Ergodic Theory of Stochastic Petri Networks

Abstract

Stochastic Petri nets are a general formalism for describing the dynamics of discrete event systems. The present paper focuses on a subclass of stochastic Petri nets called stochastic event graphs. Under the assumption that the variables used for the timing of an event graph form stationary and ergodic sequences of random variables, we make use of an associated stochastic recursive equation in order to construct its stationary and ergodic regime. In particular, we determine the conditions under which the existence of this regime is guaranteed.