A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks
AbstractIn 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.
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Bibliographic InfoArticle provided by INFORMS in its journal Management Science.
Volume (Year): 50 (2004)
Issue (Month): 7 (July)
importance sampling; rare events; cross-entropy; queueing networks; simulation;
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- Chan, Joshua & Eisenstat, Eric, 2012.
"Marginal Likelihood Estimation with the Cross-Entropy Method,"
40051, University Library of Munich, Germany.
- Joshua C C Chan & Eric Eisenstat, 2012. "Marginal Likelihood Estimation with the Cross-Entropy Method," CAMA Working Papers 2012-18, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
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