State-dependent importance sampling for a Jackson tandem network


Miretskiy, D.I. and Scheinhardt, W.R.W. and Mandjes, M.R.H. (2008) State-dependent importance sampling for a Jackson tandem network. [Report]

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Abstract:This paper 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 distribution 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) Our method for proving asymptotic efficiency is substantially more straightforward than some that have been used earlier. The paper is concluded by simulation experiments that show a considerable speed up.
Item Type:Report
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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