In this paper we propose a multifractal traffic model that is based on a multiplicative cascade presenting specific multiplier distributions in each cascade stage. In the proposed model, the multipliers are obtained through the estimate of their probability densities found in real network traffic by using Kernel and Acceptance/Rejection methods. Statistical analysis and queueing behavior study ...

This paper describes three visually interactive tools for the analysis, modeling, and generation of long-range dependent (LRD) network traffic. The synTraff toolkit uses a three-step modeling approach based on F-ARIMA processes to generate monofractal traffic; the WsynTraff toolkit implements the Wavelet-domain Independent Gaussian (WIG) model from the literature for representing multifractal t...

Multifractal analyses of binary images of soil thin sections (STS) are widely used to characterize pore structure. However, no geometrical model is known to exist for a binary multifractal. Thus, the multifractality of binary images, and the accuracy of multifractal parameters estimated from them, need to be carefully evaluated. We captured 8-bit depth resolution digital grayscale images of thr...

We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the transition will have to satisfy. We find a nonparabolic multifractal spectrum and determine the ratio of boundary to bulk multifractal exponents. Our results r...

This is a short review in honor of B. Mandelbrot’s 80st birthday, to appear in Wilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial time series, in particular the intermittent, long-memory nature of the volatility. We describe in details the Bacry-Muzy-Delour multifractal random walk. We poi...

A new generation of instruments in astrophysics or vision now provide spherical data. These spherical data may present a selfsimilarity property while no spherical analysis tool is yet available to characterize this property. In this paper we present a first numerical study of the extension of multifractal analysis onto the sphere using spherical wavelet transforms. We use a model of multifract...

The apparent fractal properties of TCP data tra c have recently attracted con siderable interest Most prominently fractional Brownian motion FBM has been used to model the long range dependence of tra c traces through self similarity Tra c being by nature a process of positive increments though a multifractal ap proach appears more natural In this study various traces of TCP tra c have been ana...

This paper proposes two local multifractal measures motivated by blanket method for calculation of fractal dimension. They cover both fractal approaches familiar in image processing. The first two measures (proposed Methods 1 and 3) support model of image with embedded dimension three, while the other supports model of image embedded in space of dimension three (proposed Method 2). While the cl...

Multifractal behavior was recently observed in several traces of IP WAN traffic. This paper proposes a novel multifractal traffic model, which characterizes the joint process of packet arrivals and packet sizes. The construction of the traffic process is based on stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. We work with a single L-Sy...

We propose a new multifractal traffic model for network traffic. The model is a combination of a multiplicative cascade with an independent lognormal process. We show that the model has all the important properties observed in data traffic including LRD, multifractality and lognormality. We also demonstrate that the model is flexible enough to capture the complete multifractal characteristics o...