A Multifractal Wavelet Model with Application to Network Traac

In this paper we develop a new multiscale modeling framework for characterizing positive valued data with long range dependent correlations f noise Using the Haar wavelet transform and a special multi plicative structure on the wavelet and scaling coe cients 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 mul tifractal analysis We derive a scheme for matching the model to real data observations and to demonstrate its e ectiveness apply the model to network tra c synthe sis 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 be havior Although for illustrative purposes we focus on applications in network tra c modeling the multifractal wavelet model could be useful in a number of other ar eas involving positive data including image processing nance and geophysics Index Terms Long range dependence multifractals network tra c positive f noise wavelets