Multiscale Modeling and Queuing Analysis of Long-range-dependent Network Traac

We develop a simple multiscale model for the analysis and synthesis of nonGaus-sian, long-range-dependent (LRD) network traac loads. The wavelet transform eeec-tively decorrelates LRD signals and hence is well-suited to model such data. However, traditional wavelet-based models are Gaussian in nature and so can at best match second-order statistics of inherently nonGaussian traac loads. Using a multiplicative superstructure atop the Haar wavelet tree, we retain the decorrelating properties of wavelets while simultaneously capturing the positivity and \spikiness" of nonGaus-sian traac. This leads to a swift O(N) algorithm for tting and synthesizing N-point data sets. The resulting model belongs to the class of multifractal cascades. Cascades are endowed with rich scaling properties that are better suited than LRD to capture burstiness. We elucidate our model's ability to capture the covariance structure of real data and then t it to real traac traces. We derive approximate analytical queuing formulas for our model, also applicable to other multiscale models, by exploiting its multiscale construction scheme. Queuing experiments demonstrate the accuracy of the model for matching real data and the precision of our theoretical queuing results, thus revealing the potential use of the model for numerous networking applications. Our results indicate that a Gaussian assumption can lead to over-optimistic predictions of tail queue probability even when taking LRD into account.