Transient analysis of Markov regenerative stochastic petri nets: a comparison of approaches

In this paper we present and compare two different approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the non-Markovian stochastic Petri net are presented and then solved either in time-domain or using a Laplace-Stieltjes transformation. Then a comparison of both approaches is presented: expressions for asymptotic computational costs and storage requirements are developed and experimental studies are performed to compare accuracy, time, and space complexity.