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The Mean Value of the Maximum

  • Henrik Bohnenkamp
  • Boudewijn Haverkort
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Generator Matrix Label Transition System Dominant Eigenvalue Positive Random Variable Sojourn Time Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Henrik Bohnenkamp
    • 1
  • Boudewijn Haverkort
    • 2
  1. 1.University of TwenteThe Netherlands
  2. 2.Technical University of AachenGermany

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