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The Mean Value of the Maximum

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Process Algebra and Probabilistic Methods: Performance Modeling and Verification (PAPM-PROBMIV 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2399))

Abstract

This paper treats a practical problem that arises in the area of stochastic process algebras. The problem is the efficient computation of the mean value of the maximum of phase-type distributed random variables. The maximum of phase-type distributed random variables is again phase-type distributed, however, its representation grows exponentially in the number of considered random variables. Although an efficient representation in terms of Kronecker sums is straightforward, the computation of the mean value requires still exponential time, if carried out by traditional means. In this paper, we describe an approximation method to compute the mean value in only polynomial time in the number of considered random variables and the size of the respective representations. We discuss complexity, numerical stability and convergence of the approach.

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Author information

Authors and Affiliations

  1. University of Twente, The Netherlands

    Henrik Bohnenkamp

  2. Technical University of Aachen, Germany

    Boudewijn Haverkort

Authors
  1. Henrik Bohnenkamp
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  2. Boudewijn Haverkort
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science Formal Methods and Tools Group, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Holger Hermanns

  2. Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Roberto Segala

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© 2002 Springer-Verlag Berlin Heidelberg

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Bohnenkamp, H., Haverkort, B. (2002). The Mean Value of the Maximum. In: Hermanns, H., Segala, R. (eds) Process Algebra and Probabilistic Methods: Performance Modeling and Verification. PAPM-PROBMIV 2002. Lecture Notes in Computer Science, vol 2399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45605-8_4

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  • DOI: https://doi.org/10.1007/3-540-45605-8_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43913-4

  • Online ISBN: 978-3-540-45605-6

  • eBook Packages: Springer Book Archive

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