Efficient approximate transient analysis for a class of deterministic and stochastic Petri nets

Transient analysis of non-Markovian Stochastic Petri nets is a theoretically interesting and practically important problem. We present a new method to compute bounds and an approximation on the average state sojourn times for a special class of deterministic and stochastic Petri nets (DSPNs). In addition to the idea of the subordinated Markov chain traditionally used for the stationary solution of DSPNs, our algorithm makes use of concepts from renewal theory. An application to a finite-capacity queue with a server subject to breakdowns is included.