On the accuracy of the simple peak hour approximation for Markovian queues

The authors 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 peridoic (sinuosidal) Poisson arrival processes. They show that the SPHA is very good for a range of parameter values corresponding to a reasonably broad spectrum of real systems. However, the authors do find and document that there are many situations in which this approximation will be very inaccurate. They 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. The authors also present results on the time-dependent behavior of these systems as a function of key parameters. Finally they 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.