A fast cross-entropy method for estimating buffer overflows in queueing networks

A fast cross-entropy method for estimating buffer overflows in queueing networks

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Article ID: iaor20073877
Country: United States
Volume: 50
Issue: 7
Start Page Number: 883
End Page Number: 895
Publication Date: Jul 2004
Journal: Management Science
Authors: , ,
Keywords: queueing networks
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.

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