The Importance of Long - Range Dependence of VBR Video

There has been a growing concern about the potential impact of long-term correlations (second-order statistic) in variable-bit-rate (VBR) video traac on ATM buuer dimen-sioning. Previous studies have shown that video traac exhibits long-range dependence (LRD) (Hurst parameter large than 0.5). We investigate the practical implications of LRD in the context of realistic ATM traac engineering by studying ATM multiplexers of VBR video sources over a range of desirable cell loss rates and buuer sizes (maximum delays). Using results based on large deviations theory, we introduce the notion of Critical Time Scale (CTS). For a given buuer size, link capacity, and the marginal distribution of frame size, the CTS of a VBR video source is deened as the number of frame correlations that contribute to the cell loss rate. In other words, second-order behavior at the time scale beyond the CTS does not signiicantly aaect the network performance. We show that whether the video source model is Markov or has LRD, its CTS is nite, attains a small value for small buuer, and is a non-decreasing function of buuer size. Numerical results show that (i) even in the presence of LRD, long-term correlations do not have signiicant impact on the cell loss rate; and (ii) short-term correlations have dominant eeect on cell loss rate, and therefore, well-designed Markov traac models are eeective for predicting Quality of Service (QOS) of LRD VBR video traac. Therefore , we conclude that it is unnecessary to capture the long-term correlations of a real-time VBR video source under realistic ATM buuer dimensioning scenarios as far as the cell loss rates and maximum buuer delays are concerned.