Efficient analysis of rare events associated with individual buffers in a tandem Jackson network

Abstract

Over the last decade, importance sampling has been a popular technique for the efficient estimation of rare event probabilities. This paper presents an approach for applying balanced likelihood ratio importance sampling to the problem of quantifying the probability that the content of the second buffer in a two node tandem Jackson network reaches some high level before it becomes empty. Heuristic importance sampling distributions are derived that can be used to estimate this overflow probability in cases where the first buffer capacity is finite and infinite. The proposed importance sampling distributions differ from previous balanced likelihood ratio methods in that they are specified as functions of the contents of the buffers. Empirical results indicate that the relative errors of these importance sampling estimators is bounded independent of the buffer size when the second server is the bottleneck and is bounded linearly in the buffer size otherwise.