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Approximating the Behavior of Nonstationary Single-Server Queues

This paper presents computationally efficient techniques for approximating several behavioral aspects of the Mxt/EY/1 queue. The nonstationary arrival stream allows demands for service to follow different distributions over different time intervals. Specific performance characteristics evaluated are the first two moments of queue length, virtual waiting time, and system utilization. These are based on approximating the distribution of Qt at the time points E[Tn] by the distribution of Qn, where Tn is the epoch of the nth departure and Qn = QTn + 0. The results are in agreement with those obtained by simulation but require much less computing time. Sample results are presented for both stationary and nonstationary examples.