We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics — and the ones obtained by combining them, are often called performability measures. We show that this computational problem can be recasted as the evaluation of a bilinear form induced by appropriate matrix functions, and thus solved by leveraging the fast methods available for this task. We provide a comprehensive analysis of the theory required to translate the problem from the language of Markov chains to the one of matrix functions. The advantages of this new formulation are discussed, and it is shown that this setting allows to easily study the sensitivities of the measures with respect to the model parameters. Numerical experiments confirm the effectiveness of our approach; the tests we have run show that we can outperform the solvers available in state of the art commercial packages on a representative set of large scale examples.

Computing performability measures in Markov chains by means of matrix functions

Robol L.
2020-01-01

Abstract

We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics — and the ones obtained by combining them, are often called performability measures. We show that this computational problem can be recasted as the evaluation of a bilinear form induced by appropriate matrix functions, and thus solved by leveraging the fast methods available for this task. We provide a comprehensive analysis of the theory required to translate the problem from the language of Markov chains to the one of matrix functions. The advantages of this new formulation are discussed, and it is shown that this setting allows to easily study the sensitivities of the measures with respect to the model parameters. Numerical experiments confirm the effectiveness of our approach; the tests we have run show that we can outperform the solvers available in state of the art commercial packages on a representative set of large scale examples.
2020
Masetti, G.; Robol, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1013002
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