  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.
