Approximations for Bursty (and Smoothed) Arrival Queueing Delays Based on Generalized Peakedness

The peakedness characterization of a teletraffic stream has long been recognized as an extremely useful one for the analysis of loss systems. In this paper, we present a preliminary investigation into the utility of this characterization for the analysis of delay systems as well. Restricting attention, for simplicity, to single server queueing systems G/G/! with FCFS service, we derive an explicit approximation to the waiting time distribution, parameterized by quantities which can be easily computed from the peakedness functional of the arrival stream and the first two moments of the service time. The peakedness functional characterization allows arbitrary stationary arrival streams to be treated, and avoids focusing attention on aspects of arrival streams which in many circumstances may be misleading, such as interarrival time statistics. The accuracy of this approximation is assessed by several examples, and rules of thumb are given predicting its degree of accuracy, or lack thereof, in potential applications.