On the Relevance of Long - Range Dependence in Network Tra

There is mounting experimental evidence that network traff c 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 imm pact 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 diss tribution of the process. We introduce and evaluate a model in which these parameters can be easily controlled. Speciically, our model is a moduu lated uid traac model in which the correlation function of the uid rate is asymptotically second-order self-similar with given Hurst parameter, then drops to zero at a cutoo time lag. We develop a very eecient numerical procedure to evall uate the performance of the 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 perforr mance evaluation depends not only on the correlation structure of the source traac, but also on time scales speciic to the syss tem under study. For example, the time scale associated to 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. Second, we nd that loss depends in a crucial way on the marginal distribution of the uid rate process. Third, our results suggest that reducc ing loss by buuering is hard. We advocate the use of source traac control and statistical multiplexing instead. sion to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proot or direct commercial advantage and that copies bear this notice and the full citation on the rst page. Copyrights for components of this work owned by others than …