In this paper, a method is presented for the efficient estimation of rare-event (overflow) probabilities in Jackson queueing networks using importance sampling. The method differs in two ways from methods discussed in most earlier literature: the change of measure is state-dependent, i.e., it is a function of the content of the buffers, and the change of measure is determined using a cross-entropy-based adaptive procedure. This method yields asymptotically efficient estimation of overflow

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... ilities of queueing models for which it has been shown that methods using a stateindependent change of measure are not asymptotically efficient. Numerical results demonstrating the effectiveness of the method are presented as well.