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Simulating Gaussian Stationary Processes with Unbounded Spectra
 Journal of Computational and Graphical Statistics
, 2000
"... We propose a new method for simulating a Gaussian process, whose spectrum diverges at one frequency in [0; 1 2 ] (not necessarily at zero). The method utilizes a generalization of the discrete wavelet transform, the discrete wavelet packet transform (DWPT), and only requires explicit knowledge ..."
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Cited by 12 (5 self)
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We propose a new method for simulating a Gaussian process, whose spectrum diverges at one frequency in [0; 1 2 ] (not necessarily at zero). The method utilizes a generalization of the discrete wavelet transform, the discrete wavelet packet transform (DWPT), and only requires explicit knowledge of the spectral density function of the process  not its autocovariance sequence. An orthonormal basis is selected such that the spectrum of the wavelet coefficients is as shallow as possible, thus producing approximately uncorrelated wavelet coefficients. We compare this method to a popular timedomain technique based on the LevinsonDurbin recursions. Simulations show that the DWPTbased method performs comparably to the timedomain technique for a variety of sample sizes and processes  at significantly reduced computational time. The degree of approximation and reduction in computer time may be adjusted through selection of the orthonormal basis. Some key words: Autocovariance...
Multiscale Modeling and Queuing Analysis of LongRangeDependent Network Traffic
, 1999
"... We develop a simple multiscale model for the analysis and synthesis of nonGaussian, longrangedependent (LRD) network traffic loads. The wavelet transform effectively decorrelates LRD signals and hence is wellsuited to model such data. However, traditional waveletbased models are Gaussian in n ..."
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We develop a simple multiscale model for the analysis and synthesis of nonGaussian, longrangedependent (LRD) network traffic loads. The wavelet transform effectively decorrelates LRD signals and hence is wellsuited to model such data. However, traditional waveletbased models are Gaussian in nature which one may at the most hope to match second order statistics of inherently nonGaussian traffic 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 nonGaussian traffic. This leads to a swift O(N) algorithm for fitting and synthesizing Npoint data sets. The resulting model belongs to the class of multifractal cascades, a set of processes with rich scaling properties which are better suited than LRD to capture burstiness. We elucidate our model's ability to capture the covariance structure of real data and then fit it to real traffic 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 overoptimistic predictions of tail queue probability even when taking LRD into account.