> 9 E@J�> �yk;$C�È 9 A8sgPF;$Vl?H=$JOLUx8GFif?HGX;$;$E<?HGFip��; 9 E<if?�J"{�GFT<>S?B>S\X>9 At�U;$=QPXG 9 L 9 iOb � � � � ÑdÈ

� �h;4> � � � �"È�3 �<-���� ��� * �SI C �S:�I �AC-=-G ?A= ?AL-:�E>G�E N ��I �A< I E � �OE�� =�K���� BON � CP< K BD< K��OE � :�K I E N �?A="BDC N�?��O:�I E N � ��C N�" ��G�IM=-G-G�= =�IR:-NRMOL�C =��Q:-=P?A=-G ?AL-:�E>G�E N �(G È �vPFÁITS;�NF; N 9 =I> 9 E@JM>��ÆhGF?Rrf;$E<TS?R>@Ze�tJO\XLUwXJ��KJM>S?H;IE��F� 9 \FL 9 \FTS; �KNFZ$=I;$V �XES; � ��� �dÈ

� � � �O�O� 6 J �¡E<;$GF=I;axvÈ 3 � � � ��� � 4 ;4> � È �eÈ B � � 3 $ *8s 9 GW>SE 9 LBLH;$NpC';4>@ES?�GF;I>ST�*KJ5>S\X> 9 E<?�JOLTS\FEcrf;IbOÈ � =-:�I �AC = �QN IM=-GPE�� 7 N �OI C N <�K��D? � ���WN C ILK I E N � � :�E =��Q:-=-G � � ��� * � Ï � 6 � � � �� ���O� È

� �kÆ � �M� �XÈ23 � &'� � � - ;4>��XÈ � � ��6 ��� * � �OI C N�?��O:�I E N � I N K��AIMN ILK I KPI MO=-N CF9 ��< K�� ��� K �A=-GK��D? :-N I�B � I K I E N � Èt�vNFNF?HT<? 9 GD^ �|;$TSLRb��8\ �FLB?HT<PF?HGFils 9 V.CKJMifGWb �K{�GF=R+æÆkwd�%,�� � ��� � È

� � 9 G ����� �5È���� ��� �*3� V5\FLB>S?R^�LHJYbf;$E@ÐMV]\FLR>@? ^�LH;4rf;ILd= 9 GW>@E 9 L�JOE<=QPF?B>S;$=4>@\FE<;hA 9 Ez= 9 VlCF\X>S;$Ez?HGW>@; ^ifE@JM>S;$NjV.JOGn\XA JO=4>@\FE<?HGFiaT<bDT<>S;$VlT$È � � � � � � � �OIM=�C �cK I E N �cK < �S9 I�BON�G�E���I N � � �OI =�< �< E �A=��OI�7 N �OI C N < �F�kL �KJOGWb �K} / �KT<;$CX>S;$V �FE<; � ����� È

Page 174: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� � Ñ �J � ���� �' ����2�� �

�:� s[�z} � � � u`\FL�J��­N B ��6 �'& $���wXJOVl?HE "%$ � � 1�� � 6 JO\FES;IGW>�� 1!�-�� �'& ;4> � ES?H=�� 1��� *e�¡;$CFE<;4^TS;IGn>@JM>@? 9 G 9 A'J�ES;YJM=I>@?Rrf;vTcbdTc>@;IV.T?�¡?B>SP)NF?BÎ';$E<;$GW>�V 9 NF;ILHT$È � � � � � � � �OIM=�C �cK I E N �cK <7 N ���W=�C =��Q:-= N � �S9�G�IM=JIKG �~K��]K��D? 7�9�"�=�C �Q=�I E :-G � ��� 7 � � �kJOVlV.JOV.;4> �K�U\FGF?BTS?H; �Ñ �f� � È�ESZ4AëZ$ES;IGF=$;e�U��Ñ 6�� TS\FEhs[y`�vu��|È

�:� s[�z} �O�O� u`\FL�J��­N B ��6 �'& $ �,wXJOVl?HED"%$ � � 1�� � 6 JO\XES;$GW>#� 1!<-�� �'& ;I> � E<?H=�� 1��� *���;IGF;4^E@JOLB?HÊ$JM>@? 9 G 9 AzNF;$T`V5\FLB>S?R^�V 9 NF;$LB?HGFiFÈ � � � � I�M � � �H7 �S9 I�BON�G�E�� I N � � ���WN C ILK I E N �7 N �OI C N < � C-N�"�<>=JIKGJE�� ��K�� � � KA:�I �ACFE�� � � � � 7 � � � �MwXJOLBrMJON 9 Ec^ � JOPF?HJ � � E<Z$TS?BL �MÑ �f�M� È

�:� �a� � �M� �hJ�>@GF;ITSP BD� 6 �2� �WÔ`? �SJÚb ( ���Q3 ;4>¡wD>S;Irf;IG�{QÈ � �2� & ���*3�8ES;$NX?H=YJ�>@;$T[JOGFNpCXES;$NX?R^=YJM>S;1>SE@JOGFTcA 9 ESVl;$T3A 9 E,TS\FC;$Ecrd?BT 9 Ecbe= 9 GW>@E 9 L 9 AKNF?BTS=$E<;I>S;[;IrO;$GW>8NXbDGKJOVl?H=$JOLnT<bDT<>S;$VlT$È� � � � 7 C�K��(GrKA:�I E N �(G@N � ���AI N ILK I E :R7 N �OI C N < � � � *ãÑ � Ñ 6 Ñ ��� �DAëZ4rDES?H;IE � ���V� È

