On the Relevance of Long-range Dependence in Network Traac

| There is much experimental evidence that network traac 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 nite range of time scales of interest in performance evaluation and prediction problems, and the rst-order statistics such as the marginal distribution of the process. We introduce and evaluate a model in which these parameters can be controlled. Speciically, our model is a modulated uid traac model in which the correlation function of the uid rate matches that of an asymptotically second-order self-similar process with given Hurst parameter up to an arbitrary cutoo time lag, then drops to zero. We develop a very eecient numerical procedure to evaluate the performance of a single server queue fed with the above uid input process. We use this procedure to examine the uid loss rate for a wide range of marginal distributions, Hurst parameters, cutoo lags, and buuer sizes. Our main results are as follows. First, we nd 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 traac, but also on time scales speciic to the system under study. For example, the time scale associated with a queueing system is a function of the maximum buuer size. Thus for nite buuer queues, we nd 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 traac up to the correlation horizon. Second, we nd that loss can depend in a crucial way on the marginal distribution of the uid rate process. Third, our results suggest that reducing loss by buuering is hard for traac with correlation over many time scales. We advocate the use of source traac control and statistical multiplexing instead.