IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v93y2019i1d10.1007_s11134-019-09623-0.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-019-09623-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-019-09623-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hult, Henrik & Nyquist, Pierre, 2016. "Large deviations for weighted empirical measures arising in importance sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 138-170.
    2. Thomas Dean & Paul Dupuis, 2011. "The design and analysis of a generalized RESTART/DPR algorithm for rare event simulation," Annals of Operations Research, Springer, vol. 189(1), pages 63-102, September.
    3. Fatma Başoğlu Kabran & Ali Devin Sezer, 2022. "Approximation of the exit probability of a stable Markov modulated constrained random walk," Annals of Operations Research, Springer, vol. 310(2), pages 431-475, March.
    4. Ad Ridder & Thomas Taimre, 2011. "State-dependent importance sampling schemes via minimum cross-entropy," Annals of Operations Research, Springer, vol. 189(1), pages 357-388, September.
    5. Paul Dupuis & Kevin Leder & Hui Wang, 2009. "Importance Sampling for Weighted-Serve-the-Longest-Queue," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 642-660, August.
    6. Kleijnen, Jack P.C. & Ridder, A.A.N. & Rubinstein, R.Y., 2010. "Variance Reduction Techniques in Monte Carlo Methods," Other publications TiSEM 87680d1a-53c1-4107-ada4-7, Tilburg University, School of Economics and Management.
    7. Zdravko I. Botev & Pierre L’Ecuyer, 2020. "Sampling Conditionally on a Rare Event via Generalized Splitting," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 986-995, October.
    8. Blanchet, Jose & Lam, Henry & Zwart, Bert, 2012. "Efficient rare-event simulation for perpetuities," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3361-3392.
    9. Jose Blanchet, 2013. "Optimal Sampling of Overflow Paths in Jackson Networks," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 698-719, November.
    10. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    11. Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.
    12. Amarjit Budhiraja & Shu Lu & Yang Yu & Quoc Tran-Dinh, 2021. "Minimization of a class of rare event probabilities and buffered probabilities of exceedance," Annals of Operations Research, Springer, vol. 302(1), pages 49-83, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:queues:v:93:y:2019:i:1:d:10.1007_s11134-019-09623-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.