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A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model


  • Sakuma, Yutaka
  • Masuyama, Hiroyuki
  • Fukuda, Emiko


This paper considers a discrete-time single-server queue with a single acceptance period for a Poissonian population of homogeneous customers. Customers are served on a first-come first-served (FCFS) basis, and their service times are independent and identically distributed with a general distribution. We assume that each customer chooses her/his arrival-time slot with the goal of minimizing her/his expected waiting time in competition with other customers. For this queueing game, we derive a symmetric (mixed-strategy) Nash equilibrium; that is, an equilibrium arrival-time distribution of homogeneous customers, where their expected waiting times are identical. We also propose an agent-based model, which simulates the dynamics of customers who try to minimize their waiting times for service. Through numerical experiments, we confirm that this agent-based model achieves, in steady state, an arrival-time distribution similar to the equilibrium arrival-time distribution analytically obtained.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:283:y:2020:i:1:p:253-264
    DOI: 10.1016/j.ejor.2019.11.003

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    References listed on IDEAS

    1. 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.
    2. Darryl Seale & James Parco & William Stein & Amnon Rapoport, 2005. "Joining a Queue or Staying Out: Effects of Information Structure and Service Time on Arrival and Staying Out Decisions," Experimental Economics, Springer;Economic Science Association, vol. 8(2), pages 117-144, June.
    3. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    4. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
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    6. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    7. 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.
    8. 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.
    9. 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.
    10. Hassin, Refael, 1985. "On the Optimality of First Come Last Served Queues," Econometrica, Econometric Society, vol. 53(1), pages 201-202, January.
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