A balanced likelihood ratio approach for analyzing rare events in a tandem Jackson network

Abstract

Balanced likelihood ratio importance sampling methods were originally developed for the analysis of fault-tolerant systems. The paper provides a basis for adapting this approach to analyze the rare event probability that total system size reaches a bound before returning to zero in tandem Jackson networks. An optimal importance sampling distribution for the single server case is derived through direct application of the balanced likelihood ratio approach. The generalization of this approach to larger systems is explored via a two-node tandem Jackson network. A general heuristic approach is outlined along with certain open questions whose answers could lead to a more robust solution. Asymptotic characteristics of the proposed importance sampling approach for the two-node network are discussed. Bounded relative error is only possible under certain conditions. Numerical results illustrate the benefits of the approach.