State-dependent importance sampling for a Jackson tandem network


Miretskiy, Denis and Scheinhardt, Werner and Mandjes, Michel (2010) State-dependent importance sampling for a Jackson tandem network. ACM Transactions on Modeling and Computer Simulation, 20 (3). p. 15. ISSN 1049-3301

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Abstract: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 istribution 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.
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Copyright:© 2010 ACM
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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