IDEAS home Printed from https://ideas.repec.org/p/hhs/sdueko/2017_003.html
   My bibliography  Save this paper

Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume

Author

Listed:
  • Breinbjerg, Jesper

    (Department of Business and Economics)

  • Østerdal, Lars Peter

    (Department of Economics)

Abstract

We consider a non-cooperative queueing environment where a finite number of customers independently choose when to arrive at a queueing system that opens at a given point in time and serves customers on a last-come first-serve preemptive-resume (LCFS-PR) basis. Each customer has a service time requirement which is identically and independently distributed according to some general probability distribution, and they want to complete service as early as possible while minimizing the time spent in the queue. In this setting, we establish the existence of an arrival time strategy that constitutes a symmetric (mixed) Nash equilibrium, and show that there is at most one symmetric equilibrium. We provide a numerical method to compute this equilibrium and demonstrate by a numerical example that the social efficiency can be lower than the efficiency induced by a similar queueing system that serves customers on a first-come first-serve (FCFS) basis.

Suggested Citation

  • 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.
    • Handle: RePEc:hhs:sdueko:2017_003
    as

    Download full text from publisher

    File URL: http://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2017/dpbe3_2017.pdf?la=en
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Erik T. Verhoef, 2002. "Inside the Queue," Tinbergen Institute Discussion Papers 02-062/3, Tinbergen Institute, revised 27 May 2003.
    3. Stein, William E. & Rapoport, Amnon & Seale, Darryl A. & Zhang, Hongtao & Zwick, Rami, 2007. "Batch queues with choice of arrivals: Equilibrium analysis and experimental study," Games and Economic Behavior, Elsevier, vol. 59(2), pages 345-363, May.
    4. Glazer, Amihai & Hassin, Refael, 1983. "?/M/1: On the equilibrium distribution of customer arrivals," European Journal of Operational Research, Elsevier, vol. 13(2), pages 146-150, June.
    5. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    6. 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.
    7. Verhoef, Erik T., 2003. "Inside the queue:: hypercongestion and road pricing in a continuous time-continuous place model of traffic congestion," Journal of Urban Economics, Elsevier, vol. 54(3), pages 531-565, November.
    8. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    9. A. Glazer & R. Hassin, 1987. "Equilibrium Arrivals in Queues with Bulk Service at Scheduled Times," Transportation Science, INFORMS, vol. 21(4), pages 273-278, November.
    10. Rapoport, Amnon & Stein, William E. & Parco, James E. & Seale, Darryl A., 2004. "Equilibrium play in single-server queues with endogenously determined arrival times," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 67-91, September.
    11. 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.
    12. 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.
    13. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Breinbjerg, Jesper, 2016. "Strategic Arrival Times to Queueing Systems," Discussion Papers on Economics 6/2016, University of Southern Denmark, Department of Economics.
    5. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Rapoport, Amnon & Stein, William E. & Mak, Vincent & Zwick, Rami & Seale, Darryl A., 2010. "Endogenous arrivals in batch queues with constant or variable capacity," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1166-1185, December.
    11. 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.
    12. Otsubo, Hironori & Rapoport, Amnon, 2008. "Vickrey's model of traffic congestion discretized," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 873-889, December.
    13. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    14. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    15. Kaddoura, Ihab & Nagel, Kai, 2019. "Congestion pricing in a real-world oriented agent-based simulation context," Research in Transportation Economics, Elsevier, vol. 74(C), pages 40-51.
    16. Ravner, Liron & Haviv, Moshe & Vu, Hai L., 2016. "A strategic timing of arrivals to a linear slowdown processor sharing system," European Journal of Operational Research, Elsevier, vol. 255(2), pages 496-504.
    17. Tzvi Alon & Moshe Haviv, 2023. "Choosing a batch to be processed," Annals of Operations Research, Springer, vol. 326(1), pages 67-87, July.
    18. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    19. 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.
    20. Arnott, Richard & Inci, Eren, 2010. "The stability of downtown parking and traffic congestion," Journal of Urban Economics, Elsevier, vol. 68(3), pages 260-276, November.

    More about this item

    Keywords

    Queueing; strategic arrival times to a queue; non-cooperative games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:sdueko:2017_003. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Astrid Holm Nielsen (email available below). General contact details of provider: https://edirc.repec.org/data/okioudk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.