Optimal Sampling of Overflow Paths in Jackson Networks

We consider the problems of computing overflow probabilities at level N in any subset of stations in a Jackson network and of simulating sample paths conditional on overflow. We construct algorithms that take O (N) function evaluations to estimate such overflow probabilities within a prescribed relative accuracy and to simulate paths conditional on overflow at level N . The algorithms that we present are optimal in the sense that the best possible performance that can be expected for conditional sampling involves Ω (N) running time. As we explain in our development, our techniques have the potential to be applicable to more general classes of networks.