�:� PKJ �O�M� � �NF;$LBPKJA@n?HV BD$ � -�� � * 7 N �OI C# <>=H=�I':-N �OI C# <>=%G�I K�"�E4< E>GrK��OIJ?A=-G �S9�G�I JI =-G � � L ��Q=JI =��OI G�G E>G�:�C =�I G 7 =JI�BON C-=�< G � �JB;BD< E :�K I E N � K�� C =-:-N ����C-=JI =��OI�?A=-G ?AL � K E4<4< K��Q:-=-G?A=-GG�9 G�I JI =-GJ?A=�BDC N�?��S:�I E N � ÈO�vPXÁ$TS;zNF;8N 9 =I> 9 E@J�> �Y{�GFTc>@?R>@\X>U}hJM>@? 9 GKJOLMNF;$T,wd=I?H;$GX=$;$T�kCFCXLH?HÃn\FZI;$T¡NF; 6 b 9 G �Ñ �f�f� È

�:� � � � � � � È�B � � 3 $����XÈ�� ��3 � -'- ;I> 6 È�3 � ��� ��� ��4 *eu`G�>@PF;)= 9 V.CXLH;4md?R>�b 9 AzA 9 E��F?BNF;$GT<>@JM>@?B=�CFE 9 �XLH;$VlTgA 9 Ev= 9 GW>@E 9 LHLB;$N�VpJME @O;IN�ifE@JOCXPFT$È � � � � I�M � � � � 7 N ���W=�C =��Q:-=KN �GH=-:�E>G�E N �~K��D? 7 N �OI C N < �FCKJOiO;$T � Ï 6 � � � � E<?HifPW> 9 G �KÆeÈ � È � � ��� � È

�:� ��} �V��� u`\FLHÊ��_N B ��6 �'& $ � 6 JM\FES;IGn>#� 1!�-�� �'& ;I> � E<?H=�� 1��� * � \FLR>@? ^�V 9 NF;IL8JOCFCXE 9 JO=QP> 9 NF?HT<=$E<;I>@;e;IrO;$GW>@TkT<bDT<>S;$VlT *�JMCFCFLH?B=YJM>S? 9 G.> 9p9 C';IE@JM>S?HGFi)V 9 NX;eV.JOGKJMif;$Vl;$GW>YÈ � �� ILKA:-G ��� < I E :-N ���W=�C =��Q:-=R7 N I�B � I K I E N �cK < � � � E��Q=-=�CFE�� � E�� �S9�G�I =JIKG �JB;BD< E :�K I E N �(G�-7 � � � � �Kx8= 9 LH;asg;$GW>SE@JOLB;eNX;eLB?HLBLH;��dÑ �O�V� È�E<;IAë;$E<;$GF=I;]wXÑ�^~�[^ �f� ^ �V� � ÏdÈ

�:� ��} �O�M� u`\FL�J��­N B ��6 �'& $ � 6 JM\FES;IGn> � 1!�-�� �'& ;I> � E<?H=�� 1��� * �vPXZ 9 E<?H;�NF;�= 9 GW>@E��OLH;CKJOE�TS\XC';IE<rD?HT<? 9 G%*UJOCFCXE 9 =QPF;.V5\FLB>S?R^�V 9 NFÁ$LB;aNF;IT5V 9 NX;$T�NF;"A 9 GF=I>S? 9 GXGF;$Vl;$GW>YÈ � �7 N ���WL�C =��Q:-= � �OI =�C �cK I E N �cK <>= � C�K��Q:-N-BgMON �Q= ?�� ���AI N ILK I E�� �O= �-7 � � � � �,y 9 \XÊ��t�U\d^GF?HT<?H; �ÒÑ �f�O� È

�:� \FV � � � � BD� 6 �2� * � ��BO=�C���E>G�N CF9PG�9 �OI MO=-G�E>GTIM=-:NM��OE�� �S=-G �WN C ? E>G�:�C =�IM=P=�� =��OI�? 9 �cKtI E :�K <G�9 G�IM=JIKG È8�vPFÁITS;eNF;�N 9 =4> 9 ESJM> �FÆhGF?Rrf;$E<TS?R>@Z�NF\��,; mFJMT�� � ��� � È

�:6 ?HG �O�O� �gÈ � 1� *Dyk?HJOifG 9 TSJ��F?BLH?B>�b 9 AXNF?HT<=$ES;4>@;z;IrO;$GW>�TcbdTc>@;IV.TtJOGFNe?B>@TUJOCXCFLH?B=YJM>S? 9 G�È G E>G�:�C =�I =� � =��OI G 9 �cKtI E : �S9�G�IM=JIKG � 7 MO=-N C�9 K��D? �JB;BD< E :�K I E N �(G � � * � ����6 Ñ � Ñ � � ���O� È

�:6 � ����� y5È � 1�� ����� � � ;4>�w'È � � � � � * � JOT<?H=`CXE 9 �FLB;$VlTg?BG�T<>QJ �F?HLB?B>�blJOGFN�NF;ITS?BifG 9 AUT��¡?R><^=QPF;$N T<bDT<>S;$VlT$È � � � � 7 N �OI C N < �S9�G�I =JIKG���K �lK �E��Q= � � � +­ÏV,F*ãÏ � 6 �O� �Xu`=I> � ��� � È

�:6 � ����� �gÈ�� 1� ;I> � È�� \FESESJYb�� � � $ �26 *eyk;$=I;$GW>@ESJOLH?BÊ$;INqTS\FC;$Ecrd?BT 9 Ecb�= 9 GW>@E 9 L 9 AzNF?BTc^=$E<;I>@;�;4rf;$GW>kT<bDT<>S;$VlT$È � ���WN C ILK I E N � � :�E =��Q:-=-G �KÑfÏA* � Ñ � Ñ 6 � Ñ ��� � � ����� È

�:6 � ����� �gÈ � 1� ;I> � ÈD��\FESESJÚb�� � � $ ��6 *�u`G 9 �FTS;IE<rMJ��F?BLH?R>�b 9 A'NF?BTS=$E<;I>S;�;4rf;IGn>gT<bDT<>S;$VlT$È� ���WN C ILK I E N ��� :�E =��Q:-=-G � �O� * � � � 6 � � � � � � ��� È

