Operational semantics for product-form solution

Abstract

In this paper we present product-form solutions from the point of view of stochastic process algebra. In previous work we have shown how to derive product-form solutions for a formalism called Labelled Markov Automata (LMA). LMA are very useful as their relation with the Continuous Time Markov Chains is very direct. The disadvantage of using LMA is that the proofs of properties are cumbersome. In fact, in LMA it is not possible to use the inductive structure of the language in a proof. In this paper we consider a simple stochastic process algebra that has the great advantage of simplifying the proofs. This simple language has been inspired by PEPA, however, detailed analysis of the semantics of cooperation will show the differences between the two formalisms. It will also be shown that the semantics of the cooperation in process algebra influences the correctness of the derivation of the product-form solutions.