IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3535-d1218143.html
   My bibliography  Save this article

On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals

Author

Listed:
  • Alexandra Borodina

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185035 Petrozavodsk, Russia
    These authors contributed equally to this work.)

  • Vladimir Mazalov

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185035 Petrozavodsk, Russia
    These authors contributed equally to this work.)

Abstract

This paper considers a callback single-server system with an orbit and a First-Come First-Served (FCFS) service discipline. Customers (users, clients) that encounter a busy server are sent into orbit and then have the option to retry service after an exponential period of time. In addition, each customer entering the system uses a strategy and must independently decide when to arrive in the system within a fixed admission period of time so that the expected sojourn time is minimal. We interpret the arrival process as a Nash equilibrium solution of a noncooperative game when the arrival intensity is completely described by an unknown distribution function, and then we propose a way to find an equilibrium for the case when the client’s waiting time for service is obviously limited. The analytical solution for the equilibrium is illustrated numerically for two-person and three-person games.

Suggested Citation

  • Alexandra Borodina & Vladimir Mazalov, 2023. "On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3535-:d:1218143
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3535/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3535/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Julia Chirkova & Vladimir Mazalov & Evsey Morozov, 2022. "Equilibrium in a Queueing System with Retrials," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    2. Moshe Haviv, 2022. "Optimal timing of arrival to a queue," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 433-435, April.
    3. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    4. Glazer, Amihai & Hassin, Refael, 1983. "?/M/1: On the equilibrium distribution of customer arrivals," European Journal of Operational Research, Elsevier, vol. 13(2), pages 146-150, June.
    5. Moshe Haviv & Liron Ravner, 2021. "A survey of queueing systems with strategic timing of arrivals," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 163-198, 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. Jesper Breinbjerg & Trine Tornøe Platz & Lars Peter Østerdal, 2024. "Equilibrium arrivals to a last-come first-served preemptive-resume queue," Annals of Operations Research, Springer, vol. 336(3), pages 1551-1572, May.
    2. Liron Ravner & Jiesen Wang, 2023. "Estimating customer delay and tardiness sensitivity from periodic queue length observations," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 241-274, April.
    3. Moshe Haviv, 2022. "Optimal timing of arrival to a queue," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 433-435, April.
    4. Tzvi Alon & Moshe Haviv, 2023. "Choosing a batch to be processed," Annals of Operations Research, Springer, vol. 326(1), pages 67-87, July.
    5. Jesper Breinbjerg & Alexander Sebald & Lars Peter Østerdal, 2016. "Strategic behavior and social outcomes in a bottleneck queue: experimental evidence," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 207-236, September.
    6. Platz, Trine Tornøe & Østerdal, Lars Peter, 2017. "The curse of the first-in–first-out queue discipline," Games and Economic Behavior, Elsevier, vol. 104(C), pages 165-176.
    7. René Caldentey & Gustavo Vulcano, 2007. "Online Auction and List Price Revenue Management," Management Science, INFORMS, vol. 53(5), pages 795-813, May.
    8. Se Won Lee & Bara Kim & Jeongsim Kim, 2022. "Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication," Annals of Operations Research, Springer, vol. 310(2), pages 505-518, March.
    9. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2020. "Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 288(1), pages 417-434, May.
    10. Bin Liu & Jie Min & Yiqiang Q. Zhao, 2023. "Refined tail asymptotic properties for the $$M^X/G/1$$ M X / G / 1 retrial queue," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 65-105, June.
    11. Raina Raj & Vidyottama Jain, 2023. "Resource optimization in $$\textit{MMAP[2]/PH[2]/S}$$ MMAP [ 2 ] / PH [ 2 ] / S priority queueing model with threshold $$\textit{PH}$$ PH retrial times and the preemptive resume policy," Annals of Operations Research, Springer, vol. 331(2), pages 1119-1148, December.
    12. Alexander Dudin & Achyutha Krishnamoorthy & Sergei Dudin & Olga Dudina, 2024. "Queueing system with control by admission of retrial requests depending on the number of busy servers and state of the underlying process of Markov arrival process of primary requests," Annals of Operations Research, Springer, vol. 335(1), pages 135-150, April.
    13. Alessandro Arlotto & Andrew E. Frazelle & Yehua Wei, 2019. "Strategic Open Routing in Service Networks," Management Science, INFORMS, vol. 65(2), pages 735-750, February.
    14. Lamia Lakaour & Djamil Aïssani & Karima Adel-Aissanou & Kamel Barkaoui, 2019. "M/M/1 Retrial Queue with Collisions and Transmission Errors," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1395-1406, December.
    15. Breinbjerg, Jesper, 2017. "Equilibrium arrival times to queues with general service times and non-linear utility functions," European Journal of Operational Research, Elsevier, vol. 261(2), pages 595-605.
    16. Sandeep Juneja, 2022. "Learning the queue arrivals game equilibrium," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 533-535, April.
    17. Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
    18. Breinbjerg, Jesper & Østerdal, Lars Peter, 2017. "Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume," Discussion Papers on Economics 3/2017, University of Southern Denmark, Department of Economics.
    19. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2022. "Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1503-1518, September.
    20. Radhika Agarwal & Divya Agarwal & Shweta Upadhyaya & Izhar Ahmad, 2023. "Optimization of a stochastic model having erratic server with immediate or delayed repair," Annals of Operations Research, Springer, vol. 331(2), pages 605-628, December.

    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:gam:jmathe:v:11:y:2023:i:16:p:3535-:d:1218143. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.