State-dependent importance sampling for a Jackson tandem network

D.I. Miretskiy, W.R.W. Scheinhardt, M.R.H. Mandjes

Onderzoeksoutput: Boek/rapportRapportAcademic


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’ stateindependent 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.
Originele taal-2Engels
Plaats van productieAmsterdam
UitgeverijCentrum voor Wiskunde en Informatica
Aantal pagina's31
StatusGepubliceerd - 2008

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