An Integrated Approach for the Specification and Analysis of Stochastic Real-Time Systems

Abstract

A formal approach for the specification and analysis of concurrent systems is proposed which integrates two different orthogonal aspects of time: (i) real-time, concerning the expression of time constraints and the verification of exact time properties, and (ii) probabilistic-time, concerning the probabilistic quantification of durations of system activities via exponential probability distributions and the evaluation of system performance. We show that these two aspects, that led to different specification paradigms called timed automata and Markovian process algebras, respectively, can be expressed in an integrated way by a single language: a process algebra capable of expressing activities with generally distributed durations. In particular, we consider the calculus of Interactive Generalized Semi-Markov Processes (IGSMPs) and we present formal techniques for compositionally deriving, from an IGSMP specification, (i) a pure real-time model (called Interactive Timed Automaton), by considering the support of general distributions, and (ii) a pure probabilistic-time model (called Interactive Weighted Markov Chain), by approximating general distributions with phase-type distributions.