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Supplementary variable approach applied to the transient analysis of age-MRSPNs

In order to assist the performance evaluation of complex stochastic models, automatic program tools have been developed for a long time. An effective model description language, supported by several software tools, is the stochastic Petri Net (SPN). But the attention to the analytical description and the numerical analysis of non-Markovian stochastic Petri Net models arose only 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 a hot research topic. The supplementary variable approach was successfully applied to the transient and steady state analysis of Markov Regenerative Stochastic Petri Nets (MSRPN) when the pre-emption policy associated with the Petri Net (PN) transitions was preemptive repeat different (prd), but it was not applicable with other pre-emption 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.