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Strategic Behavior and Optimization in an Unobservable Constant Retrial Queue with Balking and Set-Up Time

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  • Wang Linlin

    (School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China)

  • Liu Liwei

    (School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China)

  • Wang Zhen

    (School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China)

  • Chai Xudong

    (School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China)

Abstract

An M/M/1 constant retrial queue with balking customers and set-up time is considered. Once the system becomes empty, the server will be turned down to reduce operating costs, and it will be activated only when there is a customers arrives. In this paper, the almost unobservable case is studied, in which the information of the queue length is unavailable, whereas the state of the server can be obtained. Firstly, the steady state solutions are derived and the individual equilibrium strategies are analyzed. In addition, social optimization problems, including cost analysis and social welfare maximization are investigated by using the PSO algorithm. Finally, by appropriate numerical examples, the sensitivity of some main system parameters is shown.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:jossai:v:8:y:2020:i:3:p:273-290:n:5
    DOI: 10.21078/JSSI-2020-273-18
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    References listed on IDEAS

    as
    1. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    2. 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.
    3. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
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