Approximate transient analysis for subclasses of deterministic and stochastic Petri nets

Transient analysis of non-Markovian stochastic Petri nets is a theoretically interesting and practically important problem. In this paper, we first present a method to compute bounds and an approximation on the average state sojourn times for a subclass of deterministic and stochastic Petri nets (DSPNs) where there is a single persistent deterministic transition that can become enabled only in a special state. Then, we extend this class by allowing the transition to become enabled in any state, as long as the time between successive enablings of the deterministic transition is independent of this state, and develop a new approximate transient analysis approach. In addition to renewal theory, we only make use of discrete and continuous Markov chain concepts. As an application, we use the model of a finite-capacity queue with a server subject to breakdowns, and assess the quality of our approximations.