Simulation methods for queues: an overview
Queueing Systems: Theory and Applications
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)
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
Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling
Mathematics of Operations Research
Uniformly Efficient Importance Sampling for the Tail Distribution of Sums of Random Variables
Mathematics of Operations Research
Asymptotically optimal importance sampling for Jackson networks with a tree topology
Queueing Systems: Theory and Applications
RESTART simulation of networks of queues with Erlang service times
Winter Simulation Conference
Efficient calculation of rare event probabilities in Markovian queueing networks
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
On Lyapunov Inequalities and Subsolutions for Efficient Importance Sampling
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Rare events in cancer recurrence timing
Proceedings of the Winter Simulation Conference
Importance sampling for stochastic recurrence equations with heavy tailed increments
Proceedings of the Winter Simulation Conference
Efficient importance sampling schemes for a feed-forward network
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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Rare event simulation in the context of queueing networks has been an active area of research for more than two decades. A commonly used technique to increase the efficiency of Monte Carlo simulation is importance sampling. However, there are few rigorous results on the design of efficient or asymptotically optimal importance sampling schemes for queueing networks. Using a recently developed game/subsolution approach, we construct simple and efficient state-dependent importance sampling schemes for simulating buffer overflows in stable open Jackson networks. The sampling distributions do not depend on the particular event of interest, and hence overflow probabilities for different events can be estimated simultaneously. A by-product of the analysis is the identification of the minimizing trajectory for the calculus of variation problem that is associated with the sample-path large deviation rate function.