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The Cross-Entropy Method with Patching for Rare-Event Simulation of Large Markov Chains

Author

Listed:
  • Bahar Kaynar

    (VU University Amsterdam)

  • Ad Ridder

    (VU University Amsterdam)

Abstract

This discussion paper resulted in a publication in the European Journal of Operations Research (2010), pages 1380-1397. There are various importance sampling schemes to estimate rare event probabilities in Markovian systems such as Markovian reliability models and Jackson networks. In this work, we present a general state dependent importance sampling method which partitions the state space and applies the cross-entropy method to each partition. We investigate two versions of our algorithm and apply them to several examples of reliability and queueing models. In all these examples we compare our method with other importance sampling schemes. The performance of the importance sampling schemes is measured by the relative error of the estimator and by the effciency of the algorithm. The results from experiments show considerable improvements both in running time of the algorithm and the variance of the estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20090084
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    References listed on IDEAS

    as
    1. T. P. I. Ahamed & V. S. Borkar & S. Juneja, 2006. "Adaptive Importance Sampling Technique for Markov Chains Using Stochastic Approximation," Operations Research, INFORMS, vol. 54(3), pages 489-504, June.
    2. Peter W. Glynn & Donald L. Iglehart, 1989. "Importance Sampling for Stochastic Simulations," Management Science, INFORMS, vol. 35(11), pages 1367-1392, November.
    3. 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.
    4. Sandeep Juneja & Perwez Shahabuddin, 2001. "Fast Simulation of Markov Chains with Small Transition Probabilities," Management Science, INFORMS, vol. 47(4), pages 547-562, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cross-Entropy; Rare Events; Importance Sampling; Large-Scale Markov Chains;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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