Adaptive state-dependent importance sampling simulation of Markovian queueing networks

In this paper, a method is presented for the efficient estimation of rare-event (buffer overflow) probabilities in queueing networks using importance sampling. Unlike previously proposed change of measures, the one used here is not static, i.e., it depends on the buffer contents at each of the network nodes. The optimal state-dependent change of measure is determined adaptively during the simulation, using the cross-entropy method. The adaptive state-dependent importance sampling algorithm proposed in this paper yields asymptotically efficient simulation of models for which it is shown (formally or otherwise) that no effective static change of measure exists. Simulation results for queueing models of communication systems are presented to demonstrate the effectiveness of the method.