1. Ref: Peter Haas’ book on Stochastic Petri Nets – resets all timers each scan, prob. deposit Remove on Fire rule – vs Remove on enable (Ref: Fishwick) Simulation – Activity Scanning algorithm. (Cancel if transition is disabled!) Inhibitor arc Examples of Petri Net Models – Activity Scanning Models

2. Multiple server queues?

3. Note: is an “event graph” – one out-transition per place State dep deposit to d 11 or d 12...

6. tFtF M B “failing” – need “new” machine get broken machine M,R R,B tRtR “fixing” – need broken machine and repairman get good machine and repairman “Modeling Activities with ERGs” “Implied ERG” tFtF M B R,M B,R tRtR {M--} {B++} M = “new” machines B = broken machines waiting R = idle repairmen {R--, B--} {R++, M++} ~ ~ (B) (R)

7. “Implied ERG” tFtF M B R,M B,R tRtR {M--} {B++} M = “new” machines B = broken machines R = idle repairmen {R--, B--} {R++, M++} ~ ~ (B) (R) “Reduced ERG – M is not tested” tFtF B R B,R tRtR {B++} {R--, B--} {R++} ~ ~ (B) (R) Exercise: can you further reduce this? hint: assume more machines than repairmen. Define new variable(s).

8. Admin Hmwk: Find counterexample to TBS PN Hmwk: Cases where ROF and ROE are equivalent Read Seila, Ceric and Tadikamalla 131 reserve – Engr. Lib. Read 6 to 6.4.3 Chpt. 8.1-8.2, skim 8.3 Reading Law and Kelton 1.3, 1.4.9, Chpt. 3 and 4 Tivo, Chpt 6 – input modeling – skim

9. tFtF B R B,R tRtR {B++} {R--, B--} {R++} ~ ~ (B) (R) tFtF tRtR {B++} {B--} ~ (B<=R) Fix ~ (B>=R) Fail R = total number of repairmen (const.) B = number of broken machines (incl in rep.)

10. Colored Petri Nets (transitions are enabled by color or tokens)

12. e 1i = Assign color i (1 to N) e 2i = Arrival color i e 3i = Register e 4i = Eval as process e 5i = Eval as archive e 6i = Return questionnaire e 7i = End timeout e 8i = Complete processing e 9i = Failure of inspection e 10i = Passing inspection e 11i = Complete archiving Color to each of N (conwip)complaints to identify transient entities... Note: 1.Color = transient entities 2. e 6 and e7 “race”

15. Note extensive use of inhibitor arcs...

17. d 1,i,j = part i waiting Or processing on mach j Hmwk: do an ERG for this system.

20. GSMP->EGM Mapping (Computer Network) Prop. Reset New Packet Clear End Trans Obs. End Tran. Start Tran

22. Need Pg 397….

24. e1 deposits in d2 or d5 with equal probabilty Transition has two times – e 3 or e 5 with 50/50 probs.

25. NEED PAGE 137 for this example

26. 1 Inhibitor arcs are note strictly necessary (but very convenient!) Add d2 had token iff d1 empty And no tokens if d1 has any.

27. Measuring Delays Need Example 1.4 of Chapter 2

30. Need figure 9.2 of section 2.6 without colors