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arXiv · 1903.07993

Parameter Synthesis for Markov Models: Covering the Parameter Space

Sebastian Junges·Erika Ábrahám·Christian Hensel·Nils Jansen·Joost-Pieter Katoen·Tim Quatmann·Matthias Volk
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Abstract

Markov chain analysis is a key technique in formal verification. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not -- or only partially -- known. This motivates considering parametric models with transitions labeled with functions over parameters. Whereas traditional Markov chain analysis relies on a single, fixed set of probabilities, analysing parametric Markov models focuses on synthesising parameter values that establish a given safety or performance specification $\varphi$. Examples are: what component failure rates ensure the probability of a system breakdown to be below 0.00000001?, or which failure rates maximise the performance, for instance the throughput, of the system? This paper presents various analysis algorithms for parametric discrete-time Markov chains and Markov decision processes. We focus on three problems: (a) do all parameter values within a given region satisfy $\varphi$?, (b) which regions satisfy $\varphi$ and which ones do not?, and (c) an approximate version of (b) focusing on covering a large fraction of all possible parameter values. We give a detailed account of the various algorithms, present a software tool realising these techniques, and report on an extensive experimental evaluation on benchmarks that span a wide range of applications.

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Sebastian Junges, Erika Ábrahám, Christian Hensel, Nils Jansen, Joost-Pieter Katoen, Tim Quatmann, Matthias Volk. 2019-03-16. Parameter Synthesis for Markov Models: Covering the Parameter Space. https://arxiv.org/abs/1903.07993

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