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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 ofdoi:10.1287/mnsc.1030.0139 fatcat:qfvcotgmbbce7cafkdxpddpe5y