Simulation methods for queues: an overview
Queueing Systems: Theory and Applications
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient simulation of buffer overflow probabilities in jackson networks with feedback
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)
Large deviations and importance sampling for a tandem network with slow-down
Queueing Systems: Theory and Applications
Fluid heuristics, Lyapunov bounds and efficient importance sampling for a heavy-tailed G/G/1 queue
Queueing Systems: Theory and Applications
Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling
Mathematics of Operations Research
Importance sampling for Jackson networks
Queueing Systems: Theory and Applications
Importance Sampling for Weighted-Serve-the-Longest-Queue
Mathematics of Operations Research
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The aim of this article is to construct efficient importance sampling schemes for a rare event, namely, the buffer overflow associated with a feed-forward network with discontinuous dynamics. This is done through a piecewise constant change of measure, which is based on a suitably constructed subsolution to an HJB equation. The main task is to change the measure such that the logarithmic asymptotic optimality is achieved. To that end, we find an upper bound on the second moment of the importance sampling estimator that yields optimality. Numerical simulations illustrate the validity of theoretical results.