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Likelihood Ratio Derivative Estimation for Finite-Time Performance Measures in Generalized Semi-Markov Processes

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  • Marvin K. Nakayama

    (Department of Computer and Information Science, New Jersey Institute of Technology, Newark, New Jersey 07102)

  • Perwez Shahabuddin

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

This paper investigates the likelihood ratio method for estimating derivatives of finite-time performance measures in generalized semi-Markov processes (GSMPs). We develop readily verifiable conditions for the applicability of this method. Our conditions mainly place restrictions on the basic building blocks (i.e., the transition probabilities, the distribution and density functions of the event lifetimes, and the initial distribution) of the GSMP, which is in contrast to the structural conditions needed for infinitesimal perturbation analysis. We explicitly show that our conditions hold in many practical settings, and in particular, for large classes of queueing and reliability models. One intermediate result we obtain in this study, which is of independent value, is to formally show that the random variable representing the number of occurring events in a GSMP in a finite time horizon, has finite exponential moments in a neighborhood of zero.

Suggested Citation

  • Marvin K. Nakayama & Perwez Shahabuddin, 1998. "Likelihood Ratio Derivative Estimation for Finite-Time Performance Measures in Generalized Semi-Markov Processes," Management Science, INFORMS, vol. 44(10), pages 1426-1441, October.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:10:p:1426-1441
    DOI: 10.1287/mnsc.44.10.1426
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    References listed on IDEAS

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    1. Ward Whitt, 1980. "Continuity of Generalized Semi-Markov Processes," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 494-501, November.
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    Cited by:

    1. Hachicha, Wafik & Ammeri, Ahmed & Masmoudi, Faouzi & Chachoub, Habib, 2010. "A comprehensive literature classification of simulation optimisation methods," MPRA Paper 27652, University Library of Munich, Germany.

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