Dependability Analysis with Markov Chains: How Symmetries Improve Symbolic Computations

We propose a novel approach that combines two general and complementary methods for dependability analysis based on the steady state or transient analysis of Markov chains. The first method allows us to automatically detect all symmetries in a compositional Markovian model with state-sharing composi...

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Bibliographic Details
Published inFourth International Conference on the Quantitative Evaluation of Systems (QEST 2007) pp. 151 - 160
Main Authors McQuinn, M.G., Kemper, P., Sanders, W.H.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2007
Subjects
Computer science
Data structures
Educational institutions
Information analysis
Numerical analysis
Particle measurements
State-space methods
Steady-state
Stochastic processes
Transient analysis
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Summary:We propose a novel approach that combines two general and complementary methods for dependability analysis based on the steady state or transient analysis of Markov chains. The first method allows us to automatically detect all symmetries in a compositional Markovian model with state-sharing composition. Symmetries are detected with the help of an automorphism group of the model composition graph, which yields a reduction of the associated Markov chain due to lumpability. The second method allows us to represent and numerically solve the lumped Markov chain, even in the case of very large state spaces, with the help of symbolic data structures, in particular matrix diagrams. The overall approach has been implemented and is able to compute stationary and transient measures for large Markovian models of dependable systems.
ISBN:076952883X
9780769528830
DOI:10.1109/QEST.2007.43