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Equilibrium joining probabilities for an M/G/1 queue

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  • Kerner, Yoav

Abstract

We study the customers' Nash equilibrium behavior in a single server observable queue with Poisson arrivals and general service times. Each customer takes a single decision upon arrival: to join or not to join. Furthermore, future regrets are not allowed. The customers are homogenous with respect to their linear waiting cost and the reward associated with service completion. The cost of joining depends on the behavior of the other customers present, which naturally forms a strategic game. We present a recursive algorithm for computing the (possibly mixed) Nash equilibrium strategy. The algorithm's output is queue-dependent joining probabilities. We demonstrate that depending on the service distribution, this equilibrium is not necessarily unique. Also, we show that depending on the service time distribution, either the 'avoid the crowd' phenomenon or the 'follow the crowd' phenomenon may hold.

Suggested Citation

  • Kerner, Yoav, 2011. "Equilibrium joining probabilities for an M/G/1 queue," Games and Economic Behavior, Elsevier, vol. 71(2), pages 521-526, March.
    • Handle: RePEc:eee:gamebe:v:71:y:2011:i:2:p:521-526
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    References listed on IDEAS

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    1. Boxma, O. J., 1984. "Joint distribution of sojourn time and queue length in the M/G/1 queue with (in) finite capacity," European Journal of Operational Research, Elsevier, vol. 16(2), pages 246-256, May.
    2. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
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    Cited by:

    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. 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.
    3. Zhineng Hu & Shiyu Yan & Chengwei Lv & Liming Yao, 2019. "Sustainable development oriented bi-level dynamic programming method toward the coal–water conflict in China," Energy & Environment, , vol. 30(8), pages 1396-1436, December.
    4. 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.
    5. 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.
    6. 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).
    7. Yoav Kerner & Ophir Shmuel-Bittner, 2020. "Strategic behavior and optimization in a hybrid M/M/1 queue with retrials," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 285-302, December.
    8. 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.
    9. Refael Hassin & Ran I. Snitkovsky, 2020. "Social and Monopoly Optimization in Observable Queues," Operations Research, INFORMS, vol. 68(4), pages 1178-1198, July.
    10. Refael Hassin & Ricky Roet-Green, 2017. "The Impact of Inspection Cost on Equilibrium, Revenue, and Social Welfare in a Single-Server Queue," Operations Research, INFORMS, vol. 65(3), pages 804-820, June.
    11. Canbolat, Pelin G., 2020. "Bounded rationality in clearing service systems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 614-626.
    12. Hassin, Refael & Roet-Green, Ricky, 2018. "Cascade equilibrium strategies in a two-server queueing system with inspection cost," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1014-1026.
    13. Boudali, Olga & Economou, Antonis, 2012. "Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes," European Journal of Operational Research, Elsevier, vol. 218(3), pages 708-715.
    14. 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.
    15. Binyamin Oz, 2022. "Optimal admission policy to an observable M/G/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 477-479, April.
    16. 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.
    17. Antonis Economou & Athanasia Manou, 2022. "A probabilistic approach for the analysis of the $$M_n/G/1$$ M n / G / 1 queue," Annals of Operations Research, Springer, vol. 317(1), pages 19-27, October.
    18. 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.

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