Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets

Abstract

We examine product form equilibrium distributions for classes of batch movement queueing networks and stochastic Petri nets (SPNs). For this class of nets we use matrix techniques to obtain a particular product form result and a condition for its existence. In addition we derive a convolution algorithm for calculating the normalising constant of product form SPNs. The convolution requires the generation of marking sets for each place in the SPN and avoids the need to generate the reachability graph.