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Ref: Peter Haas’ book on Stochastic Petri Nets – resets all timers each scan, prob. deposit Remove on Fire rule – vs Rem

Examples of Petri Net Models – Activity Scanning Models. Inhibitor arc. 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)

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Ref: Peter Haas’ book on Stochastic Petri Nets – resets all timers each scan, prob. deposit Remove on Fire rule – vs Rem

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  1. Examples of Petri Net Models – Activity Scanning Models Inhibitor arc 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!)

  2. Multiple server queues?

  3. Note: is an “event graph” – one out-transition per place State dep deposit to d11 or d12...

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

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

  6. 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

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

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

  9. e1i = Assign color i (1 to N) e2i = Arrival color i e3i = Register e4i = Eval as process e5i = Eval as archive e6i = Return questionnaire e7i = End timeout e8i = Complete processing e9i = Failure of inspection e10i = Passing inspection e11i = Complete archiving Color to each of N (conwip)complaints to identify transient entities... • Note: • Color = transient entities • e6 and e7 “race”

  10. Note extensive use of inhibitor arcs...

  11. d1,i,j = part i waiting Or processing on mach j Hmwk: do an ERG for this system.

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

  13. Need Pg 397….

  14. Transition has two times – e3 or e5 with 50/50 probs. e1 deposits in d2 or d5 with equal probabilty

  15. NEED PAGE 137 for this example

  16. 1 Inhibitor arcs are note strictly necessary (but very convenient!) Add d2 had token iff d1 empty And no tokens if d1 has any.

  17. Need Example 1.4 of Chapter 2 Measuring Delays

  18. Need figure 9.2 of section 2.6 without colors

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