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

P. T. de Boer, D. P. Kroese, R. Y. Rubinstein
2004 Management science  
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
more » ... bability 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.
doi:10.1287/mnsc.1030.0139 fatcat:qfvcotgmbbce7cafkdxpddpe5y