IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v310y2022i2d10.1007_s10479-020-03830-2.html
   My bibliography  Save this article

Delay analysis of a discrete-time single-server queue with an occasional extra server

Author

Listed:
  • Freek Verdonck

    (Ghent University (UGent))

  • Herwig Bruneel

    (Ghent University (UGent))

  • Sabine Wittevrongel

    (Ghent University (UGent))

Abstract

In this work we look at the delay analysis of a customer in a discrete-time queueing system with one permanent server and one occasional extra server. The arrival process is assumed to be general independent, the buffer size infinite and the service times deterministically equal to one slot. The system is assumed to be in one of two different states; during the UP-state 2 servers are available and during the DOWN-state 1 server is available. State changes can only occur at slot boundaries and mark the beginnings and ends of UP-periods and DOWN-periods. The lengths of the UP-periods, expressed in their number of slots, are assumed to follow a geometric distribution, while the lengths of the DOWN-periods follow a general distribution with rational probability generating function. We provide a method to compute the tail characteristics of the delay of an arbitrary customer based on the theory of the dominant singularity. We illustrate the developed method with several numerical examples.

Suggested Citation

  • Freek Verdonck & Herwig Bruneel & Sabine Wittevrongel, 2022. "Delay analysis of a discrete-time single-server queue with an occasional extra server," Annals of Operations Research, Springer, vol. 310(2), pages 551-575, March.
    • Handle: RePEc:spr:annopr:v:310:y:2022:i:2:d:10.1007_s10479-020-03830-2
    DOI: 10.1007/s10479-020-03830-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03830-2
    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/s10479-020-03830-2?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. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    2. Moeko Yajima & Tuan Phung-Duc, 2017. "Batch arrival single-server queue with variable service speed and setup time," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 241-260, August.
    3. 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.
    4. Vinck, Bart & Bruneel, Herwig, 2006. "System delay versus system content for discrete-time queueing systems subject to server interruptions," European Journal of Operational Research, Elsevier, vol. 175(1), pages 362-375, November.
    5. Laevens, Koenraad & Bruneel, Herwig, 1995. "Delay analysis for discrete-time queueing systems with multiple randomly interrupted servers," European Journal of Operational Research, Elsevier, vol. 85(1), pages 161-177, 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. Sheng Zhu & Jinting Wang & Bin Liu, 2020. "Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs," Operational Research, Springer, vol. 20(4), pages 2163-2187, December.
    2. Freek Verdonck & Herwig Bruneel & Sabine Wittevrongel, 2021. "Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals," Mathematics, MDPI, vol. 9(14), pages 1-17, July.
    3. Michiel Muynck & Sabine Wittevrongel & Herwig Bruneel, 2017. "Analysis of discrete-time queues with general service demands and finite-support service capacities," Annals of Operations Research, Springer, vol. 252(1), pages 3-28, May.
    4. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    5. KM Rashmi & S. K. Samanta, 2024. "Analysis of Two-Way Communication in $$M_1^X, M_2/G_1,G_2/1$$ M 1 X , M 2 / G 1 , G 2 / 1 Retrial Queue Under the Constant Retrial Policy," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-32, December.
    6. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    7. 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.
    8. 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.
    9. Yusei Koyama & Ayane Nakamura & Tuan Phung-Duc, 2024. "Sojourn Time Analysis of a Single-Server Queue with Single- and Batch-Service Customers," Mathematics, MDPI, vol. 12(18), pages 1-27, September.
    10. Opher Baron & Antonis Economou & Athanasia Manou, 2018. "The state-dependent M / G / 1 queue with orbit," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 89-123, October.
    11. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.
    12. H. Bruneel & W. Rogiest & J. Walraevens & S. Wittevrongel, 2015. "Analysis of a discrete-time queue with general independent arrivals, general service demands and fixed service capacity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 285-315, December.
    13. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    14. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    15. Paola Cappanera & Filippo Visintin & Carlo Banditori & Daniele Feo, 2019. "Evaluating the long-term effects of appointment scheduling policies in a magnetic resonance imaging setting," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 212-254, March.
    16. Zamani, Shokufeh & Arkat, Jamal & Niaki, Seyed Taghi Akhavan, 2022. "Service interruption and customer withdrawal in the congested facility location problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    17. Herwig Bruneel & Sabine Wittevrongel & Dieter Claeys & Joris Walraevens, 2016. "Discrete-time queues with variable service capacity: a basic model and its analysis," Annals of Operations Research, Springer, vol. 239(2), pages 359-380, April.
    18. Dieter Claeys & Stijn De Vuyst, 2019. "Discrete-time modified number- and time-limited vacation queues," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 297-318, April.
    19. Maertens, Tom & Walraevens, Joris & Bruneel, Herwig, 2007. "A modified HOL priority scheduling discipline: Performance analysis," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1168-1185, August.
    20. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, 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:annopr:v:310:y:2022:i:2:d:10.1007_s10479-020-03830-2. 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.