Page 175: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�J �J� �� �' ������� � � � �

��6 � �f�M� �gÈ � 1� ;4> � ÈÒ� \FE<E@JYb�� � � $ �26 *�yh;$=$;IGW>@E@JMLH?HÊI;$N�TS\FC;$EcrD?HT 9 E<bj= 9 GW>@E 9 L�JOGFN�= 9 ^9 ESNF?BGKJM>S? 9 G 9 A�NF?HT<=$ES;4>@;);4rf;$GW>aT<bDT<>S;$VlT �¡?B>SPqCKJOE<>S?�JOL 9 �FT<;$E<rMJM>S? 9 GXT$È � � � � I C�K�� �GrKA:�I E N �(GHN � K��AIMN ILK I E :H:-N �OI C N < � �f� * � � ����6 � ÑfÑ � � � � �f� È

��6 b � �M� �gÈ � 4 * 7 N �OI CFE " � I E N �RB K C%< K G��AC � =�E4<4< K��Q:-=JBDC L ? E :�I E�� = E��D? E4C =-:�I = �R< � N-BDI E I E>GrK I E N �?A=%< K ILK E��OI =��cK��Q:-=�?lK��(G�<>=-G�G�9�G�I JI =-G2.�=��VE "�<>=-G�?A= BDC-N�?��O:�I E N �HILK�� � � KA:�I �ACFE �C = È�vPFÁ$T<;jNF;lN 9 =4> 9 ESJM> �UÆ�GF?BrO;$EST<?B>SZ.NF;IT)wd=I?H;IGF=$;IT5;I>a�U;$=QPFG 9 L 9 if?B;$TeNF; 6 ?BLHLB; � ��VpJM?� ����� È

� � � � Ñ � �hZ$=4> 9 ED� ���� 2��� � � � � * �S9 �OI�M -G�= ?A= <>N E>G"?A=HG��AC � =�E4<4< K��Q:-=�BON �AC <>=-G�BDC N�:-L ?AL-GE��D?���G�I CFE =�< G :-N I�BD<>=�� =-G È��vPFÁITS;jNX;jN 9 =I> 9 E@JM>��U{�GXT<>@?R>@\X>]}kJM>S? 9 GFJOL�� 9 LRbn>@;$=QPXGF?HÃn\F;NF;a��E<;$G 9 �XLH;��KÑ �f� ÑdÈ

� ��J�� � � � �|È � ��� � ��� � * � C N-BON�G�E4I E N � ?�� ���Q=�I L�I�MON�?A= =�IT?�� ��� N �AI E4< ?�� K E ?A=�� < K C = �:-N � � ��� C�K I E N � ?A=-G"G�9�G�I JI =-G K�� IMN ILK I E>G�L-G ?A= BDC N�?��S:�I E N � È��vPXÁ$TS;�NX;jN 9 =I> 9 E@JM>��ÆhGF?Rrf;$E<TS?R>@Z�NF;�ÔzJOLH;IGF=$?B;$GFGX;$T¡;I>�NF\ �kJO?BGKJO\X>c^cs[JOV �FESZITS?HT � � � � �XÈ

� � � ����� w'È � �'&'� �2��� ;4>`�)È 1� � $�� � ��* ��< �A= "�C�K ÈzsgPF;ILHTSJl}�; � /z9 E @ � � ����� È� ��� � Ñ � �aÈ5� ��� & $ �2�� ;I> � È ( � � �1� *�wd\FC;$Ecrd?BT 9 Ecb)= 9 Gn>SE 9 LÒCFE 9 �FLB;$VlT 9 A�PX?H;$ESJOES=QPX?H=YJML

ÓKGF?B>S;.Tc>QJM>S;.V.JO=QPF?BGF;$TIÈ � � � � I M � � � � 7 N ���W=�C =��Q:-=TN �]GH=-:�E>G�E N � K��D? 7 N �OI C N < �6 JMT¡Ô�;IiWJOT �ÒÆ`wd� �Ñ �f� ÑdÈ

� ��� ���M� ��È9� ��� � ;I> �XÈ ��1 � & $"*|yk?BTS=$E<;I>S;�= 9 GW>@E 9 L 9 AhT��¡?R>@=QPF;IN LB?HGF;$JOE5TcbdTc>@;IV.TIÈ � �

� 7�7 � ��� � � ����� È� } � � Ñ � � E<?H= � 1��� ;I>h�kLHJO?HG ��� - ���� *gs 9 GW>@ES? �F\X>S? 9 G ÂlLHJ"A 9 ESV.JOLH?BT@JM>S? 9 G.NF;aLHJlT<Z$=I\FES?R>@Z9 C'ZIE@JM>S? 9 GXGF;$LBLH;OÈ �'=�� �S=�?�� ���AI N ILK I E�� �O= =�I?A= � C N�?��O:�I E�� �O= �JB;BD< E�� �OL-=-G �DÏ +­ÑV,F*ãÏ ��6� � � � � � ÑdÈ

� } 9 \ ����� � 9 \FTc>QJOCFPFJ � ��� ����� � � - $"* � �VIM=��(G�E N �R?A= < K%I�MOL-N CFE = ?A=J< K�G���BO=�C ��E>G�E N � � < K�G��AC �� =�E4<4< K��Q:-=@=�I �"< KT:-N I ILK��D?A= ?A=-G�G�9 G�I JI =-G"�TL�� L��Q=JI =��OI G%? E>G�:�C =�I G �[K�B;BD< E :�K I E N �� < KRG�L-:��ACFE4I L N-BOL�C�K I E N � �Q=�<4<>= ?A=-G G�9�G�I JI =-GK?A=�BDC N�?��O:�I E N � È1�vPFÁ$T<;]NF;eN 9 =I> 9 E@JM>��{�GFT<>S?B>@\d>k}hJM>@? 9 GKJOL'NF;$Thwd=I?H;IGF=$;ITh�hCFCFLH?BÃn\FZ$;IT�NX; 6 b 9 G � �<\F?BLHLH;4> � � ��� È

