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

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

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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 Jackson 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 is provably 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. Keywords: Rare event simulation, importance sampling, state-dependent change of measure, asymptotic optimality, tandem queue
Original languageEnglish
Title of host publication3rd International ICST Conference on Performance Evaluation Methodologies and Tools
PublisherAssociation for Computing Machinery, Inc
ISBN (Print)978-963-9799-31-8
Publication statusPublished - 2008


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