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Equilibrium threshold strategies in observable queueing systems with setup/closedown times

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  • Wei Sun
  • Pengfei Guo
  • Naishuo Tian

Abstract

This paper considers two types of setup/closedown policies: interruptible and insusceptible setup/closedown policies. When all customers are served exhaustively in a system under the interruptible setup/closedown policy, the server shuts down (deactivates) by a closedown time. When the server reactivates since shutdown, he needs a setup time before providing service again. If a customer arrives during a closedown time, the service is immediately started without a setup time. However, in a system under the insusceptible setup/closedown policy, customers arriving in a closedown time can not be served until the following setup time finishes. For the systems with interruptible setup/closedown times, we assume both the fully and almost observable cases, then derive equilibrium threshold strategies for the customers and analyze the stationary behavior of the systems. On the other hand, for the systems with insusceptible setup/closedown times, we only consider the fully observable case. We also illustrate the equilibrium thresholds and the social benefits for systems via numerical experiments. As far as we know, there is no work concerning equilibrium behavior of customers in queueing systems with setup/closedown times. Copyright Springer-Verlag 2010

Suggested Citation

  • Wei Sun & Pengfei Guo & Naishuo Tian, 2010. "Equilibrium threshold strategies in observable queueing systems with setup/closedown times," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 241-268, September.
    • Handle: RePEc:spr:cejnor:v:18:y:2010:i:3:p:241-268
    DOI: 10.1007/s10100-009-0104-4
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    References listed on IDEAS

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    1. 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. 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.
    2. Economou, Antonis & Logothetis, Dimitrios & Manou, Athanasia, 2022. "The value of reneging for strategic customers in queueing systems with server vacations/failures," European Journal of Operational Research, Elsevier, vol. 299(3), pages 960-976.
    3. 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.
    4. Shuo Wang & Xiuli Xu, 2021. "Equilibrium strategies of the fluid queue with working vacation," Operational Research, Springer, vol. 21(2), pages 1211-1228, June.
    5. 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.
    6. Gopinath Panda & Veena Goswami, 2022. "Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1439-1466, September.
    7. 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.
    8. Jie Liu & Jinting Wang, 2017. "Strategic joining rules in a single server Markovian queue with Bernoulli vacation," Operational Research, Springer, vol. 17(2), pages 413-434, July.
    9. Wojciech M. Kempa & Dariusz Kurzyk, 2022. "Analysis of Non-Steady Queue-Length Distribution in a Finite-Buffer Model with Group Arrivals and Power Saving Mechanism with Setups," Energies, MDPI, vol. 15(22), pages 1-15, November.
    10. Wei Sun & Shiyong Li, 2014. "Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 694-715, July.
    11. 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.
    12. 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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