� u�y¡� � � � � 9d9 NXb � 9 PFG�� 5 � 6 ;$VlV 9 GÍ� ?H=QPKJM;$L � 5 ;I>l�,JOG 9 T �XÈ�� ��- � � ���A1 ��*�wd\FC;$Ecrd? ^T 9 Ecbq= 9 GW>SE 9 L 9 A1C;I>@E<?8GF;I>ST��¡?B>@Po\FGX= 9 GW>@E 9 LHLHJ��FLB;ÚÐM\FG 9 �FTS;IE<rMJ��FLB;5>@ESJOGFT<?B>@? 9 GFTIÈ � �� I�M � � � � 7 N ���W=�C-=��Q:-=�N � GK=-:�E>G�E N � 7 N �OI C N < �-7mG"7 � �fCFJOif;$T �f�;� � 6D�f�;� � � ��9 �'; ��fJOC 9 G �KNFZ$=I;$V �XES; � ��� �dÈ

� �zs[� � Ñ � 6 JM\FES;IGn>)� 1!�-�� �'& �zwdJOV.?BE " $ � � 1�� ;4> 6 \F= �S316 � �2� * �kCFCFLB?H=$JM>@? 9 GÍNF;�LHJ>@PFZ 9 ES?B;]NF;)L�J.TS\FC;$Ecrd?BTS? 9 G%*�\FGo; mX;IV.CXLH;]NF;)= 9 GF=I;$CX>S? 9 GqNF;)CXE 9 ifESJOVlV.;ITkN 7 JOCF?æÈ� � 7 N ���WL�C =��Q:-= � �OIM=�C �cK I E N �cK <>= � C�K��Q:-N-BgMON �Q=H?�� ��� IMN ILK I E�� �S= �-7 � � � � ��}hJOGW>@;IT���ÒESJOGF=I;��Ñ �f� ÑdÈ

� �8���asv� � �M� �kLH; mXJOGFNFE<;�� $ 1� 1 �� - �Ú� �NF;IL 9 \KJMPF;$N � ��� ��� �Y�KE@JOGXÄ 9 ?BT (���� � � - ;I>3Ô`ZIE 9 GX?HÃn\F;" ������!�� � !���!�-�� 1��� *twnbdGW>SPFÁ$T<;eNX;`L�Je= 9 VlVpJMGFNF;kT<C'ZI=$?RÓKZ$;`;IG�ifE@J�Aë=$;I> *FJOCFCXLH?R^

Page 176: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� �M� �J � ���� �' ����2�� �

=YJM>S? 9 GlÂ�\FGlCFESZIPF;$GFT<;$\FE1CFGF;I\FVpJ�>@?HÃn\F;MÈ � ��� N�?AL�< E>GrK I E N � ?A=-G �S9 G�I JI =-G �'L�KA:�I E � G� � � � � �FCFJOif;$T�� � 6 � Ï �K��;I>@Ê ��ÒESJOGF=I;�� 9 =I> 9 �FES;aÑ �O�V� È

� �¡;$Ê � � � }h?BNKJOL � ��3 * 7 N �OI C�E " �AI E N � ��< K�G�L-:��AC�E4IML�N-BOL�C�K I E N � �Q=�<4<>=J?A=-GG�9�G�I JI =-G �TI E>G�=�=��N�=�� ��C = ?�� � �Q= G�I C �S:�I � C = ?A= G��AC � =�E4<4< K��Q:-= "NK G�L-= G��ACK<>=-G@C L-G�=�K����P?A= �'=�I CFE � " �W=�I G7 N �OI C N <>L-G Èz�vPFÁ$T<;5NF;eN 9 =I> 9 E@JM>��F{�GFTc>@?B>S\X>h}kJM>S? 9 GFJOL�NF;IT`wd=I?H;IGF=$;ITk�kCXCFLH?BÃD\XZ$;$T�NF;6 b 9 G � �SJMGnrD?B;$E � ��� �dÈ

� �h��� �V��� �O;YJOGD^c��JOE<= ;�����+� ��� ���hGn> 9 GF? 9 � �� �1� � ;I>�O;YJOGD^c��JOE<= 0 � � ��� *DwDbDGW>@PFÁITS;[N 7 \FGCFE 9 ifE@JOVlVl;gNF;¡= 9 V.V.JOGFNF;gN 7 \XGlTcbDT<>@ÁIV.;�L 9 if?HÃn\F;gÂ�CFJOE<>S?HE�NF;vL 7 ; mdCFES;ITSTS? 9 G.JOLHifZ ^�FES?BÃn\F;aNX;5TS;ITkT<C'ZI=$?BÓF=YJM>S? 9 GFTIÈ � � �&N�?AL�< E>GrK I E N �&?A=-G �S9�G�I JI =-G �'L�KA:�I E � G � � � � � �CKJOif;IT � ��6 �V� �K� ;4>@Ê���KE@JMGF=$; � 9 =4> 9 �FE<;eÑ �f�V� È

� � � � Ñ � �,;4>@;$E �XÈ��)È �26 �� �3�� ;I> � È���\FESESJÚb � � � $ ��6 *Íwd\FC;$EcrD?HTS? 9 G 9 AhNF?HT<=$ES;4>@;;IrO;$GW>[CFE 9 =I;$T<TS;$TIÈ � � � � G�I � � � � 7 N ���W=�C =��Q:-= � � GH=-:�E>G�E N � K��D?T7 N �OI C N <��-7mG 7 � �CKJOif;IT � ÑfÑ � 6 � ÑfÑ � �X}h; � /z9 E�@ �KNXZ$=$;IV �FE<; � ��� ÑdÈ

