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Equilibrium and optimal arrival patterns to a server with opening and closing times

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  • Refael Hassin
  • Yana Kleiner

Abstract

This article considers a first-come first-served single-server system with opening and closing times. Service durations are exponentially distributed, and the total number of arrivals is a Poisson random variable. Naturally each customer wishes to minimize his/her waiting time. The process of choosing an arrival time is presented as a (non-cooperative) multi-player game. The overall goal of this work is to find a Nash equilibrium game strategy. It is assumed in the literature that arrivals before the opening time of the system are allowed. In this work the case where early arrivals are forbidden is studied. It turns out that unless the system is very heavily loaded, the equilibrium solution with such a restriction does not reduce the expected waiting time in a significant way. The equilibrium solution is compared with the solution which maximizes social welfare. Finally, it is show that social welfare can be increased in equilibrium by restricting arrivals to certain points of time.

Suggested Citation

  • Refael Hassin & Yana Kleiner, 2011. "Equilibrium and optimal arrival patterns to a server with opening and closing times," IISE Transactions, Taylor & Francis Journals, vol. 43(3), pages 164-175.
    • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:3:p:164-175
    DOI: 10.1080/07408171003792449
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    Citations

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    Cited by:

    1. Breinbjerg, Jesper & Østerdal, Lars Peter, 2017. "Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume," Discussion Papers on Economics 3/2017, University of Southern Denmark, Department of Economics.
    2. Jesper Breinbjerg & Alexander Sebald & Lars Peter Østerdal, 2016. "Strategic behavior and social outcomes in a bottleneck queue: experimental evidence," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 207-236, September.
    3. Platz, Trine Tornøe & Østerdal, Lars Peter, 2017. "The curse of the first-in–first-out queue discipline," Games and Economic Behavior, Elsevier, vol. 104(C), pages 165-176.
    4. Moshe Haviv & Liron Ravner, 2021. "A survey of queueing systems with strategic timing of arrivals," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 163-198, October.
    5. Breinbjerg, Jesper, 2016. "Strategic Arrival Times to Queueing Systems," Discussion Papers on Economics 6/2016, University of Southern Denmark, Department of Economics.
    6. Alon, Tzvi & Haviv, Moshe, 2022. "Discrete-time strategic job arrivals to a single machine with waiting and lateness penalties," European Journal of Operational Research, Elsevier, vol. 303(1), pages 480-486.
    7. 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.
    8. 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.
    9. Eitan Altman & Nahum Shimkin, 2016. "The Ordered Timeline Game: Strategic Posting Times Over a Temporally Ordered Shared Medium," Dynamic Games and Applications, Springer, vol. 6(4), pages 429-455, December.
    10. Sakuma, Yutaka & Masuyama, Hiroyuki & Fukuda, Emiko, 2020. "A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 253-264.
    11. Liron Ravner & Yutaka Sakuma, 2021. "Strategic arrivals to a queue with service rate uncertainty," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 303-341, April.
    12. Tzvi Alon & Moshe Haviv, 2023. "Choosing a batch to be processed," Annals of Operations Research, Springer, vol. 326(1), pages 67-87, July.
    13. Breinbjerg, Jesper & Platz, Trine Tornøe & Østerdal, Lars Peter, 2020. "Equilibrium Arrivals to a Last-come First-served Preemptive-resume Queue," Working Papers 17-2020, Copenhagen Business School, Department of Economics.
    14. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    15. Breinbjerg, Jesper, 2017. "Equilibrium arrival times to queues with general service times and non-linear utility functions," European Journal of Operational Research, Elsevier, vol. 261(2), pages 595-605.
    16. Moshe Haviv & Liron Ravner, 2014. "Strategic timing of arrivals to a finite queue multi-server loss system," Discussion Paper Series dp675, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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