Stochastic model checking with stochastic comparison

Abstract

This paper presents a stochastic comparison based method to check state formulas defined over Discrete Time Markov Reward Models. High-level specifications like stochastic Petri nets, Stochastic Automata Networks, Stochastic Process Algebras have been developed to construct large Markov models. However computation of transient and steady-state distributions are limited to relatively small parameter sizes because of the state space explosion problem. Stochastic comparison technique by which both transient and steady-state bounding distributions can be computed, lets to overcome this problem. On the other hand, bounding techniques are useful in Model Checking, since we check generally formulas to see if they meet some bounds or not. We propose to apply stochastic bounding algorithms to construct bounding distributions and to check formulas through these distributions. © Springer-Verlag Berlin Heidelberg 2005.