Transient Analysis of Age-MRSPNs by the Method of Supplementary Variables

Miklós Telek, András Horváth

Abstract:

In order to assist the performance evaluation of complex stochastic models, automatic program tools were developed since a long time. Stochastic Petri Nets (SPN) are applied as an effective model description language supported by several analytical and simulation tools. The analytical description and the numerical analysis of non-Markovian stochastic Petri Net models gained attention recently. There are different theoretical approaches and numerical methods considered in recent works, such as the Markov renewal theory and the supplementary variable approach, but to find the most effective way of the analysis of such models is still an open research problem.

The supplementary variable approach was successfully applied to the transient and steady state analysis of Markov Regenerative Stochastic Petri Nets (MSRPN) when the preemption policy associated with the Petri Net (PN) transitions was preemptive repeat different (prd), but it was not applicable with other preemption mechanisms. In this paper we extend the applicability of the supplementary variable approach to a class of MRSPNs in which preemptive resume (prs) policy can also be assigned to the transitions of the PN.

Keywords: Markov Regenerative Stochastic Petri Nets, Preemption Policies, Supplementary Variable Approach.

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