Computational algorithms for product-form of competing Markov chains

Abstract

We consider a particular class of Stochastic Petri Nets exhibiting a Product Form Solution over sub-nets. For this type of product form models we provide a normalisation constant algorithm for computing the performance indices of such SPNs. The considered Product Form Solution criterion is based on a factorisation of the equilibrium distribution of the model in terms of distributions of the Continuous Time Markov Chains of the basic sub-models and hence, although all the derivations presented in this paper concern Stochastic Petri Net models, they can easily be adapted to other performance formalisms where the identification of classes of models exhibiting a Product Form Solution over sub-models is possible.