Wavelet-based queueing analysis of Gaussian and nonGaussian long-range-dependent network traffic

Abstract

In this thesis, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, long-range-dependent (LRD) network traffic. The wavelet transform effectively decorrelates LRD signals and hence is well-suited to model such data. However, wavelet-based models have generally been used for modeling Gaussian data which can be unrealistic for traffic. Using a multiplicative superstructure atop the Haar wavelet transform, we exploit the decorrelating properties of wavelets while simultaneously capturing the positivity and "spikiness" of nonGaussian traffic. We develop a queuing analysis for our model by exploiting its multiscale construction scheme. We elucidate our model's ability to capture the covariance structure of real data and then fit it to real traffic traces. Queuing experiments demonstrate the accuracy of the model for matching real data and the precision of our theoretical queuing result. Our results indicate that a Gaussian assumption can lead to over-optimistic predictions of tail queue probability.