� � � ��� J � �,;4>@;$E �XÈD�)È �26 �� �3�� ;I> � ÈD� \FE<E@JYb � � � $ �26 *'� 9 NF\FLHJOE�Aë;$;IN �KJO= @]L 9 if?B=gA 9 ENF?HT<=$E<;I>@;l;IrO;$GW>aT<bDT<>S;$VlT$È � � � � �ON � C �cK <JN � 7 N �OI C N < K��D? N-BDI E I E>GrK I E N � �3ÑOÏ +­ÏV,F*� Ñ � Ñ 6 � Ñ � � � � ��� � È

� � � ��� � � �,;4>@;$E �XÈ1�"È �26 �� �3�� ;4> � È1� \XESE@JYb � � � $ �26 *±wd\XC';IE<rD?HT 9 E<b�= 9 Gn>SE 9 L 9 A=$LHJOTST 9 ANF?BTS=IES;I>S;v;IrO;$GW>gCXE 9 =$;$T<TS;IT$È � � � ���ON �AC��cK <DN � 7 N �OI C N <gK��D? N-BDI E I E>GrK I E N � �ÑfÏ *çÑ � � 6 Ñ �f� � � ����� È

� � � ���M� �,;4>@;$E �XÈF�)È ��6 �2 ��3�� ;4> � ÈX� \FE<E@JYb � � � $ ��6 *,s 9 GW>SE 9 L 9 A�NF?BTS=IES;I>S;4^_;Irf;IGW>T<bDT<>S;$VlT$È � � � � I C�K��(GrKA:�I E N � N ��K��AI N ILK I E : :-N �OI C N < � ��� + � ,F* � � 6 ��� � � ����� È� wXJMP ����� �5È�xvÈ � È � � $ � � ��� 1 * � �AC < K&G�� C � =�E4<4< K��Q:-= ?A=-GHK I =�< E =�C G .'=��VE "�<>=-G ÈÌ�vPFÁ$T<;�NF;N 9 =I> 9 E@JM>��KÆhGF?Rrf;IESTS?R>@Ze�tJM\FLUwXJ��KJ�>@?H;IE��F� 9 \FL 9 \FT<;�� 9 =I> 9 �FES; � � ��� È

� wXJME ���M� �tJM>SES?B= @ � �2��� 1 * �SI K�"�E4< E>GrK I E N � N-BDI E ILK <>= ?A=-G"G�9�G�I JI =-G � L�� L��Q=JI =��OI4G ? E>G�:�C =�I G� G�I C��O:�I � C = � =-:�IMN C�E =�<4<>= �[K�B;BD< E :�K I E N � �"< K G�L-:��AC�E4IML N-BOL�C�K I E N � �Q=�<4<>=%?A=-G�G�9�G�I JI =-G?A=�BDC-N�?��O:�I E N � È��vPFÁ$T<;`NF;hN 9 =4> 9 ESJM> �W{�GXT<>@?R>@\X>g}kJ�>@? 9 GKJOLKNF;ITvwd=I?H;$GX=$;$T1�kCFCXLH?HÃn\FZI;$TNF; 6 b 9 G � �SJMGnrD?B;$E � ����� È

� wFs � �M� �|È � 1� 0�� ;I> �XÈ " ��6 �����*,�,;IE<A 9 E<VpJMGF=$;`;4rMJOLH\KJ�>@? 9 G 9 A3NX;$NFT9�¡?R>@Pj= 9 G �K?B=I>ST[JOGFNT<bDGF=QPFE 9 GF?BÊYJM>S? 9 GFTvGX;I>¡NFE<?Brf;IG�NF;$= 9 V.C 9 T<?B>@? 9 Gp>S;$=QPFGF?BÃn\F;$TIÈ � � � I M � �OIM=�C �cK I E N �cK <*"N C ��GNMON-B�N � G E>G�:�C =�IM= � � =��OI �S9�G�I =JIKG �+* � G � ��� �tCKJOif;IT ��� � 6D� � � ��s[JOifLB?�JOE<?{_>QJOLRb �KJ 9 �X> � ��� � È

� � � �h� ��� Ñ � w'È � ����6 ��� �1 �¡��È� ��� � � �� ��� ��� � � � È;� � ������ � $ 16 ;4>o�|È�BD�+��� � 1 *� \FLR>@?R^_V 9 NFÁILH;�;I>�V5\FLB>S?R^�= 9 VlVpJOGXNF;�GF;$\XE 9 GKJM\dm C 9 \FE.L�J�= 9 GFNF\F?R>@;�Gn\FVlZ$E<?HÃn\F;NF;$TeT<bDTc>@Á$Vl;$T5G 9 Gd^_LH?HGXZYJO?BES;$Tk;I>aG 9 Gd^_T<>QJ�>@? 9 GFGKJO?BES;$TIÈ � � 7 N ���WL�C =��Q:-= � �OIM=�C �cK I E N���cK <>=-G � C�K��Q:-N-BgMON �Q=�?�� ���AIMN ILK I E�� �O= �-7 � � � � ��CKJOiO;$T ��� � 6 ��� � � � = 9 LH;¡sg;IGn>SE@JOLB;[NF;}kJOGW>S;$T��'Ñ �O� ÑdÈ

Page 177: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

�J �J� �� �' ������� � � � Ï

� � 9 i � Ñ � � �N 9 \FL � JMES?HV �hESV.JOGFN � � 3 � 4�! ��1 * � �AC � =�E4<4< K��Q:-=�=�I�? E�K ���QN�G�I E :�=��R< E ���Q='?lK��(G<>=-GLK IM=�< E =�C-G .'=��VE "�<>=-G ?A=K< � E��D?���G�I CFE =�ILK�� � � KA:�I � CFE �C = È`�vPFÁITS;)NF;)N 9 =I> 9 E@J�> �'ÆhGF? ^rf;$E<TS?R>@ZeNF;$Thwd=I?H;$GX=$;$T�;I>��U;$=QPFG 9 L 9 iO?H;$TvNX; 6 ?BLHLH; � �KG 9 rf;IV �FE<; � � � ÑdÈ

