IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v27y2025i1d10.1007_s11009-025-10145-x.html
   My bibliography  Save this article

On a Balking M/G/1 Queue with General Differentiated Vacations

Author

Listed:
  • Abdoun Sylia

    (RIIMA Laboratory, University of Science and Technology Houari Boumediene USTHB)

  • Taleb Samira

    (RIIMA Laboratory, University of Science and Technology Houari Boumediene USTHB)

Abstract

This paper focuses on analyzing a balking M/G/1 queue with general differentiated vacations. The server can take two types of vacations, each with a general distribution. We establish the stability condition for the model and employ the supplementary variable technique to derive the probability generating functions. Furthermore, we determine the distribution of the number of customers in the system, waiting time, and sojourn time. Additionally, we present the performance measures of the model. To examine customers’ behavior in the fully unobservable scenario, we conduct a game-theoretic analysis and derive optimal individual Nash equilibrium and socially optimal equilibrium strategies. Through numerical experiments, we investigate the impact of various system parameters on performance measures, individual and social optimal equilibrium mixed strategies, social benefit, throughput, and the price of anarchy. These experiments provide valuable insights into how different factors influence the system performance and efficiency.

Suggested Citation

  • Abdoun Sylia & Taleb Samira, 2025. "On a Balking M/G/1 Queue with General Differentiated Vacations," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-32, March.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-025-10145-x
    DOI: 10.1007/s11009-025-10145-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-025-10145-x
    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/s11009-025-10145-x?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. Ghosh, Souvik & Hassin, Refael, 2021. "Inefficiency in stochastic queueing systems with strategic customers," European Journal of Operational Research, Elsevier, vol. 295(1), pages 1-11.
    2. Priyanka Kalita & Dharmaraja Selvamuthu, 2023. "Stochastic modelling of sleeping strategy in 5G base station for energy efficiency," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 83(2), pages 115-133, June.
    3. Preetjot Kaur & Roopali Garg & Vinay Kukreja, 2023. "Energy-efficiency schemes for base stations in 5G heterogeneous networks: a systematic literature review," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 84(1), pages 115-151, September.
    4. M. I. G. Suranga Sampath & K. Kalidass & Jicheng Liu, 2020. "Transient Analysis of an M/M/1 Queueing System Subjected to Multiple Differentiated Vacations, Impatient Customers and a Waiting Server with Application to IEEE 802.16E Power Saving Mechanism," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 297-320, March.
    5. Srinagesh Gavirneni & Vidyadhar G. Kulkarni, 2016. "Self-Selecting Priority Queues with Burr Distributed Waiting Costs," Production and Operations Management, Production and Operations Management Society, vol. 25(6), pages 979-992, June.
    6. Kerner, Yoav, 2011. "Equilibrium joining probabilities for an M/G/1 queue," Games and Economic Behavior, Elsevier, vol. 71(2), pages 521-526, March.
    7. Yu Zhang & Jinting Wang, 2023. "Effectiveness, fairness and social welfare maximization: service rules for the interrupted secondary users in cognitive radio networks," Annals of Operations Research, Springer, vol. 323(1), pages 247-286, April.
    8. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, June.
    9. V. Deepa & M. Haridass & Dharmaraja Selvamuthu & Priyanka Kalita, 2023. "Analysis of energy efficiency of small cell base station in 4G/5G networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 82(3), pages 381-401, March.
    10. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    11. Sun, Wei & Zhang, Zhiyuan & Xie, Xumeng & Li, Shiyong, 2024. "Heterogeneity of delay information and revenue-cost structure in a multi-server queue with threshold policy: Customer behaviors and optimization," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    12. Liuqing He & Ruiling Tian & Yunna Han & Xinyu Wu, 2024. "Optimal joining strategies in a repairable retrial queue with reserved time and N-policy," Operational Research, Springer, vol. 24(1), pages 1-22, March.
    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. Sylia Abdoun & Samira Taleb, 2025. "Efficiency of a markovian queue with non homogeneous vacations and strategic customers under partial vacation interruption," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 88(2), pages 1-18, June.
    2. 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.
    3. 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.
    4. Dieter Fiems & Koen Turck, 2025. "The delay-energy trade-off for advanced sleep modes in radio access networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 88(1), pages 1-8, March.
    5. Zhao, Chen & Wang, Zhongbin, 2023. "The impact of line-sitting on a two-server queueing system," European Journal of Operational Research, Elsevier, vol. 308(2), pages 782-800.
    6. Athanasia Manou & Antonis Economou & Fikri Karaesmen, 2014. "Strategic Customers in a Transportation Station: When Is It Optimal to Wait?," Operations Research, INFORMS, vol. 62(4), pages 910-925, August.
    7. Benjamin Legros, 2021. "Agents’ Self‐Routing for Blended Operations to Balance Inbound and Outbound Services," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3599-3614, October.
    8. 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).
    9. Jake Clarkson & Konstantin Avrachenkov & Eitan Altman, 2025. "Queues with inspection cost: To see or not to see?," Queueing Systems: Theory and Applications, Springer, vol. 109(2), pages 1-34, June.
    10. 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.
    11. Zhongbin Wang & Luyi Yang & Shiliang Cui & Jinting Wang, 2021. "In-queue priority purchase: a dynamic game approach," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 343-381, April.
    12. Luyi Yang & Zhongbin Wang & Shiliang Cui, 2021. "A Model of Queue Scalping," Management Science, INFORMS, vol. 67(11), pages 6803-6821, November.
    13. Moshe Haviv & Binyamin Oz, 2021. "A busy period approach to some queueing games," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 261-277, April.
    14. Oz, Binyamin & Adan, Ivo & Haviv, Moshe, 2019. "The Mn/Gn/1 queue with vacations and exhaustive service," European Journal of Operational Research, Elsevier, vol. 277(3), pages 945-952.
    15. İşlier, Zeynep Gökçe & Güllü, Refik, 2024. "On strategic customers with correlated utility attributes: Effects and information benefits," European Journal of Operational Research, Elsevier, vol. 313(1), pages 258-269.
    16. Luyi Yang & Shiliang Cui & Zhongbin Wang, 2022. "Design of Covid‐19 testing queues," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2204-2221, May.
    17. R. Harini & K. Indhira, 2024. "Dynamical modelling and cost optimization of a 5G base station for energy conservation using feedback retrial queue with sleeping strategy," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 86(4), pages 661-690, August.
    18. Chai, Xudong & Jiang, Tao & Chang, Baoxian & Liu, Liwei, 2021. "On a multiple priorities matching system with heterogeneous delay sensitive individuals," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    19. Refael Hassin & Yair Y. Shaki & Uri Yovel, 2015. "Optimal service‐capacity allocation in a loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 81-97, March.
    20. A. Mohammed Shapique & R. Sudhesh & S. Dharmaraja, 2024. "Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-33, September.

    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:27:y:2025:i:1:d:10.1007_s11009-025-10145-x. 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.