The Waiting Time Process for a Certain Correlated Queue

A brief description is given of a problem that arose in a nonqueuing context but that can be interpreted in queuing terms. The result is the unusual single-server system in which the length of a customer's service is determined by the length of the interarrival interval separating himself and his predecessor. The main result is the distribution of waiting time, and its moments. It is shown numerically that this pattern of server behavior results in a drastic reduction of the mean and variance of the waiting time as compared with a conventional M/M/l system.