Note—Patience is a Virtue in a Simple Model of Repetitively Joining a Queue

Each of n members of a finite customer population must weigh the rewards of service completion against the cost of waiting in a single exponential server queuing system. After completing service, a customer may re-enter the system. In attempting to maximize average return per unit time over an infinite horizon each customer must make a single decision, a choice of arrival rate which must then be used to determine the time until re-entry whenever the customer finishes being served.

Equilibrium behavior in the resulting n person game is investigated. Equilibria exist involving a subset of the players who re-enter instantaneously after service while all others abstain from entry. In instances where all customers re-enter instantaneously, everyone could be made better off if it were possible to impose a non-instantaneous arrival rate.