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Towards a Product Form Solution for Stochastic Process Algebras

We examine product form equilibrium distributions for stochastic process algebra models, finding conditions that guarantee the existence of a solution for the traffic equations. These equations are a set of linear equations, which are the basis of exact analysis of product form models like queueing networks, stochastic Petri nets, as well as stochastic process algebras. This paper illustrates how the equilibrium distribution can be expressed as a product for a certain class of stochastic process algebra models that satisfy certain conditions. Although the product form criterion derived in this paper is developed in the context of Performance Evaluation Process Algebra (PEPA), the results can be easily generalised to any of the other stochastic process algebras.