Efficient simulation of a tandem Jackson network

We consider a two-node tandem Jackson network. Starting from a given state, we are interested in estimating the probability that the content of the second buffer exceeds some high level L before it becomes empty. The theory of Markov additive processes is used to determine the asymptotic decay rate of this probability, for large L. Moreover, the optimal exponential change of measure to be used in importance sampling is derived and used for efficient estimation of the rare event probability of interest. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer, and yields asymptotically efficient simulation for any set of arrival and service rates. The relative error is bounded independent of the level L, except when the first server is the bottleneck and its buffer is infinite, in which case the relative error is bounded linearly in L