On Competition to Join a Simple Queueing System Before the Facility Opens

A single server provides FIFO services commencing at time 0. Each member of a population of N potential customers must decide whether or not to arrive at the facility. Customers choosing to arrive must do so no later than time 0. This paper studies the benefit to customers: the value of service received minus the cost of waiting time.

This model is studied under a variety of assumptions and the impact of customer behavior on average benefit (value of service minus cost of waiting) is examined. Self-interested customers compete with each other (by arriving sufficiently early) to the extent that much of the potential benefit is dissipated through high waiting costs before time 0. A common finding is that no customer can attain a benefit which improves on that which would result from arriving exactly at time 0 and being last in line. The impact of charging entrance tolls is investigated.