We obtain an optimal spacing for arrivals to a single server queue with exponential service time. This is a continuation of work by Jansson [2], Mercer [3] and Pegden and Rosenshine [1]. Pegden and Rosenshine determined spacings minimizing the sum of the expected costs of customer waiting and server availability. We also determine the optimal solution for equally spaced arrivals. For a large number of customers to be scheduled, n, we show the equally spaced model is a limiting case of the model of Pegden and Rosenshine. This provides a simple large n approximation which avoids considerable computation. 1994.
