The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals

We empirically explore the accuracy of an easily computed approximation for long run, average performance measures such as expected delay and probability of delay in multiserver queueing systems with exponential service times and periodic (sinusoidal) Poisson arrival processes. The pointwise stationary approximation is computed by integrating over time (that is taking the expectation of) the formula for the stationary performance measure with the arrival rate that applies at each point in time. This approximation, which has been empirically confirmed as a tight upper bound of the true value, is shown to be very accurate for a range of parameter values corresponding to a reasonably broad spectrum of real systems.