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Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue

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Author Info

  • Rajan Suri

    (Department of industrial Engineering, University of Wisconsin, Madison, Wisconsin 53706)

  • Michael A. Zazanis

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60201)

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    Abstract

    The technique of perturbation analysis has recently been introduced as an efficient way to compute parameter sensitivities for discrete event systems. Thus far, the statistical properties of perturbation analysis have been validated mainly through experiments. This paper considers, for an M/G/1 queueing system, the sensitivity of mean system time of a customer to a parameter of the arrival or service distribution. It shows analytically that (i) the steady state value of the perturbation analysis estimate of this sensitivity is unbiased, and (ii) a perturbation analysis algorithm implemented on a single sample path of the system gives asymptotically unbiased and strongly consistent estimates of this sensitivity. (No previous knowledge of perturbation analysis is assumed, so the paper also serves to introduce this technique to the unfamiliar reader.) Numerical extensions to GI/G/1 queues, and applications to optimization problems, are also illustrated.

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    File URL: http://dx.doi.org/10.1287/mnsc.34.1.39
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 34 (1988)
    Issue (Month): 1 (January)
    Pages: 39-64

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    Handle: RePEc:inm:ormnsc:v:34:y:1988:i:1:p:39-64

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    Related research

    Keywords: discrete event systems; simulation; queueing systems; sample path analysis; stochastic systems;

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    Cited by:
    1. Mark J. Cathcart & Steven Morrison & Alexander J. McNeil, 2011. "Calculating Variable Annuity Liability 'Greeks' Using Monte Carlo Simulation," Papers 1110.4516, arXiv.org.
    2. Cao, Xi-Ren, 1996. "Perturbation analysis of discrete event systems: Concepts, algorithms, and applications," European Journal of Operational Research, Elsevier, vol. 91(1), pages 1-13, May.
    3. Rubinstein, Reuven Y. & Shapiro, Alexander, 1990. "Optimization of static simulation models by the score function method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(4), pages 373-392.

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