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Distributed disk-based algorithms for model checking very large Markov chains

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Abstract

In this paper we present data structures and distributed algorithms for CSL model checking-based performance and dependability evaluation. We show that all the necessary computations are composed of series or sums of matrix-vector products. We discuss sparse storage structures for the required matrices and present efficient sequential and distributed disk-based algorithms for performing these matrix-vector products. We illustrate the effectivity of our approach in a number of case studies in which continuous-time Markov chains (generated in a distributed way from stochastic Petri net specifications) with several hundreds of millions of states are solved on a workstation cluster with 26 dual-processor nodes. We show details about the memory consumption, the solution times, and the speedup. The distributed message-passing algorithms have been implemented in a tool called PARSECS, that also takes care of the distributed Markov chain generation and that can also be used for distributed CTL model checking of Petri nets.

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Acknowledgments

The work presented in this paper has largely been performed in the period 1999–2003 when the authors were working in the Department of Computer Science of the RWTH Aachen, Germany. The work was supported by the DFG (projects HA2666/1-1,2).

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Authors and Affiliations

  1. Numerical Analysis and Computational Mechanics, Department for Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands

    Alexander Bell

  2. Design and Analysis of Communication Systems, Department for Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands

    Boudewijn R. Haverkort

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  1. Alexander Bell
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  2. Boudewijn R. Haverkort
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Correspondence to Alexander Bell.

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Bell, A., Haverkort, B.R. Distributed disk-based algorithms for model checking very large Markov chains. Form Method Syst Des 29, 177–196 (2006). https://doi.org/10.1007/s10703-006-0007-0

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