Stochastic Petri nets with timed and immediate transitions

Stochastic Petri nets with timed and immediate transitions permit representation of concurrency, synchronization, and communication and provide a general framework for discrete event simulation. Formal definition of the marking process of a stochastic Petri net is in terms of a general state space Markov chain that describes the net at successive marking change epochs. The authors obtain a limit theorem for irreducible marking processes with finite timed marking set. In addition, they provide conditions on the building blocks of a stochastic Petri net under which the marking process is a regenerative process in continuous time with finite cycle length moments. These results establish the regenerative method for simulation analysis in the stochastic Petri net setting.