On the Accuracy of the Simple Peak Hour Approximation for Markovian Queues

Abstract

We empirically explore the accuracy of the simple stationary peak hour approximation (SPHA) for estimating peak hour performance in multiserver queuing systems with exponential service times and periodic (sinusoidal) Poisson arrival processes. We show that the SPHA is very good for a range of parameter values corresponding to a reasonably broad spectrum of real systems. However, we do find and document that there are many situations in which this approximation will be very inaccurate. We postulate and then support empirically a set of hypotheses that link the accuracy of the SPHA and the related point-wise stationary approximation (PSA) to key parameter values and model characteristics. We also present results on the time-dependent behavior of these systems as a function of key parameters. Finally we present results which indicate that our findings, developed for models with sinusoidal input streams, may apply to a much broader range of Markovian models with more general cyclic inputs.