IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i2d10.1007_s11009-023-10029-y.html
   My bibliography  Save this article

Equilibrium Joining Strategies in the Retrial Queue with Two Classes of Customers and Delayed Vacations

Author

Listed:
  • Xianyue Shi

    (Nanjing University of Science and Technology)

  • Liwei Liu

    (Nanjing University of Science and Technology)

Abstract

We consider a non-preemptive priority M/M/1 retrial queue with two classes of customers (low-priority and high-priority customers) and delayed vacations. When the server is unavailable, an arriving high-priority customer can wait in line, whereas an arriving low-priority customer needs to enter a virtual queue and retry later. After completing a service, the server will remain idle for a reserved idle time if it finds no high-priority customers in the system. Arrivals during the reserved idle period will be served immediately. Otherwise, if no customers arrive during this interval, the server will switch to the vacation state. By constructing a three-dimensional Markov chain, we successively obtain the stability condition of the system and some main performance measures. Then depending on a linear reward-cost structure, we derive customers’ two-dimensional equilibrium joining strategies in the fully unobservable case. Due to the complexity of the social welfare function, we explore the socially optimal joining strategies through the Particle Swarm Optimization (PSO) algorithm. Finally, we illustrate the impact of system parameters on the two types of joining strategies via numerical experiments.

Suggested Citation

  • Xianyue Shi & Liwei Liu, 2023. "Equilibrium Joining Strategies in the Retrial Queue with Two Classes of Customers and Delayed Vacations," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10029-y
    DOI: 10.1007/s11009-023-10029-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-10029-y
    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/s11009-023-10029-y?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. Ziani, Sofiane & Rahmoune, Fazia & Radjef, Mohammed Said, 2015. "Customers’ strategic behavior in batch arrivals M2/M/1 queue," European Journal of Operational Research, Elsevier, vol. 247(3), pages 895-903.
    2. Antonis Economou & Spyridoula Kanta, 2011. "Equilibrium customer strategies and social–profit maximization in the single‐server constant retrial queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 107-122, March.
    3. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    4. Hung Q. Nguyen & Tuan Phung-Duc, 2022. "Strategic customer behavior and optimal policies in a passenger–taxi double-ended queueing system with multiple access points and nonzero matching times," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 481-508, December.
    5. Ioannis Dimitriou, 2022. "Stationary analysis of certain Markov-modulated reflected random walks in the quarter plane," Annals of Operations Research, Springer, vol. 310(2), pages 355-387, March.
    6. Bountali, Olga & Economou, Antonis, 2017. "Equilibrium joining strategies in batch service queueing systems," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1142-1151.
    7. Wang, Jinting & Zhang, Xuelu & Huang, Ping, 2017. "Strategic behavior and social optimization in a constant retrial queue with the N-policy," European Journal of Operational Research, Elsevier, vol. 256(3), pages 841-849.
    8. Bara Kim & Jeongsim Kim, 2017. "Waiting time distributions in an M/G/1 retrial queue with two classes of customers," Annals of Operations Research, Springer, vol. 252(1), pages 121-134, May.
    9. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    10. Amita Bhagat & Madhu Jain, 2020. "Retrial queue with multiple repairs, multiple services and non preemptive priority," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 787-814, September.
    11. Guo, Pengfei & Hassin, Refael, 2012. "Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 222(2), pages 278-286.
    12. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lingjiao Zhang & Jinting Wang & Yilin Wang, 2023. "Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-29, December.

    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. Zhen Wang & Liwei Liu & Yiqiang Q. Zhao, 2022. "Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and N-policy," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 870-908, May.
    2. Opher Baron & Antonis Economou & Athanasia Manou, 2022. "Increasing social welfare with delays: Strategic customers in the M/G/1 orbit queue," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2907-2924, July.
    3. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.
    4. Bountali, Olga & Economou, Antonis, 2017. "Equilibrium joining strategies in batch service queueing systems," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1142-1151.
    5. Shan Gao & Hua Dong & Xianchao Wang, 2021. "Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation," Operational Research, Springer, vol. 21(1), pages 621-643, March.
    6. Wang, Jinting & Zhang, Feng, 2013. "Strategic joining in M/M/1 retrial queues," European Journal of Operational Research, Elsevier, vol. 230(1), pages 76-87.
    7. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).
    8. Zhongbin Wang & Yunan Liu & Lei Fang, 2022. "Pay to activate service in vacation queues," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2609-2627, June.
    9. Apostolos Burnetas & Antonis Economou & George Vasiliadis, 2017. "Strategic customer behavior in a queueing system with delayed observations," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 389-418, August.
    10. Economou, Antonis & Logothetis, Dimitrios & Manou, Athanasia, 2022. "The value of reneging for strategic customers in queueing systems with server vacations/failures," European Journal of Operational Research, Elsevier, vol. 299(3), pages 960-976.
    11. Ziani, Sofiane & Rahmoune, Fazia & Radjef, Mohammed Said, 2015. "Customers’ strategic behavior in batch arrivals M2/M/1 queue," European Journal of Operational Research, Elsevier, vol. 247(3), pages 895-903.
    12. Lingjiao Zhang & Jinting Wang & Yilin Wang, 2023. "Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-29, December.
    13. Gopinath Panda & Veena Goswami & Abhijit Datta Banik, 2016. "Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-34, October.
    14. Qingqing Ma & Yiqiang Q. Zhao & Weiqi Liu & Jihong Li, 2019. "Customer Strategic Joining Behavior in Markovian Queues with Working Vacations and Vacation Interruptions Under Bernoulli Schedule," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-26, February.
    15. Lan Lu & Zheng Zhu & Pengfei Guo & Qiao‐Chu He, 2022. "Service Operations for Mixed Autonomous Paradigm: Lane Design and Subsidy," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1595-1612, April.
    16. Wang, Jinting & Zhang, Xuelu & Huang, Ping, 2017. "Strategic behavior and social optimization in a constant retrial queue with the N-policy," European Journal of Operational Research, Elsevier, vol. 256(3), pages 841-849.
    17. Olga Boudali & Antonis Economou, 2013. "The effect of catastrophes on the strategic customer behavior in queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(7), pages 571-587, October.
    18. Dimitrakopoulos, Y. & Burnetas, A.N., 2016. "Customer equilibrium and optimal strategies in an M/M/1 queue with dynamic service control," European Journal of Operational Research, Elsevier, vol. 252(2), pages 477-486.
    19. Olga Bountali & Antonis Economou, 2019. "Equilibrium threshold joining strategies in partially observable batch service queueing systems," Annals of Operations Research, Springer, vol. 277(2), pages 231-253, June.
    20. Bu, Qihui & Sun, Yun & Chai, Xudong & Liu, Liwei, 2020. "Strategic behavior and social optimization in a clearing queueing system with N-policy and stochastic restarting scheme," Applied Mathematics and Computation, Elsevier, vol. 381(C).

    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:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10029-y. 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.