Large deviations and importance sampling for a tandem network with slow-down

Authors:
Paul Dupuis;Kevin Leder;Hui Wang
Affiliations:
Lefschetz Center for Dynamical Systems, Brown University, Providence, USA 02912;Lefschetz Center for Dynamical Systems, Brown University, Providence, USA 02912;Lefschetz Center for Dynamical Systems, Brown University, Providence, USA 02912
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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Simulation of a Jackson tandem network using state-dependent importance sampling

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Importance sampling for Jackson networks

Queueing Systems: Theory and Applications
Efficient calculation of rare event probabilities in Markovian queueing networks

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On Lyapunov Inequalities and Subsolutions for Efficient Importance Sampling

ACM Transactions on Modeling and Computer Simulation (TOMACS)
Rare event simulation techniques

Proceedings of the Winter Simulation Conference
Efficient importance sampling schemes for a feed-forward network

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New efficient estimators in rare event simulation with heavy tails

Journal of Computational and Applied Mathematics

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Abstract

We consider a variant of the two-node tandem Jackson network where the upstream server reduces its service rate when the downstream queue exceeds some prespecified threshold. The rare event of interest is the overflow of the downstream queue. Based on a game/subsolution approach, we rigorously identify the exponential decay rate of the rare event probabilities and construct asymptotically optimal importance sampling schemes.