A Multifractal Wavelet Model with Application to Network Traac Riedi Et Al.: Multifractal Wavelet Model with Application to Network Traffic 1

In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coeecients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing N-point data sets. We study both the second-order and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its eeectiveness, apply the model to network traac synthesis. The exibility and accuracy of the model and tting procedure result in a close t to the real data statistics (variance-time plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traac modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, nance, and geophysics.