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Equilibrium Joining Strategies in the Geo / Geo K /1 Queueing System

Author

Listed:
  • Zaiming Liu

    (School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China)

  • Can Cao

    (School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
    College of Mathematics and Statistics, Jishou University, Jishou 416000, Hunan, China)

  • Shan Gao

    (Department of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, Anhui, China)

Abstract

We study strategic behavior in the G e o / G e o K / 1 queueing system under both fully observable case and fully unobservable case. Furthermore, equilibrium and socially optimal strategies are obtained according to the available information and the linear utility function. We compare the impact of system parameters on the equilibrium strategies and socially optimal strategies. At the same time, we illustrate the effects of parameters on the obtained equilibrium social benefit. Finally, some numerical examples are presented.

Suggested Citation

  • Zaiming Liu & Can Cao & Shan Gao, 2019. "Equilibrium Joining Strategies in the Geo / Geo K /1 Queueing System," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1029-:d:282622
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    References listed on IDEAS

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    1. Uri Yechiali, 1971. "On Optimal Balking Rules and Toll Charges in the GI / M /1 Queuing Process," Operations Research, INFORMS, vol. 19(2), pages 349-370, April.
    2. Antonis Economou & Athanasia Manou, 2013. "Equilibrium balking strategies for a clearing queueing system in alternating environment," Annals of Operations Research, Springer, vol. 208(1), pages 489-514, September.
    3. Haim Mendelson & Seungjin Whang, 1990. "Optimal Incentive-Compatible Priority Pricing for the M/M/1 Queue," Operations Research, INFORMS, vol. 38(5), pages 870-883, October.
    4. Yu, Senlin & Liu, Zaiming & Wu, Jinbiao, 2016. "Equilibrium strategies of the unobservable M/M/1 queue with balking and delayed repairs," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 56-65.
    5. 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.
    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. 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.
    8. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    9. 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.
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    Cited by:

    1. Abdoun Sylia & Taleb Samira, 2024. "Strategic Joining in an Unobservable Markovian Queue with Differentiated Vacations," SN Operations Research Forum, Springer, vol. 5(3), pages 1-27, September.

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