IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v252y2017i1d10.1007_s10479-015-2049-4.html
   My bibliography  Save this article

Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance

Author

Listed:
  • Bart Steyaert

    (Ghent University - UGent)

  • Sabine Wittevrongel

    (Ghent University - UGent)

  • Herwig Bruneel

    (Ghent University - UGent)

Abstract

In this paper we use the burst factor of a packet stream, which is defined in a general setting, to quantify the long-term variability, or burstiness, of such a stream. We briefly review some existing results to show that this parameter plays an important role in the performance assessment and dimensioning of buffers in network nodes, even in a non-Markovian setting. We then focus on the calculation of this parameter at the egress of a discrete-time GI / D / 1 queueing system, considering different routing scenarios, and show how it can be expressed in terms of the parameters that characterise the arrival process in such a queue. In addition, we demonstrate how these results can be applied to evaluate the buffer performance in the subsequent nodes of a network. The analytic results that are derived throughout this paper are supported by simulations.

Suggested Citation

  • Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2017. "Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance," Annals of Operations Research, Springer, vol. 252(1), pages 175-190, May.
    • Handle: RePEc:spr:annopr:v:252:y:2017:i:1:d:10.1007_s10479-015-2049-4
    DOI: 10.1007/s10479-015-2049-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-015-2049-4
    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/s10479-015-2049-4?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. Bruneel, Herwig & Steyaert, Bart & Desmet, Emmanuel & Petit, Guido H., 1994. "Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues," European Journal of Operational Research, Elsevier, vol. 76(3), pages 563-572, August.
    2. Joseph Abate & Gagan L. Choudhury & Ward Whitt, 1995. "Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times," Operations Research, INFORMS, vol. 43(5), pages 885-901, October.
    3. Masuyama, Hiroyuki, 2011. "Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains," European Journal of Operational Research, Elsevier, vol. 213(3), pages 509-516, September.
    4. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    5. Joseph Abate & Gagan L. Choudhury & Ward Whitt, 1996. "Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload," Operations Research, INFORMS, vol. 44(5), pages 758-763, October.
    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. Gad Allon & Awi Federgruen, 2008. "Service Competition with General Queueing Facilities," Operations Research, INFORMS, vol. 56(4), pages 827-849, August.
    2. So, Kut C. & Song, Jing-Sheng, 1998. "Price, delivery time guarantees and capacity selection," European Journal of Operational Research, Elsevier, vol. 111(1), pages 28-49, November.
    3. Asmussen, Søren & Klüppelberg, Claudia & Sigman, Karl, 1999. "Sampling at subexponential times, with queueing applications," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 265-286, February.
    4. Jalili Marand, Ata & Li, Hongyan & Thorstenson, Anders, 2019. "Joint inventory control and pricing in a service-inventory system," International Journal of Production Economics, Elsevier, vol. 209(C), pages 78-91.
    5. Søren Asmussen & Colm O'cinneide, 2002. "On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue," Operations Research, INFORMS, vol. 50(3), pages 559-565, June.
    6. Avishai Mandelbaum & Petar Momčilović, 2017. "Personalized queues: the customer view, via a fluid model of serving least-patient first," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 23-53, October.
    7. Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
    8. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    9. Josh Reed & Yair Shaki, 2015. "A Fair Policy for the G / GI / N Queue with Multiple Server Pools," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 558-595, March.
    10. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    11. S. Pradhan & U.C. Gupta & S.K. Samanta, 2016. "Queue-length distribution of a batch service queue with random capacity and batch size dependent service: M / G r Y / 1 $M/{G^{Y}_{r}}/1$," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 329-343, June.
    12. Achal Bassamboo & Assaf Zeevi, 2009. "On a Data-Driven Method for Staffing Large Call Centers," Operations Research, INFORMS, vol. 57(3), pages 714-726, June.
    13. Jalili Marand, Ata & Tang, Ou & Li, Hongyan, 2019. "Quandary of service logistics: Fast or reliable?," European Journal of Operational Research, Elsevier, vol. 275(3), pages 983-996.
    14. Ari Arapostathis & Hassan Hmedi & Guodong Pang, 2021. "On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 772-796, May.
    15. van Leeuwaarden, Johan S.H. & Knessl, Charles, 2011. "Transient behavior of the Halfin-Whitt diffusion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1524-1545, July.
    16. Ramandeep S. Randhawa & Sunil Kumar, 2008. "Usage Restriction and Subscription Services: Operational Benefits with Rational Users," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 429-447, December.
    17. Jianpei Wen & Hanyu Jiang & Jie Song, 2019. "A Stochastic Queueing Model for Capacity Allocation in the Hierarchical Healthcare Delivery System," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-24, February.
    18. Martino Banchio & Giacomo Mantegazza, 2022. "Artificial Intelligence and Spontaneous Collusion," Papers 2202.05946, arXiv.org, revised Sep 2023.
    19. Zhang, Ping & Serban, Nicoleta, 2007. "Discovery, visualization and performance analysis of enterprise workflow," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2670-2687, February.
    20. Hsiao-Hui Lee & Edieal J. Pinker & Robert A. Shumsky, 2012. "Outsourcing a Two-Level Service Process," Management Science, INFORMS, vol. 58(8), pages 1569-1584, August.

    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:annopr:v:252:y:2017:i:1:d:10.1007_s10479-015-2049-4. 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.