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

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 rareevent simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jackson twonode 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 importancesampling 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 largedeviations theory. (iii) Our method for proving asymptotic efficiency is substantially more straightforward than some that have been used earlier.
Original languageUndefined
Title of host publicationProceedings of the 3rd International Workshop on Tools for Solving Structured Markov Chains, SMCTools 2008
PublisherICST
Pages1-9
Number of pages9
ISBN (Print)978-963-9799-31-8
DOIs
Publication statusPublished - 2008
Event3rd International Workshop on Tools for Solving Structured Markov Chains, SMCTools 2008 - Athens, Greece
Duration: 20 Oct 200824 Oct 2008

Publication series

Name
PublisherInstitute for Computer Sciences, Social-Informatics and Telecommunications Engineering (ICST)

Workshop

Workshop3rd International Workshop on Tools for Solving Structured Markov Chains, SMCTools 2008
Period20/10/0824/10/08
Other20-24 October 2008

Keywords

  • EWI-14674
  • METIS-255425
  • IR-65242

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