Towards Performance Evaluation with General Distributions in Process Algebras

We present a process algebra for the performance modeling and evaluation of concurrent systems whose activity durations are expressed through general probability distributions. We first determine the class of generalized semi-Markov processes (GSMPs) as being the class of stochastic processes on which we must rely for performance evaluation to be possible. Then we argue that in this context the right semantics for algebraic terms is a variant of the ST semantics which accounts for both functional and performance aspects. The GSMP based process algebra we propose is introduced together with its formal semantics, an example of performance evaluation, and a notion of probabilistic bisimulation based equivalence accounting for action durations which is shown to be a congruence.