The multifractal property of bursty traffic and its parameter estimation based on wavelets

“Fractal” analysis of computer network traffic has been the subject of various studies. Most of the effort has been concentrated on measuring and modeling a possible long range dependence (LRD) process of the traffic trace. However, long range dependence is only one feature of the “fractal” behavior. In this paper, we study rather different properties which are conveniently described by using multifractal analysis. After a basic introduction to the definition of self-similar and multifractal process in traffic modeling, we use parsimonious traffic traces to examine the effectiveness of multifractal traffic modeling. Some MPEG-1 coded traces and TCP packets monitored at CERNET are used to give the statistical evidence of the multifractal nature through coarse grain. We find that using only the Hurst index in the self-similar approach is not enough to capture the burstiness in both small and large time scales while the Holder exponent provides insight into the bursty nature of the traffic sources. We propose a multiwindow wavelet transform method for the purpose of estimating the time varying scaling Holder exponent. Numerical results are also given to show the accuracy of multifractal modeling using real traffic traces