Symmetric stochastic Petri nets
IBM Journal of Research and Development
Stochastic petri net simulation
WSC '89 Proceedings of the 21st conference on Winter simulation
Simulation output analysis using standardized time series
Mathematics of Operations Research
GreatSPN 1.7: graphical editor and analyzer for timed and stochastic Petri nets
Performance Evaluation - Special issue: performance modeling tools
Simulation modeling with event graphs
Communications of the ACM
Distributed Simulation of Petri Nets
IEEE Parallel & Distributed Technology: Systems & Technology
Regenerative Simulation of Stochastic Petri Nets
International Workshop on Timed Petri Nets
Efficient simulation of SWN models
PNPM '95 Proceedings of the Sixth International Workshop on Petri Nets and Performance Models
Stochastic Petri Nets: Modelling, Stability, Simulation
Stochastic Petri Nets: Modelling, Stability, Simulation
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Long-run stochastic stability is a precondition for applying steady-state simulation output analysis methods to a stochastic Petri Net (SPN), and is of interest in its own right. A fundamental stability requirement for an irreducible SPN is that the markings of the net be recurrent, in that the marking process visits each marking infinitely often with probability 1. We study recurrence properties of irreducible non-Markovian SPNs with finite marking set. Our focus is on the "clocks" that govern the transition firings, and we consider SPNs in which zero, one, or at least two simultaneously-enabled transitions can have very heavy-tailed clock-setting distributions. We establish positive recurrence, null recurrence, and, perhaps surprisingly, possible transience of markings for these respective regimes. The transience result stands in strong contrast to Markovian or semi-Markovian SPNs, where irreducibility and finiteness of the marking set guarantee positive recurrence.