The theory of interactive generalized semi-Markov processes

Abstract

In this paper we introduce the calculus of interactive generalized semi-Markov processes (IGSMPs), a stochastic process algebra which can express probabilistic timed delays with general distributions and synchronizable actions with zero duration, and where choices may be probabilistic, non-deterministic and prioritized. IGSMP is equipped with a structural operational semantics which generates semantic models in the form of generalized semi-Markov processes (GSMPs), i.e. probabilistic systems with generally distributed time, extended with action transitions representing interaction among system components. This is obtained by expressing the concurrent execution of delays through a variant of ST semantics which is based on dynamic names. The fact that names for delays are generated dynamically by the semantics makes it possible to define a notion of observational congruence for IGSMP (that abstracts from internal actions with zero duration) simply as a combination of standard observational congruence and probabilistic bisimulation. We also present a complete axiomatization for observational congruence over IGSMP. Finally, we show how to derive a GSMP from a given IGSMP specification in order to evaluate the system performance and we present a case study.