Dynamic importance sampling for queueing networks

Details Dynamic importance sampling for queueing networks Dynamic importance sampling for queueing networks

2007-10-24

arxiv.org/abs/0710.4389v1

Annals of Applied Probability 2007, Vol. 17, No. 4, 1306-1346

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/105051607000000122 the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051607000000122

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The standard approach, which simulates the system using an a priori fixed change of measure suggested by large deviation analysis, has been shown to fail in even the simplest network setting (e.g., a two-node tandem network). Exploiting connections between importance sampling, differential games, and classical subsolutions of the corresponding Isaacs equation, we show how to design and analyze simple and efficient dynamic importance sampling schemes for general classes of networks. The models used to illustrate the approach include $d$-node tandem Jackson networks and a two-node network with feedback, and the rare events studied are those of large queueing backlogs, including total population overflow and the overflow of individual buffers.

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