Rare event simulation and combinatorial optimization using cross entropy: estimating buffer overflows in three stages using cross-entropy

Authors:
P. T. de Boer;D. P. Kroese;R. Y. Rubinstein
Affiliations:
University of Twente, The Netherlands;University of Queensland, Brisbane, Australia;Faculty of Industrial Engineering and Management Technion, Haifa, Israel.
Venue:
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Year:
2002

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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 recognize three distinct properties of the method which together explain why the method works well; we conjecture that they hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.