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

P. T. de Boer (), D. P. Kroese () and R. Y. Rubinstein ()
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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

Management Science, 2004, vol. 50, issue 7, 883-895

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.

Keywords: importance sampling; rare events; cross-entropy; queueing networks; simulation (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (16)

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