Discrete-Time Markovian Stochastic Petri Nets

Gianfranco Ciardo ()
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Gianfranco Ciardo: College of William and Mary, Department of Computer Science

Chapter 20 in Computations with Markov Chains, 1995, pp 339-358 from Springer

Abstract: Abstract We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a “defective discrete phase distribution”. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for of each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.

Keywords: Sojourn Time; Transition Probability Matrix; Transient Analysis; Firing Time; Reward Rate (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-2241-6_20

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DOI: 10.1007/978-1-4615-2241-6_20

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