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Compositionality for Markov Reward Chains with Fast Transitions

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Formal Methods and Stochastic Models for Performance Evaluation (EPEW 2007)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4748))

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Abstract

A parallel composition is defined for Markov reward chains with fast transitions and for discontinuous Markov reward chains. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are τ-lumping and τ-reduction. Discontinuous Markov reward chains are ‘limits’ of Markov reward chains with fast transitions, and have related notions of lumping and reduction. In total, four compositionality results are shown. In addition, the two parallel operators are related by a continuity property.

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Authors and Affiliations

  1. Technische Universiteit Eindhoven, Formal Methods Group, Den Dolech 2, 5612 AZ, Eindhoven, The Netherlands

    J. Markovski, N. Trčka & E. P. de Vink

  2. University of Salzburg, Computational Systems Group, Jakob-Haringer-Straße 2, 5020 Salzburg, Austria

    A. Sokolova

Authors
  1. J. Markovski
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  2. A. Sokolova
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  3. N. Trčka
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  4. E. P. de Vink
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Katinka Wolter

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© 2007 Springer-Verlag Berlin Heidelberg

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Markovski, J., Sokolova, A., Trčka, N., de Vink, E.P. (2007). Compositionality for Markov Reward Chains with Fast Transitions. In: Wolter, K. (eds) Formal Methods and Stochastic Models for Performance Evaluation. EPEW 2007. Lecture Notes in Computer Science, vol 4748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75211-0_3

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  • DOI: https://doi.org/10.1007/978-3-540-75211-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75210-3

  • Online ISBN: 978-3-540-75211-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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