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Strategic joining in M/M/1 retrial queues

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  • Wang, Jinting
  • Zhang, Feng

Abstract

The equilibrium and socially optimal balking strategies are investigated for unobservable and observable single-server classical retrial queues. There is no waiting space in front of the server. If an arriving customer finds the server idle, he occupies the server immediately and leaves the system after service. Otherwise, if the server is found busy, the customer decides whether or not to enter a retrial pool with infinite capacity and becomes a repeated customer, based on observation of the system and the reward–cost structure imposed on the system. Accordingly, two cases with respect to different levels of information are studied and the corresponding Nash equilibrium and social optimization balking strategies for all customers are derived. Finally, we compare the equilibrium and optimal behavior regarding these two information levels through numerical examples.

Suggested Citation

  • Wang, Jinting & Zhang, Feng, 2013. "Strategic joining in M/M/1 retrial queues," European Journal of Operational Research, Elsevier, vol. 230(1), pages 76-87.
    • Handle: RePEc:eee:ejores:v:230:y:2013:i:1:p:76-87
    DOI: 10.1016/j.ejor.2013.03.030
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    1. Eitan Altman & Nahum Shimkin, 1998. "Individual Equilibrium and Learning in Processor Sharing Systems," Operations Research, INFORMS, vol. 46(6), pages 776-784, December.
    2. Refael Hassin & Moshe Haviv, 1997. "Equilibrium Threshold Strategies: The Case of Queues with Priorities," Operations Research, INFORMS, vol. 45(6), pages 966-973, December.
    3. Ward Whitt, 1999. "Improving Service by Informing Customers About Anticipated Delays," Management Science, INFORMS, vol. 45(2), pages 192-207, February.
    4. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    5. Tilt, Borge & Balachandran, K. R., 1979. "Stable and superstable customer policies in queues with balking and priority options," European Journal of Operational Research, Elsevier, vol. 3(6), pages 485-498, November.
    6. Refael Hassin & Moshe Haviv, 2002. "Nash Equilibrium and Subgame Perfection in Observable Queues," Annals of Operations Research, Springer, vol. 113(1), pages 15-26, July.
    7. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    8. Guo, Pengfei & Hassin, Refael, 2012. "Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 222(2), pages 278-286.
    9. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    10. Hassin, Refael, 1985. "On the Optimality of First Come Last Served Queues," Econometrica, Econometric Society, vol. 53(1), pages 201-202, January.
    11. 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. 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.
    2. 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.
    3. 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.
    4. Zhou, Wenhui & Lian, Zhaotong & Wu, Jinbiao, 2014. "When should service firms provide free experience service?," European Journal of Operational Research, Elsevier, vol. 234(3), pages 830-838.
    5. 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.
    6. Brill, P.H. & Huang, M.L. & Hlynka, M., 2020. "On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers," European Journal of Operational Research, Elsevier, vol. 283(1), pages 235-243.
    7. 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.
    8. Xinlei Liu & Xiuli Xu & Mingxin Liu, 2024. "Strategy Analysis of Retrial Queue with Parallel Customer and Standby Server," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-22, September.
    9. Lian, Zhaotong & Gu, Xinhua & Wu, Jinbiao, 2016. "A re-examination of experience service offering and regular service pricing under profit maximization," European Journal of Operational Research, Elsevier, vol. 254(3), pages 907-915.
    10. Jalili Marand, Ata & Tang, Ou & Li, Hongyan, 2019. "Quandary of service logistics: Fast or reliable?," European Journal of Operational Research, Elsevier, vol. 275(3), pages 983-996.
    11. Fan Xu & Ruiling Tian & Qi Shao, 2024. "Optimal Pricing Strategy in an Unreliable M/M/1 Retrial Queue with Delayed Repair and Breakdown Deterioration," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-22, June.
    12. 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.
    13. Gopinath Panda & Veena Goswami & Abhijit Datta Banik, 2016. "Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-34, October.
    14. Olga Bountali & Apostolos Burnetas & Lerzan Örmeci, 2022. "Join, balk, or jettison? The effect of flexibility and ranking knowledge in systems with batch arrivals," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3505-3524, September.

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