On the relevance of long-range dependence in network traffic

Abstract

There is much experimental evidence that network traffic processes exhibit ubiquitous properties of self-similarity and long-range dependence, i.e., of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much previous modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process. We introduce and evaluate a model in which these parameters can be controlled. Specifically, our model is a modulated fluid traffic model in which the correlation function of the fluid rate matches that of an asymptotically second-order self-similar process with given Hurst parameter up to an arbitrary cutoff time lag, then drops to zero. We develop a very efficient numerical procedure to evaluate the performance of a single-server queue fed with the above fluid input process. We use this procedure to examine the fluid loss rate for a wide range of marginal distributions, Hurst (1950) parameters, cutoff lags, and buffer sizes. Our main results are as follows. First, we find that the amount of correlation that needs to be taken into account for performance evaluation depends not only on the correlation structure of the source traffic, but also on time scales specific to the system under study. For example, the time scale associated with a queueing system is a function of the maximum buffer size. Thus, for finite buffer queues, we find that the impact on loss of the correlation in the arrival process becomes nil beyond a time scale we refer to as the correlation horizon. This means, in particular, that for performance-modeling purposes, we may choose any model among the panoply of available models (including Markovian and self-similar models) as long as the chosen model captures the correlation structure of the source traffic up to the correlation horizon. Second, we find that loss can depend in a crucial way on the marginal distribution of the fluid rate process. Third, our results suggest that reducing loss by buffering is hard for traffic with correlation over many time scales. We advocate the use of source traffic control and statistical multiplexing instead.