Product form solution for a class of PEPA models

Abstract

The advantages of the compositional structure within the Markovian process algebra PEPA for model construction and simplification have already been demonstrated. In this paper we show that for some PEPA models this structure may also be used to advantage during the solution of the model. Several papers offering product form solutions of stochastic Petri nets have been published during the last 10 years. In [R. Boucherie, A characterisation of independence for competing Markov chains with applications to stochastic Petri nets, IEEE Trans. Software Engrg. 20 (7) (1994) 536–544], Boucherie showed that these solutions were a special case of a simple exclusion mechanism for the product process of a collection of Markov chains. The results presented in this paper take advantage of his observation. In particular we show that PEPA models that generate such processes may be readily identified and show how the product form solution may be obtained. Although developed here in the context of PEPA the results presented can be easily generalised to any of the other Markovian process algebra languages.