State-dependent importance sampling for a Jackson tandem network

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

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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.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty of Mathematical Sciences
Number of pages31
Publication statusPublished - May 2008

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherDepartment of Applied Mathematics, University of Twente
No.274/1867
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • EWI-12734
  • METIS-250977
  • IR-64760

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