Analysis of an importance sampling estimator for tandem queues

Paul Glasserman · Shing-Gang Kou

136 citations0/0 files storedACM Transactions on Modeling and Computer Simulation

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Advanced Queuing Theory Analysis Simulation Techniques and Applications Probability and Risk Models

Abstract

We analyze the performance of an importance sampling estimator for a rare-event probability in tandem Jackson networks. The rare event we consider corresponds to the network population reaching K before returning to ø, starting from ø, with K large. The estimator we study is based on interchanging the arrival rate and the smallest service rate and is therefore a generalization of the asymptotically optimal estimator for an M/M/1 queue. We examine its asymptotic performance for large K , showing that in certain parameter regions the estimator has an asymptotic efficiency property, but that in other regions it does not. The setting we consider is perhaps the simplest case of a rare-event simulation problem in which boundaries on the state space play a significant role.

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References

1987Applied Probability and Queues 2003Applied Probability and Queues 1989Importance Sampling for Stochastic Simulations 1991Large deviations theory and efficient simulation of excessive backlogs in a GI/GI/m queue 1994Effective bandwidth and fast simulation of ATM intree networks

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1999Multilevel Splitting for Estimating Rare Event Probabilities 2006Chapter 11 Rare-Event Simulation Techniques: An Introduction and Recent Advances 2004Importance Sampling, Large Deviations, and Differential Games 2005Dynamic Importance Sampling for Queueing Networks 2007Dynamic importance sampling for queueing networks 1998A large deviations perspective on the efficiency of multilevel splitting 2002On the importance function in splitting simulation 2006Adaptive Importance Sampling Technique for Markov Chains Using Stochastic Approximation

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