On state-independent importance sampling for the GI|GI|1 tandem queue

Anne Buijsrogge* (Corresponding Author), Pieter-Tjerk de Boer, Willem R.W. Scheinhardt

*Corresponding author for this work

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Abstract

In this paper, we consider a d-node GI|GI|1 tandem queue with i.i.d. inter-arrival process and service processes that are independent of each other. Our main interest is to estimate the probability to reach a high level N in a busy cycle of the system using simulation. As crude simulation does not give a sufficient precision in reasonable time, we use importance sampling. We introduce a method to find a state-independent change of measure and we show that this is equivalent to a change of measure that was earlier, but implicitly, described by Parekh and Walrand [8]. We also show that this change of measure is the only exponential state-independent change of measure that may result in an asymptotically efficient estimator. Lastly, we provide necessary conditions for this state-independent change of measure to give an asymptotically efficient estimator.
Original languageEnglish
Pages (from-to)131-156
Number of pages26
JournalProbability in the engineering and informational sciences
Volume34
Issue number1
DOIs
Publication statusPublished - 5 Nov 2018

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Keywords

  • UT-Hybrid-D
  • Tandem queue
  • Rare event simulation
  • Importance sampling
  • GI|GI|1 queue

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