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Equilibrium customer strategies and social–profit maximization in the single‐server constant retrial queue

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  • Antonis Economou
  • Spyridoula Kanta

Abstract

We consider the single‐server constant retrial queue with a Poisson arrival process and exponential service and retrial times. This system has not waiting space, so the customers that find the server busy are forced to abandon the system, but they can leave their contact details. Hence, after a service completion, the server seeks for a customer among those that have unsuccessfully applied for service but left their contact details, at a constant retrial rate. We assume that the arriving customers that find the server busy decide whether to leave their contact details or to balk based on a natural reward‐cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine the customers' behavior, and we identify the Nash equilibrium joining strategies. We also study the corresponding social and profit maximization problems. We consider separately the observable case where the customers get informed about the number of customers waiting for service and the unobservable case where they do not receive this information. Several extensions of the model are also discussed. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:2:p:107-122
    DOI: 10.1002/nav.20444
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    References listed on IDEAS

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    1. Refael Hassin & Moshe Haviv, 1997. "Equilibrium Threshold Strategies: The Case of Queues with Priorities," Operations Research, INFORMS, vol. 45(6), pages 966-973, December.
    2. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    3. 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. 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.
    3. 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.
    4. Nam H. Do & Tien Do & Agassi Melikov, 2020. "Equilibrium customer behavior in the M/M/1 retrial queue with working vacations and a constant retrial rate," Operational Research, Springer, vol. 20(2), pages 627-646, June.
    5. 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.
    6. Zhongbin Wang & Jinting Wang, 2019. "Information heterogeneity in a retrial queue: throughput and social welfare maximization," Queueing Systems: Theory and Applications, Springer, vol. 92(1), pages 131-172, June.
    7. 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.
    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. Kalpana Devarajan & Muthukrishnan Senthilkumar, 2021. "On the Retrial-Queuing Model for Strategic Access and Equilibrium-Joining Strategies of Cognitive Users in Cognitive-Radio Networks with Energy Harvesting," Energies, MDPI, vol. 14(8), pages 1-21, April.
    11. 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.
    12. Wang Linlin & Liu Liwei & Wang Zhen & Chai Xudong, 2020. "Strategic Behavior and Optimization in an Unobservable Constant Retrial Queue with Balking and Set-Up Time," Journal of Systems Science and Information, De Gruyter, vol. 8(3), pages 273-290, June.
    13. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik, 2023. "Robustness of the cμ -Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    14. S. Srivatsa Srinivas & Rahul R. Marathe, 2020. "Equilibrium in a finite capacity M/M/1 queue with unknown service rates consisting of strategic and non-strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 329-356, December.
    15. 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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