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International Conference on Modelling Techniques and Tools for Computer Performance Evaluation

TOOLS 2003: Computer Performance Evaluation. Modelling Techniques and Tools pp 200–217Cite as

A Closed-Form Solution for Mapping General Distributions to Minimal PH Distributions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2794))

Abstract

Approximating general distributions by phase-type (PH) distributions is a popular technique in queueing analysis, since the Markovian property of PH distributions often allows analytical tractability. This paper proposes an algorithm for mapping a general distribution G to a PH distribution where the goal is to find a PH distribution which matches the first three moments of G. Since efficiency of the algorithm is of primary importance, we first define a particular subset of the PH distributions, which we refer to as EC distributions. The class of EC distributions has very few free parameters, which narrows down the search space, making the algorithm efficient – In fact we provide a closed-form solution for the parameters of the EC distribution. Our solution is general in that it applies to any distribution whose first three moments can be matched by a PH distribution. Also, our resulting EC distribution requires a nearly minimal number of phases, always within one of the minimal number of phases required by any acyclic PH distribution. Lastly, we discuss numerical stability of our solution.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Takayuki Osogami & Mor Harchol-Balter

Authors
  1. Takayuki Osogami
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  2. Mor Harchol-Balter
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Editor information

Editors and Affiliations

  1. Universität Dortmund, P.O. Box, D-44221, Dortmund, Germany

    Peter Kemper

  2. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 W. Main Street, P.O. Box, 61801, Urbana, IL, USA

    William H. Sanders

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© 2003 Springer-Verlag Berlin Heidelberg

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Osogami, T., Harchol-Balter, M. (2003). A Closed-Form Solution for Mapping General Distributions to Minimal PH Distributions. In: Kemper, P., Sanders, W.H. (eds) Computer Performance Evaluation. Modelling Techniques and Tools. TOOLS 2003. Lecture Notes in Computer Science, vol 2794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45232-4_13

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  • DOI: https://doi.org/10.1007/978-3-540-45232-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40814-7

  • Online ISBN: 978-3-540-45232-4

  • eBook Packages: Springer Book Archive

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