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Importance sampling for non-Markovian tandem queues using subsolutions

Author

Listed:
  • Anne Buijsrogge

    (University of Twente)

  • Pieter-Tjerk Boer

    (University of Twente)

  • Werner R. W. Scheinhardt

    (University of Twente)

Abstract

In this paper, we use importance sampling simulation to estimate the probability that the number of customers in a d-node GI|GI|1 tandem queue reaches some high level N in a busy cycle of the system. We present a state-dependent change of measure for a d-node GI|GI|1 tandem queue based on the subsolution approach, and we prove, under a mild conjecture, that this state-dependent change of measure gives an asymptotically efficient estimator for the probability of interest when all supports are bounded.

Suggested Citation

  • Anne Buijsrogge & Pieter-Tjerk Boer & Werner R. W. Scheinhardt, 2019. "Importance sampling for non-Markovian tandem queues using subsolutions," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 31-65, October.
    • Handle: RePEc:spr:queues:v:93:y:2019:i:1:d:10.1007_s11134-019-09623-0
    DOI: 10.1007/s11134-019-09623-0
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    References listed on IDEAS

    as
    1. Dean, Thomas & Dupuis, Paul, 2009. "Splitting for rare event simulation: A large deviation approach to design and analysis," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 562-587, February.
    2. Paul Dupuis & Hui Wang, 2007. "Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 723-757, August.
    3. Anne Buijsrogge & Pieter-Tjerk Boer & Karol Rosen & Werner Scheinhardt, 2017. "Large deviations for the total queue size in non-Markovian tandem queues," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 305-312, April.
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