A Class of PEPA Models Exhibiting Product Form Solution over Submodels

Jane Hillston


The advantages of the compositional structure within 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 ten years. In a recent paper, Boucherie showed that some of 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. Moreover, 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 stochastic process algebra languages.


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