� � 9 T �f�M� ÆaÈ � ���+$ 16%1 - �+� *p�K;$;IN �KJO= @qL 9 if?B=5A 9 E�NF?BTS=$E<;I>S;.;4rf;$GW>5T<bDT<>S;$VlT �¡?R>@P|JOE��F?R>@ESJOE<b= 9 GW>@E 9 L�CKJM><>@;IESGFTIÈ � �OI =�C �cK I E N �cK < �ON � C �cK <�N �"7 N �OI C N < �ÒÏfÑ * � Ï ��6 � �M� � � ���f� È

� ÆhÊ$J � Ñ � �|È � ���26 *X�hG 9 Cd>@?HV.JOLWNF;$JONFL 9 = @�CFE<;IrO;$GW>@? 9 G)C 9 LH?H=4b`A 9 E �K;4md? �FLH;zVpJMGD\dA JO=I>S\FES?BGFiT<bDT<>S;$VlTg\FT<?HGFiaC';4>@ES?KGX;I>1V 9 NF;$LBT��¡?B>@PlES;IT 9 \XES=$;ITvJOGFN">@PX;�>SPF; 9 Ecb 9 A�E<;$if? 9 GFT$È � � �I =�C �cK I E N �cK < �ON �AC��cK <N � ��?�� =��Q:-= ? �~K�� � � KA:�I � CFE�� � 7 =-:NM��QN <>N � 9 � � � + � ,�* � � Ñ 6 Ñ ��� �Ñ �f� ÑdÈ

� Ô�� �V�M� Ô�;$G @�JM>@[email protected] ����� � 3 � �2� ;I> 6 J �¡E<;$GF=I;�x¡È?3 � � � ��� ��4 *�s 9D9 E<NF?HGKJ�>@?HGXi= 9 GF=I\FESE<;$GF=4b > 9 JYr 9 ?HN A 9 E��F?BNFNF;$G T<>@JM>@;ITp?HG = 9 GXNF?B>S? 9 GÌV 9 NF;ILHTIÈ � � � � � � � � �I =�C �cK I E N �cK < 7 N ���W=�C =��Q:-= N � � I =�C � E�� � 7 =-:NM��QN <>N � E =-G�K��D? � KA:�I N CF9 ���AIMN ILK I E N �� � 7 � � � �FCFJOif; � �ÒÑ �O�V� È� � 9 G � Ñ � � ÈF� \XESE@JYb � � � $ ��6 *3} 9 >S; 9 Gp= 9 GW>@E 9 L 9 A�NF?BTS=$E<;I>S;k;IrO;$GW>@;�TcbDT<>@;IV.TIÈtG 9 >@;$T1NF;= 9 \FE<T��UNF;$CFJOE<>S;$Vl;$GW> 9 Avx�LB;$=4>@ES?B=YJOLzJOGXNÍs 9 VlCF\X>S;$Eax�GXif?HGF;I;$E<?HGFi �UÆ�GF?BrO;$ES?BT<>�b 9 A� 9 E 9 GW> 9 � �<\X?HLHLB;I>vÑ �f� ÑdÈ

� �±��� � �O�M�½� È�� � ��3 � �XÈW�)È � $ 1 � -�� � �O��È � �2� $ ��6�� ;I>��eÈ13 � �2��3 *Òwd\FC;$Ecrd?BT 9 Ecb5= 9 GW>@E 9 L9 AÒNF?HTc>@E<? �F\X>S;$N]TcbDT<>@;IV.T *f= 9 G �K?H=4>�E<;$T 9 LH\X>S? 9 G�È G E>G�:�C =�I = � � =��OI G 9 �cKtI E : �S9�G�I =JIKG �7 MO=-N C�9 K��D? K�B;BD< E :�K I E N �(G � � � * � � � 6 � � � �KÑ �f�O� È� /�63� Ñ � w'È������|;4>¡wD>SZ$CFPKJMGF; � � � � ��- � ��� *�yk;I=$;$GW>SE@JOLB?HÊ$;INjTS\XC';IE<rD?HT 9 E<bl= 9 Gn>SE 9 L *DJ5GF; �JOES=QPF?R>@;I=I>@\XES;,�¡?B>SP.J�NXbDGKJMV.?B=vNF;$=I?HTS? 9 G)Aë\FTS? 9 G)ES\XLH;OÈ � � � I�M"E��OIM=�C �cK I E N �cK <?*"N C ���GNMON-B � � G E>G�:�C =�IM= � � =��OI �S9�G�IM=JIKG �+* � G � ��� ��CKJOiO;$T � � 6 � � �gwXJOESJOi 9 T<TS;��gx8Tc^CKJOifGF; � 9 =4> 9 �XES;aÑ �f� ÑDÈ

� : JOV ����� � E<?H= = ��6 ��> * ��C :NMAE4I =-:�I � C = ?A= � �AC � =�E4<4< K��Q:-= �F7 N I ILK��D?A=�BON �AC <>=-G �S9�G�I JI =-G � � L��Q=JI =��OI4G G E>G�:�C =�I4GT7 N I�BD<>=�� =-G È1�vPFÁ$T<;5NF;aN 9 =I> 9 E@JM>��ÒÆhGF?Rrf;$E<TS?R>@Za�tJO\FLtwXJ��FJ�^>@?H;IE��F� 9 \FL 9 \FT<;��KTS;ICX>@;IV �FE<; � � ��� È

