Process algebras for quantitative analysis

In the 1980s process algebras became widely accepted formalisms for describing and analysing concurrency. Extensions of the formalisms, incorporating some aspects of systems which had previously been abstracted, were developed for a number of different purposes. In the area of performance analysis models must quantify both timing and probability. Addressing this domain led to the formulation of stochastic process algebras. In this paper we give a brief overview of stochastic process algebras and the problems which motivated them, before focussing on their relationship with the underlying mathematical stochastic process. This is presented in the context of the PEPA formalism.