Analyzing Non-Markovian Systems by Using a Stochastic Process Calculus and a Probabilistic Model Checker

Abstract

The non-Markovian systems represent almost all stochastic processes, except of a small class having the Markov property; it is a real challenge to analyze these systems. In this article, we present a general method of analyzing non-Markovian systems. The novel viewpoint is given by the use of a compact stochastic process calculus developed in the formal framework of computer science for describing concurrent systems. Since phase-type distributions can approximate non-Markovian systems with arbitrary precision, we approximate a non-Markovian system by describing it easily in our stochastic process calculus, which employs phase-type distributions. The obtained process (in our calculus) are then translated into the probabilistic model checker PRISM; by using this free software tool, we can analyze several quantitative properties of the Markovian approximation of the initial non-Markovian system.