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Moment characterization of matrix exponential and Markovian arrival processes

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  • Levente Bodrog
  • András Horváth
  • Miklós Telek

Abstract

This paper provides a general framework for establishing the relation between various moments of matrix exponential and Markovian processes. Based on this framework we present an algorithm to compute any finite dimensional moments of these processes based on a set of required (low order) moments. This algorithm does not require the computation of any representation of the given process. We present a series of related results and numerical examples to demonstrate the potential use of the obtained moment relations. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Levente Bodrog & András Horváth & Miklós Telek, 2008. "Moment characterization of matrix exponential and Markovian arrival processes," Annals of Operations Research, Springer, vol. 160(1), pages 51-68, April.
    • Handle: RePEc:spr:annopr:v:160:y:2008:i:1:p:51-68:10.1007/s10479-007-0296-8
    DOI: 10.1007/s10479-007-0296-8
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    References listed on IDEAS

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    1. Asmussen, Søren & Bladt, Mogens, 1999. "Point processes with finite-dimensional conditional probabilities," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 127-142, July.
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    Cited by:

    1. Peter Buchholz & Miklós Telek, 2013. "On minimal representations of Rational Arrival Processes," Annals of Operations Research, Springer, vol. 202(1), pages 35-58, January.
    2. Sunkyo Kim, 2016. "Minimal LST representations of MAP(n)s: Moment fittings and queueing approximations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(7), pages 549-561, October.
    3. Wanlu Gu & Neng Fan & Haitao Liao, 2019. "Evaluating readmission rates and discharge planning by analyzing the length-of-stay of patients," Annals of Operations Research, Springer, vol. 276(1), pages 89-108, May.

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