� : � ���M� �|È�= � � � ��� ;I> �XÈ � �� �1& � *Fyh;$TS?BifG 9 AÒT �¡?B>S=QPF?HGFih= 9 GW>SE 9 LBLH;$E<TUA 9 EtT<bDTc>@;$VlT2�¡?R>@P=QPKJOGFif?BGFi�NXbDGKJMV.?B=$T$È � � � �WI�M 7 N ���W=�C =��Q:-= N � GK=-:�E>G�E N ��K��D?87 N �OI C N < �-7mG"7 � �CKJOif;ITkÑ � � � 6 Ñ � � � � � ����� È

� : y � ����� �|È'= � � � �2� � �XÈ � � � ��1 ;4>�Ô5È BD� 6 ��� *[s 9 GW>@?BGD\ 9 \FT�V 9 >S? 9 G�CXL�JOGFTvA 9 EvE<;�� 9 >@?B=T<bDT<>S;$VlT �¡?R>@P�=QPFJOGFif?BGFi�NXbDGKJOVl?H= �';IPKJYrd? 9 E$È � � �'N�"�N I E :�I N I E N � K��D? ILK��OE B � �< K I E N � �FCFJOif;$T � � � 6 � Ñ � � � ��� � È

� : P 9 ����� �kJ 9 =�$�� ��3 * 7 N �OI C N <'N � G E>G�:�C =�IM= � � =��OI �S9 G�IM=JIKG � GH=-:-=��OI C�K < E� = ? K��D?���E = �C�K C :NMAE :�K <�7 N �OI C N < Èz�vPXÁ$TS;aNF;�N 9 =I> 9 E@JM>��Òyk;$CX>$È 9 A�x8LB;$=I>SL­ÈÒx8GFifE<iFÈ �ÒÆhGF?Rrf;$E<TS?R>@Z�NF;� 9 E 9 GW> 9 �KNXZ$=$;IV �FE<; � � ��� È

� : P 9 � Ñ � �kJ 9 =�$�� ��3 * ��E =�C�K C :NMAE :�K <�:-N �OI C-N <�N �K? E>G�:�C =�I = =�� =��OI�G�9 G�IM=JIKG Èv�vPFÁ$T<;]NF;aN 9 = ^> 9 ESJM> �KÆ�GF?BrO;$E<TS?B>SZ�NF;�� 9 E 9 GW> 9 �Ks[JOGKJONKJ � � ��� ÑdÈ

Page 178: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

� : � �f��� �kJ 9 =�$�� ��3 ;I>�� È,� \FESESJYb � � � $ ��6 *�u�G�>@PF;l= 9 GFTS?BT<>@;IGF=Ib 9 AgPF?H;IE@JOE<=QPF?H=$JOLTS\FC;$EcrD?HTS? 9 G±?HG NF?BTS=IES;I>S;o;Irf;IGW>�TcbdTc>@;IV.TIÈ � � � � 7 C�K��(GrKA:�I E N �(G N � ��� IMN ILK I E :7 N �OI C N < � � Ï + � � ,�* � � ÑfÏ 6 � � �O� � � ���O� È

Page 179: Approche multi-modèle pour les Systèmes à Evènements ...theses.insa-lyon.fr/publication/2004ISAL0102/these.pdf · lolololol]lol]lolol]lol]lplol]lol Õ 1l 9lrq9lrv wxl inacb pu;

SiSm�u\_s��iU��pnif�Pud����p\x^ �f�U SV\cn`� f�U�q�� �`q P �Z]U�q�� O �|j�a`U�Z]U�a|Puq � d�q s �uU�PRq YQTSiS[f�d��s Q PRd�\ca� f�Q � U�q Pud�\cak^`U qLZ]\_^`U�q ^iU� \|aistPud�\cama`U�Z]U�a|P

� j�q niZ]j�Y �������������������� �"!��"��#$�"!��&%'��#'�)(��+*,!�*,-/.0�"�1�2-/���"��#3�)��� ��45�768������.9-/#:% ���;*,-<% ���&% �>=?-/#'(���.9-/# #'��*,��#3�

% ���A@<BDCFEHG�-/���"�I(�-/#3����.0J � ��.9-/#K�"�LJM�/�"�,��� �145�N��O'!�-/��.9�P% �L(�-/#3���"Q/49�I�M���1�"� �R�����<.9��.9-/#�ESG&-/���"�L-/J�T���(���.U=�����V%XWY��# ��.9("O .0�Z(������"�&��O'!�-/��.9�&�M���V% ���[*,!�(\��# .9��*,���V�2����*,��������#3�]4^WY!����'% �)% ���[*,-<% ���[% ��=?-/#'(���.9-/# #'��*,��#3��"-/� �;��#N63���"%'��#3�&% ���]*,-<% _�49���;% �)����.04049�`����.9�"-/# #M��J 49��E

G&-/�'�a� �"-/�R-��"-/#'�a� #'�]��� � �"-<("O'��b8%�.0�"�[*1� 40��.Uc^*,-$% _�49��b$d3� .<�R����*,���D% �[�"��� �"!��"��#$�"���D49���e@<BDCf!��8-/40�M��#3�%'��#'��%�.UgX!��"��#3�"�&*,-<% ����% �>=�-/#'(���.9-/# #'��*,��#$�)�M���;� #:��#'�"��*+J 49�A% �>*,-<% _�49�����".0*7� 49����% !�(���.0����#3�`("OM�/(�� #49�I(�-/*7�2-/���"��*,��#3�I%��h��i����"_�*,�P%'��#'�A� #h*,-<% �j% -/# #'!�Ea DWk��40�"����#M��#'(��N% �P*,-$% ���F�����7�/�"��� �"!��I�M���F� #*,!�(\��# .9��*,�e% �l�"� .0�$.3% �D4^WY!��8-/40� ��.9-/#1% ����� �"-<(�!�% !��Sd$� .��2����*,���m% �l% !��"����*7.0#'���H49����!������"�mnV�M������.0�H% ���"d$�'��49�� #poA���/(�(�-/�"% ��*,��#3�>qL=?-/#'(���.9-/# #'��4S�����Z�2����*7.9�\E

