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Evaluation of Iterative Methods on Large Markov Chains Generated by GSPN Models

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New Frontiers in Quantitative Methods in Informatics (InfQ 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 825))

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Abstract

GSPN models often generate high cardinality state spaces, whose analysis requires the solution of very large and sparse nonsymmetric linear systems for the associated Markov chain. In this paper we report the results of an empirical investigation of three well-known iterative methods for linear systems of equations: Gauss-Seidel, GMRES, and Bi-CGstab. We evaluate these methods on several large Markov chains generated by GSPN models proposed in the literature. Issues addressed include state space characterization, problem conditioning, numerical accuracy and stability, and computation time. Results show that increased attention should be paid to the numerical issues underlying performance and reliability analyses when dealing with large state spaces.

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Acknowledgment

We are grateful to Enrico Riccardi and Lorenzo Amighetti for their contribution to the initial phase of this research.

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Authors and Affiliations

  1. Dip. Ingegneria e Architettura, University of Parma, Parma, Italy

    Stefano Caselli & Gianni Conte

  2. Dip. Scienze Matematiche, Fisiche e Informatiche, University of Parma, Parma, Italy

    Mauro Diligenti

Authors
  1. Stefano Caselli
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  2. Gianni Conte
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  3. Mauro Diligenti
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Corresponding author

Correspondence to Stefano Caselli .

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Editors and Affiliations

  1. Ca’ Foscari University of Venice, Venice, Italy

    Simonetta Balsamo

  2. Ca’ Foscari University of Venice, Venice, Italy

    Andrea Marin

  3. University of Florence, Florence, Italy

    Enrico Vicario

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Caselli, S., Conte, G., Diligenti, M. (2018). Evaluation of Iterative Methods on Large Markov Chains Generated by GSPN Models. In: Balsamo, S., Marin, A., Vicario, E. (eds) New Frontiers in Quantitative Methods in Informatics. InfQ 2017. Communications in Computer and Information Science, vol 825. Springer, Cham. https://doi.org/10.1007/978-3-319-91632-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-91632-3_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91631-6

  • Online ISBN: 978-3-319-91632-3

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