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)
Proceedings of the 32nd conference on Winter simulation
Efficient simulation of a tandem Jackson network
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Analysis of state-independent importance-sampling measures for the two-node tandem queue
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Alternative proof and interpretations for a recent state-dependent importance sampling scheme
Queueing Systems: Theory and Applications
Rare-Event Simulation for Tandem Queues: A Simple and Efficient Importance Sampling Scheme
NET-COOP '09 Proceedings of the 3rd Euro-NF Conference on Network Control and Optimization
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This article considers importance sampling as a tool for rare-event simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jacksonian two-node tandem queue; it is known that in this setting “traditional” state-independent importance-sampling distributions perform poorly. We therefore concentrate on developing a state-dependent change of measure, that we prove to be asymptotically efficient. More specific contributions are the following. (i) We concentrate on the probability of the second queue exceeding a certain predefined threshold before the system empties. Importantly, we identify an asymptotically efficient importance-sampling distribution for any initial state of the system. (ii) The choice of the importance-sampling distribution is backed up by appealing heuristics that are rooted in large-deviations theory. (iii) The method for proving asymptotic efficiency relies on probabilistic arguments only. The article is concluded by simulation experiments that show a considerable speedup.