Year: 2019
Type: preprint
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 $φ$. 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 $φ$?, (b) which regions satisfy $φ$ 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.
Source: arXiv (Cornell University)
Authors: Junges, Sebastian, Ábrahám, Erika, Hensel, Christian, Jansen, Nils, Katoen, Joost-Pieter, Quatmann, Tim, Volk, Matthias
Institution: Radboud University Nijmegen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4288414444