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

Author

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

Abstract

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

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