The Cross-Entropy Method With Patching For Rare-Event Simulation Of Large Markov Chains
AbstractThere 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.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 09-084/4.
Date of creation: 30 Sep 2009
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Web page: http://www.tinbergen.nl
Cross-Entropy; Rare Events; Importance Sampling; Large-Scale Markov Chains;
Other versions of this item:
- 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, Elsevier, vol. 207(3), pages 1380-1397, December.
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-10-31 (All new papers)
- NEP-ECM-2009-10-31 (Econometrics)
- NEP-ORE-2009-10-31 (Operations Research)
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