Model-checking algorithms for continuous-time Markov chains

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Model-checking algorithms for continuous-time Markov chains (2003)

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by Christel Baier , Boudewijn Haverkort , Holger Hermanns , Joost-Pieter Katoen

Venue:	IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
Citations:	233 - 47 self

BibTeX

@ARTICLE{Baier03model-checkingalgorithms,
    author = {Christel Baier and Boudewijn Haverkort and Holger Hermanns and Joost-Pieter Katoen},
    title = {Model-checking algorithms for continuous-time Markov chains},
    journal = {IEEE TRANSACTIONS ON SOFTWARE ENGINEERING},
    year = {2003},
    volume = {29},
    number = {7},
    pages = {2003}
}

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Abstract

Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a time-bounded until operator to express probabilistic timing properties over paths as well as an operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady-state operator) and a Volterra integral equation system (for time-bounded until). We then show that the problem of model-checking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all formulas in the logic.

Keyphrases

continuous-time markov chain model-checking algorithm probabilistic timing property well-known notion branching temporal logic steady-state probability logic reduces transient analysis system performance linear equation dependability characteristic transient-state probability model checking problem transient state probability volterra integral equation system real-time probabilistic property continuous stochastic logic csl efficient technique steady-state operator

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