Fast simulation of excessive population size in tandem Jackson networks

Abstract

We consider the probability that the population in a two node tandem Jackson network reaches some high level during a busy period. For estimating this rare event probability we apply fast simulation using importance sampling. Our focus is thereby on systems without a single bottleneck queue, which has turned out to be the most critical case for existing methods. A state independent change of measure is developed heuristically based on typical system behavior and the likelihood ratio properties on state cycles. Neither complicated large deviations analysis nor costly presimulations are needed to determine the change of measure. Although state independent changes of measure are known to have limitations, they also provide several advantages. They are easy to use and understand, and they do not cause space complexity problems often strongly limiting state-dependent approaches. The efficiency of our change of measure is demonstrated by numerical results.