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Strategic arrivals to a queue with service rate uncertainty

Author

Listed:
  • Liron Ravner

    (University of Amsterdam
    Eindhoven University of Technology)

  • Yutaka Sakuma

    (National Defense Academy of Japan)

Abstract

We study the problem of strategic choice of arrival time to a single-server queue with opening and closing times when there is uncertainty regarding service speed. A Poisson population of customers choose their arrival time with the goal of minimizing their expected waiting times and are served on a first-come first-served basis. There are two types of customers that differ in their beliefs regarding the service-time distribution. The inconsistent beliefs may arise from randomness in the server state along with noisy signals that customers observe. Customers are aware of the two types of populations with differing beliefs. We characterize the Nash equilibrium dynamics for exponentially distributed service times and show how they substantially differ from the model with homogeneous customers. We further provide an explicit solution for a fluid approximation of the game. For general service-time distributions we provide an algorithm for computing the equilibrium in a discrete-time setting. We find that in equilibrium customers with different beliefs arrive during different (and often disjoint) time intervals. Numerical analysis further shows that the mean waiting time increases with the coefficient of variation of the service time. Furthermore, we present a learning agent-based model (ABM) in which customers make joining decisions based solely on their signals and past experience. We numerically compare the long-term average outcome of the ABM with that of the equilibrium and find that the arrival distributions are quite close if we assume (for the equilibrium solution) that customers are fully rational and have knowledge of the system parameters, while they may greatly differ if customers have limited information or computing abilities.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:97:y:2021:i:3:d:10.1007_s11134-020-09683-7
    DOI: 10.1007/s11134-020-09683-7
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    References listed on IDEAS

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    1. Hong Chen & Avi Mandelbaum, 1991. "Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 408-446, May.
    2. Economou, Antonis & Manou, Athanasia, 2016. "Strategic behavior in an observable fluid queue with an alternating service process," European Journal of Operational Research, Elsevier, vol. 254(1), pages 148-160.
    3. Senthil Veeraraghavan & Laurens Debo, 2009. "Joining Longer Queues: Information Externalities in Queue Choice," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 543-562, April.
    4. Harsha Honnappa & Rahul Jain, 2015. "Strategic Arrivals into Queueing Networks: The Network Concert Queueing Game," Operations Research, INFORMS, vol. 63(1), pages 247-259, February.
    5. 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.
    6. Haviv, Moshe & Milchtaich, Igal, 2012. "Auctions with a random number of identical bidders," Economics Letters, Elsevier, vol. 114(2), pages 143-146.
    7. Rouba Ibrahim, 2018. "Managing Queueing Systems Where Capacity is Random and Customers are Impatient," Production and Operations Management, Production and Operations Management Society, vol. 27(2), pages 234-250, February.
    8. Shiliang Cui & Senthil Veeraraghavan, 2016. "Blind Queues: The Impact of Consumer Beliefs on Revenues and Congestion," Management Science, INFORMS, vol. 62(12), pages 3656-3672, December.
    9. 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.
    10. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    11. Laurens Debo & Senthil Veeraraghavan, 2014. "Equilibrium in Queues Under Unknown Service Times and Service Value," Operations Research, INFORMS, vol. 62(1), pages 38-57, February.
    12. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    13. Tingliang Huang & Ying-Ju Chen, 2015. "Service Systems with Experience-Based Anecdotal Reasoning Customers," Production and Operations Management, Production and Operations Management Society, vol. 24(5), pages 778-790, May.
    14. Huiming Zhang & Bo Li, 2016. "Characterizations of discrete compound Poisson distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(22), pages 6789-6802, November.
    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.
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