Impact of aggregated, self-similar ON/OFF traffic on delay in stationary queueing models (extended version)

The impact of the now widely acknowledged self-similar property of network traffic on cell-delay in a single server queueing model is investigated. The analytic traffic model, called N-Burst, uses the superposition of N independent cell streams of ON/OFF type with power-tail distributed ON periods. Queueing-delay for such arrival processes is mainly caused by over-saturation periods, which occur when too many sources are in their ON-state. The duration of the over-saturation periods is shown to have a power-tail distribution, whose exponent β is in most scenarios different from the tail exponent of the individual ON-period. Conditions on the model parameters, for which the mean and higher moments of the delay distribution become infinite, are investigated. Since these conditions depend on traffic parameters as well as on network parameters, careful network design can alleviate the performance impact of such self-similar traffic. Finally, a characterization of truncated tails by the so-called power-tail range is developed. Based on the power-tail range of the burst-length distribution, the additional parameter maximum burst size (MBS) is introduced in the N-Burst model. An asymptotic relationship between the moments of the delay distribution and the MBS is derived and is validated by the corresponding numerical results of the analytic N-Burst/M/1 queueing model.