Bl#'��� .0�"�F#'-/�'�>*,-/#3���"-/#'�`4^W � # .9(�.0�"!,%��r��� �2�����<.9�"��� �>% �A*,-$% ��ESs[�����"�F� # .9(�.0�"!F�2����*,���>%XWk�/�"�"-<(�.9���>n("OM�/(�� #�% ���,*,-$% _�49���I% ���7� �"-$(�!�% !��,� #K*,-$% _�49�N� # .9d$�'�N% �t���2!�(�.UuM(\����.9-/#�Evs[-/*7*,�N49���,*,-$% _�49���,% ���� �"-$(�!�% !��wb (����]*,-$% _�49���;% �`���R!�(�.UuM(\����.9-/#t��-/#3�;�"-/� *7.9��n+� #�*,!�(\��# .9��*,�>% �`(�-/*7*+� ������.9-/#>xM.049�Z% -/.0�8��#3�y ���"�e�/(���.0�8!��H% ��� � .9�S� #+!������m�R����*,��������#$�H%XWk�zT{�'���"����45�Z#'-/� �8��4049�e%�i<#M��*7.9d3�'�v%��+� �"-<(�!�% !v�\�8��(D49���m�/(���.9-/#'�% �Z(�-/#3���"Q/49�)n`*,��#'���\E$C`��#'�e49�Z% ����# .9���V("OM��� .0���"��b$� #I�|� ��*7� 49�Z#'-/�'�e�R����*,���[% �Z*,-/#$���"���v4^Wk��� � 40.9(\��J .040.0�"!% �)#'-/���"�+��� � �"-<("O'��E

� \gPuq slf�j�q Yy`xzw �U>@PFZ 9 ES?B;.NF\�= 9 GW>@E��fLH;lCKJOEaTS\FC;$EcrD?HTS? 9 G �UV]\FLR>@?R^_V 9 NFÁILH;��if;IT<>@? 9 GËNF;IT5V 9 NX;$T5NX;.A 9 GF= ^

>S? 9 GFGX;$Vl;$GW>Y�pnmf Pud���� \_^`U�f�QTSiSm�u\ Qgs��} \ � � deqrs � UlPRU�~��cU acP�� �`q PRU�ZXq Y QTSmSmf�des Q PRd�\ca PR\ \ SVU��uQ��

Pud�a`�]Z]\x^iU Z]Qga`QT� U Z U acP �mq PR�uQgstPlY�VO .9�l�[-/���F% �\��49�D�].0��OL-/�R��������.0# 6+*,-$% �V*L��#M��68��*,��#$�V��� � 40.9��%7�"-`C&.9�"(��"���"�;Bl�8��#3�]@$i<���"��*,�Z��C)Bv@ �|E

� � �&(�-/#$����.0J � ��.9-/#r.9�&JM�/�"��%�-/#���O'�7@$� �R�����<.9�"-/��it�VO'��-/��i:s[-/#$���"-/4Z�^@ s[�;�|E����F��.0*����&�|���"��#'%�.0# 6j��O'�@ s[��J$it.0#3���"-<%��'(�.0# 6j*,��("OM��# .9��*�=?-/���"���'% %�.0# 6P��O'�A%�.UgX���"��#3�`-/�R��������.0# 6j*,-<% ����-�=D��O'�F��i����"��*}�"-LJ2�(�-/#3���"-/4049��%XE��[���".9% ���\b��v�+�].9��ON�"-FOM��#'%�49�>*,-<% ��49�Z-�=a�"�\�/�"-/#M��J 49�>��.0�\��E

� � �N��� � �"-8�/("O�.9�P*+� 40��.Uc^*,-<% ��4^bV.0#3�8-/40�8���j�"��� �"���"��#$��.0# 6���(�-/*7� 49�|�f��i����"��*�J$i��������P-�=1�".0*7� 49�*,-$% ��49�wbe�\�/("Of-�=>�]O .9("Of% ���"(���.0J2���L��O'����i����"��*�.0#f�r6�.0�8��#f-/�R��������.0# 6h*,-$% ��Ev��6�49-/JM��4�*,-/# .0�"-/��.0# 6*,��("OM��# .9��*���#'��� �"���]��O'�>(�-/���"��(������].0�"("O .0# 6IJR�����v����#�*,-<% ���\E

�VO'��#�bR�v�F��O'-w����OM���&��O'�A*,-$% �A��� �2�����$.9��-/��.9�&� # .9d$�'��ER�VO$�'�\b2�L� # .9d$�'�A���R��(�.UuM(\����.9-/#:*,-<% ��4l(\��#JR�>�/���"-$(�.5���"��%t�"-,�\�/("O�� 45��#3�;*,-<% ��4^ER@$�2��(�.UuM(\����.9-/#�*,-<% ��49�����"�1��49�"-,��� J�T���(��Z�"-,���].0�"(�O�b��/(�(�-/�"%�.0# 6I�"-("OM��# 68���A-$(�(�� ����.0# 6�.0#���O'�7� 45��#$�1*,-<% ��4e%�i<#M��*7.9(��\bm��#'%���O'�,(�-/#3���"-/4]�/(���.9-/#'�1�"-NJR�,�����8��#�Em�VO'�745�/�"�("OM��� �"����.04040�'���������"���;-/� �;��� � �"-8�/(�O�-/#���#��|�'��*7� 49��E

�HU ����\ � ^iqtYwXx�y �'wd\FC;$EcrD?HT 9 E<b��vPF; 9 E<b�s 9 GW>@E 9 L �Òwd\XC';IE<rD?HT 9 E<b���u`C;$ESJM>@?BGFil� 9 NF;a��JOGKJOiO;$Vl;$GW>YÈ