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Customers' Optimal Joining Rules for the GI/M/s Queue

Author

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  • Uri Yechiali

    (Tel-Aviv University)

Abstract

A GI/M/s queue with a stationary balking sequence is considered. For the infinite horizon average reward criterion, it is shown that among all stationary joining policies the optimal ones are nonrandomized control limit rules of the form: join if and only if the queue size is smaller than some specific number. It is shown that, in general, exercising self-optimization by individual customers does not optimize public good. The M/M/s queue is then treated as an example, and a "direct" proof for the optimality of the control limit rule is given.

Suggested Citation

  • Uri Yechiali, 1972. "Customers' Optimal Joining Rules for the GI/M/s Queue," Management Science, INFORMS, vol. 18(7), pages 434-443, March.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:7:p:434-443
    DOI: 10.1287/mnsc.18.7.434
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    Cited by:

    1. Radhakrishnan, Suresh & Balachandran, Kashi R., 1995. "Stochastic choice hazard and incentives in a common service facility," European Journal of Operational Research, Elsevier, vol. 81(2), pages 324-335, March.
    2. 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).
    3. Prabhudev Konana & Alok Gupta & Andrew B. Whinston, 2000. "Integrating User Preferences and Real-Time Workload in Information Services," Information Systems Research, INFORMS, vol. 11(2), pages 177-196, June.
    4. Tingliang Huang & Gad Allon & Achal Bassamboo, 2013. "Bounded Rationality in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 263-279, May.
    5. Ivo J. B. F. Adan & Onno J. Boxma & Stella Kapodistria & Vidyadhar G. Kulkarni, 2016. "The shorter queue polling model," Annals of Operations Research, Springer, vol. 241(1), pages 167-200, June.
    6. Shiliang Cui & Xuanming Su & Senthil Veeraraghavan, 2019. "A Model of Rational Retrials in Queues," Operations Research, INFORMS, vol. 67(6), pages 1699-1718, November.
    7. Refael Hassin & Ran I. Snitkovsky, 2020. "Social and Monopoly Optimization in Observable Queues," Operations Research, INFORMS, vol. 68(4), pages 1178-1198, July.
    8. Zhang, Zhe George & Yin, Xiaoling, 2021. "Information and pricing effects in two-tier public service systems," International Journal of Production Economics, Elsevier, vol. 231(C).
    9. Philipp Afèche & Haim Mendelson, 2004. "Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure," Management Science, INFORMS, vol. 50(7), pages 869-882, July.
    10. Eitan Altman & Nahum Shimkin, 1998. "Individual Equilibrium and Learning in Processor Sharing Systems," Operations Research, INFORMS, vol. 46(6), pages 776-784, December.
    11. Knight, Vincent A. & Harper, Paul R., 2013. "Selfish routing in public services," European Journal of Operational Research, Elsevier, vol. 230(1), pages 122-132.
    12. Chia-Li Wang, 2016. "On Socially Optimal Queue Length," Management Science, INFORMS, vol. 62(3), pages 899-903, March.
    13. Canbolat, Pelin G., 2020. "Bounded rationality in clearing service systems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 614-626.
    14. A C Brooms & E J Collins, 2013. "Stochastic Order Results and Equilibrium Joining Rules for the Bernoulli Feedback Queue," Birkbeck Working Papers in Economics and Finance 1305, Birkbeck, Department of Economics, Mathematics & Statistics.
    15. van Ackere, Ann, 1996. "The management of congestion," European Journal of Operational Research, Elsevier, vol. 89(2), pages 223-225, March.
    16. 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.
    17. Gabi Hanukov & Shoshana Anily & Uri Yechiali, 2020. "Ticket queues with regular and strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 145-171, June.
    18. Yarlin Kuo, 2008. "Admission control of a service station when the arrivals are internal," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 285-297, April.
    19. Shone, Rob & Knight, Vincent A. & Williams, Janet E., 2013. "Comparisons between observable and unobservable M/M/1 queues with respect to optimal customer behavior," European Journal of Operational Research, Elsevier, vol. 227(1), pages 133-141.
    20. Shu Zhang & Jeffrey W. Ohlmann & Barrett W. Thomas, 2018. "Dynamic Orienteering on a Network of Queues," Transportation Science, INFORMS, vol. 52(3), pages 691-706, June.
    21. Zhang, Shu & Ohlmann, Jeffrey W. & Thomas, Barrett W., 2014. "A priori orienteering with time windows and stochastic wait times at customers," European Journal of Operational Research, Elsevier, vol. 239(1), pages 70-79.

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