Fractal traffic: measurements, modelling and performance evaluation

Observations of both Ethernet traffic and variable bit rate (VBR) video traffic have demonstrated that these traffics exhibit "self-similarity" and/or infinite asymptotic index of dispersion for counts (IDC). We report here on measurements of traffic in a commercial public broadband network where similar characteristics have been observed. For the purpose of analysis and dimensioning of the central links of an ATM network we analyse in this paper the performance of a single server queue fed by Gaussian traffic with infinite IDC. The analysis lends to an approximation for the performance of a queue in which the arriving traffic is "fractal" Gaussian and consequently where there does not exist a dominant negative-exponential tail. The term "fractal" is used here in the sense that the autocovariance of the traffic exhibits self-similarity, that is to say, where the autocovariance of an aggregate of the traffic is the same, or asymptotically the same for large time lags, as the original traffic. We are not concerned with proving or exploiting this self-similarity property as such, but only with performance analysis techniques which are effective for such processes. In order to be able to test the performance analysis formulae, we show that traffic with the same autocovariance as measured in a real network over a wide range of lags (sufficiently wide a range for the traffic to be equivalent from the point of view of queueing performance) can be generated as a mixture of two Gaussian AR(1) processes. In this way we demonstrate that the analytic performance formulae are accurate.