Approximating the Behavior of Nonstationary Single-Server Queues

This paper presents computationally efficient techniques for approximating several behavioral aspects of the M^x(t)/E_Y/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 Q(t) at the time points E[T_n] by the distribution of Q_n, where T_n is the epoch of the nth departure and Q_n = Q(T_n + 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.