Analysis of an importance sampling estimator for tandem queues
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Optimal importance sampling for Markovian systems with applications to tandem queues
Mathematics and Computers in Simulation - Special issue: papers presented at the MSSA/IMACS 11th biennial conference on modelling and simulation
The balanced likelihood ratio method for estimating performance measures of highly reliable systems
Proceedings of the 30th conference on Winter simulation
Efficient simulation of a tandem Jackson network
Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future - Volume 1
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Importance Sampling and the Cyclic Approach
Operations Research
Proceedings of the 35th conference on Winter simulation: driving innovation
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Balanced likelihood ratio importance sampling methods were originally developed for the analysis of fault-tolerant systems. This 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.