Scheduling arrivals to a queue

The authors obtain an optimal spacing for arrivals to a single server queue with exponential service time. This is a continuation of work by Jansson, Mercer and Pegden and Rosenshine. Pegden and Rosenshine determined spacings minimizing the sum of the expected costs of customer waiting and server availability. The authors also determine the optimal solution for equally spaced arrivals. For a large number of customers to be scheduled, n, they show the equally spaced model is a limiting case of the model of Pegden and Rosenshine. This provides a simple large n apprximation which avoids considerable computation.