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Strategic behavior and social optimization in a constant retrial queue with the N-policy

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  • Wang, Jinting
  • Zhang, Xuelu
  • Huang, Ping

Abstract

We consider customers’ strategic behavior and the corresponding social maximization problem in an M/M/1 constant retrial queue with the N-policy. There is no waiting space in front of the server and customers who find the server busy have to abandon the system, but they can leave their contact details to stay on a waiting list. Consequently, after a service completion, the server will seek a customer from the waiting list at a constant retrial rate on an FCFS basis. The server is switched off whenever the system becomes empty, and is resumed only when the number of waitlisted customers reaches a given threshold. We assume that the arriving customers who find the server busy or down decide whether to leave their contact details or to balk based on a linear reward-cost structure. We examine customers’ strategic response to this mechanism and compare it to the social optimal behavior with delay information. It is shown that both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors exist in our system, and therefore, both multiple and unique equilibrium arrival rates could exist. Through the Particle Swarm Optimization (PSO) algorithm, we numerically obtain the optimal solution of the social welfare maximization problem. The individual equilibrium strategies are compared with the social optimum and the Price of Anarchy (PoA) is studied as a measure to quantify the inefficiency of the equilibrium strategies. Finally, numerical examples are presented to illustrate the sensitivity of some key system performance measures.

Suggested Citation

  • Wang, Jinting & Zhang, Xuelu & Huang, Ping, 2017. "Strategic behavior and social optimization in a constant retrial queue with the N-policy," European Journal of Operational Research, Elsevier, vol. 256(3), pages 841-849.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:3:p:841-849
    DOI: 10.1016/j.ejor.2016.06.034
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    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. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    5. Bu, Qihui & Sun, Yun & Chai, Xudong & Liu, Liwei, 2020. "Strategic behavior and social optimization in a clearing queueing system with N-policy and stochastic restarting scheme," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    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. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    8. Stark, Oded & Budzinski, Wiktor & Kosiorowski, Grzegorz, 2019. "Switching queues, cultural conventions, and social welfare," European Journal of Operational Research, Elsevier, vol. 278(3), pages 837-844.
    9. 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.
    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. Yang, Qiaoli & Qiao, Zheng & Yang, Bo & Shi, Zhongke, 2021. "Modeling and uncovering the passenger–taxi dynamic queues at taxi station with multiple boarding points using a Markovian environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    12. 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.
    13. Hassin, Refael & Nowik, Irit & Shaki, Yair Y., 2018. "On the price of anarchy in a single-server queue with heterogeneous service valuations induced by travel costs," European Journal of Operational Research, Elsevier, vol. 265(2), pages 580-588.
    14. 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).
    15. S Srivatsa Srinivas, 2023. "To increase or to decrease the price? Managing public transport queues during COVID-19 in the presence of strategic commuters," Public Transport, Springer, vol. 15(1), pages 275-285, March.
    16. 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.

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