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

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