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A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks

Author

Listed:
  • P. T. de Boer

    () (Department of Electrical Engineering, Mathematics, and Computer Science, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

  • D. P. Kroese

    () (Department of Mathematics, University of Queensland, Brisbane 4072, Australia)

  • R. Y. Rubinstein

    () (Faculty of Industrial Engineering and Management, Technion, Haifa, Israel)

Abstract

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.

Suggested Citation

  • P. T. de Boer & D. P. Kroese & R. Y. Rubinstein, 2004. "A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks," Management Science, INFORMS, vol. 50(7), pages 883-895, July.
  • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:7:p:883-895
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    File URL: http://dx.doi.org/10.1287/mnsc.1030.0139
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    References listed on IDEAS

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    1. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
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    Citations

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    Cited by:

    1. Joshua C. C. Chan & Eric Eisenstat, 2015. "Marginal Likelihood Estimation with the Cross-Entropy Method," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 256-285, March.
    2. repec:eee:reensy:v:131:y:2014:i:c:p:109-117 is not listed on IDEAS
    3. Kaynar, Bahar & Ridder, Ad, 2010. "The cross-entropy method with patching for rare-event simulation of large Markov chains," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1380-1397, December.
    4. repec:eee:rensus:v:80:y:2017:i:c:p:1175-1186 is not listed on IDEAS
    5. Bahar Kaynar & Ad Ridder, 2009. "The Cross-Entropy Method with Patching for Rare-Event Simulation of Large Markov Chains," Tinbergen Institute Discussion Papers 09-084/4, Tinbergen Institute.

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