On the relevance of long-range dependence in network traffic

Abstract

There is mounting experimental evidence that network traffic processes exhibit ubiquitous properties of self-similarity and long range dependence (LRD), 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 recent 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 easily controlled. Specifically, our model is a modulated fluid traffic model in which the correlation function of the fluid rate is asymptotically second-order self-similar with given Hurst parameter, then drops to zero at a cutoff time lag. We develop a very efficient numerical procedure to evaluate the performance of the 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 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 to 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. Second, we find that loss depends in a crucial way on the marginal distribution of the fluid rate process. Third, our results suggest that reducing loss by buffering is hard. We advocate the use of source traffic control and statistical multiplexing instead.