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

Bahar Kaynar and Ad Ridder
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Bahar Kaynar: VU University Amsterdam
Ad Ridder: VU University Amsterdam

No 09-084/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Cross-Entropy; Rare Events; Importance Sampling; Large-Scale Markov Chains (search for similar items in EconPapers)
JEL-codes: C6 (search for similar items in EconPapers)
Date: 2009-09-30
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20090084

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