A multifractal wavelet model with application to network traffic

• Published in: IEEE transactions on information theory Vol. 45; no. 3; pp. 992 - 1018
• Main Authors: Riedi, R.H., Crouse, M.S., Ribeiro, V.J., Baraniuk, R.G.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-04-1999; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Analysis; Biological system modeling; Cascades; Communication system traffic control; Computer networks; Data transmission; Discrete wavelet transforms; Fractals; Image processing; Information theory; Network synthesis; Networks; Predictive models; Telecommunication traffic; Traffic control; Traffic engineering; Traffic flow; Wavelet; Wavelet transforms
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.761337

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 coefficients 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 effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variance-time plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.