A multifractal wavelet model with application to network traffic

Rudolf H. Riedi, Matthew S. Grouse, Vinay J. Ribeiro, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

462 Scopus citations


In this paper we develop a new multiscale modeling framework for characterizing positive-valued data with longrange-dependent correlations (I// 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 TVpoint 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.

Original languageEnglish (US)
Pages (from-to)992-1018
Number of pages27
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - 1999


  • Long-range dependence
  • Multifractals
  • Network traffic
  • Positive i// noise
  • Wavelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Information Systems


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