2. 1 MODELING BY HYBRID PETRI NETS In collaboration with René DAVID Directeur de recherche émérite CNRS Hassane ALLA Professeur à l'UJF

3. 2 Discrete Event Systems état de la vanne temps fermée en ouverture ouverte t1t2 t3 t4   en fermeture  

4. 3 Motivation Objective : Systems Dynamic Analysis

5. 4 Motivation (cont’d) t t Large numbers: continuous approximation may be convenient

6. 5 Outline DISCRETE, CONTINUOUS and HYBRID PETRI NETS TIMING IN DISCRETE & CONTINUOUS PETRI NETS AUTONOMOUS and TIMED HYBRID PETRI NETS APPLICATION EXAMPLES CONCLUSION

7. 6 DISCRETE PETRI NETS CONTINUOUS PETRI NETS HYBRID PETRI NETS

8. 7 Discrete PN

9. 8 Continuous PN

10. 9 Hybrid PN m 2 m 1 0 1 0 1 2 4 T 1 T 2 T 3 T 4 T 2

11. 10 TIMING IN DISCRETE PETRI NETS & CONTINUOUS PETRI NETS

12. 11 Timing in a Discrete PN Machine M1 Buffer 2 Machine M2 Buffer 1 P1P1 P2P2 T1T1 T2T2 P3P3 P4P4 1 2 1 3

13. 12 Timing in a Continuous PN Pump Tank 1 Tank 2 V 1 = 3 liter/sec V 2 = 2 liter/sec

14. 13 Discrete System : Approximation Discrete model P1P1 P2P2 T1T1 T2T2 P3P3 P4P4 2 1 3 1 d1=d1= d2=d2= Continuous model P1P1 P2P2 T1T1 T2T2 75 V 1 = 2 V2= 3V2= 3

15. 14 Continuous System : Approximation 75 P1P1 P2P2 T1T1 T2T2 V 1 =2 V 2 =3 m 2 (t)=75-t m2m2 75 m 1 (t) = (3-2) t = t t m1m1 0 0 75 pour 3)( 2)( 22 11        t Vtv Vtv  75 pour 2)( 2)( 12 11        t Vtv Vtv

16. 15 Continuous System : exact model

17. 16 Maximum Firing Speeds Depending on Time

18. 17 Generalization The basic rules related to an autonomous continuous PN are verified The instantaneous firing speeds may be defined in various ways First example Second example

19. 18 AUTONOMOUS HYBRID PETRI NETS

20. 19 Influence of the Discrete Part on the Continuous Part

21. 20 Influence of the Continuous Part on the Discrete Part

22. 21 Transformation of Continuous Marking into Discrete Marking

23. 22 Transformation of Discrete Marking into Continuous Marking

24. 23 General Case

25. 24 TIMED HYBRID PETRI NETS

26. 25 Example of Hybrid PN V 3 = 3 liter/sec Pump V 4 =2 liter/sec Tank 1 Tank 2 Valve L

27. 26 APPLICATION EXAMPLES

28. 27 Electronic components assembly-test workshop (diodes and transistors) (Motorola in Toulouse – France) Performance evaluation of a production System Wafer 400-5000 Chips Chip

29. 28 Cutting Molding FurnaceTest Electronic components assembly-test workshop (diodes and transistors) (Motorola in Toulouse – France) Performance evaluation of a production System (cont’d) Wafer

30. 29 Production System

31. 30 Water Supply System

32. 31 Water Supply System

33. 32 Transfer Line

34. 33 Controlled system via Communication Networks  Network Control System NECS Project  Not deformed reception of informations: (delays, flows capacities, losses)  Real time System : Temporal accuracy ActuatorsSensorsSystem Controller Communication Networks  Use of the communication networks to carry out tasks of control

35. 34  Open loop control Messages: Continuous flows Decisions of routing or emission: Discrete events  Networks communications can be represented by hybrid tools of modeling :  Modeling of the networks Communication networks Control device Process  hybrid Petri Nets Communication networks Controlled system via Communication Networks -Motivations

36. 35 Modeling Tools buffer Emitter1 Emitter2 Receiver2 Receiver1 Communication network  Water supply system: Natural sources Consumptions Tank valve

37. 36 An analogy buffer Consumption 1 Tank V1V1 Natural source 1 Natural source 2 T3 T3 T2 T2 V3V3 V2V2 T1 T1 T4 T4 V4V4 Consumption 2 t V4V4 t V3V3 V1V1 V2V2 Flow of messages V1V1 Transmitting sources V2V2 V4V4 Receiving sources V3V3 t V4V4 t V3V3

38. 37 Internet = Set of interconnected sub-network Network IP bus Network IP ring Network IP bus Backbone of US Backbone of Europe National network Regional network Selected reference model: TCP/IP Communication Network: Network architectures

39. 38 Network capacity? Congestednetwork E1E1 E2E2 E3E3 Rt 4 R Rt 3 Rt 2 Rt 1 Networks architecture

40. 39 Congestionontrol Congestion control E R Tempo cwnd = 1 acq cwnd = 2 Tempo acq cwnd = 4 Tempo 1 2 4 8 16 Number of transmission congestion window (Ko) 22 11 Expiration of Tempo  Losses of data Thres 2 Thres 1 Slow start Congestion Avoidance Resume of slow start Algorithms of TCP: Slow start Congestion Avoidance

41. 40 Case of transmission line merged in Internet environment V T3T3 Rt V1V1 V1V1 V2V2 V2V2 E1E1 R T1T1 T’ 1 T2T2 T’ 2 Cnl 1 0+0+ Cnl 2 0+0+ C T ” 1 V1V1 A transmission line

42. 41 Related Models

43. 42 Conclusion Continuous systems havebeenstudied for a long time Modeling,analysis andcontrol of DES haveundergone majordevelopments inrecentdecades In recentyears aneedhasemergedtoconsidersystemswhich arepartiallycontinuous andpartially discrete CONTINUOUS Petri nets and HYBRID Petri nets can be used for modeling these systems

44. 43 Bibliography SURVEY REFERENCES BIBLIOGRAPHY ON HYBRID PETRI NETS www.diee.unica.it/~aldo/bibliohpn.html by AlessandroGiua &AldoPiccaluga, Dip.diIngegneriaElettricaed Elettronica,UniversitàdiCagliari, Italy. R. David and H. Alla, Discrete, Continuous, and Hybrid Petri Nets, in preparation, to be published by Springer, Heidelberg, 2004. H. Alla, R. David, Continuous and Hybrid Petri Nets, Journal of Circuits, Systems and Computers, Special Issue on Petri Nets, Vol 8 No 1, 1998 pp. 159-188. R. David, H. Alla, On Hybrid Petri Nets, Discrete Event Dynamic Systems, Theory and Applications, Kluwer Academic Publishers, 11, 9-40, 2001.