Browsing by Author "Abry, Patrice"

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    Compound Poisson Cascades
    (2002-05-01) Chainais , Pierre; Riedi, Rudolf H.; Abry, Patrice; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
    Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic, to name but two. Placing multifractal analysis in the more general framework of infinitely divisible laws, we design processes which possess at the same time stationary increments as well as multifractal and more general infinitely divisible scaling over a continuous range of scales. The construction is based on a Poissonian geometry to allow for continuous multiplication. As they possess compound Poissonian statistics we term the resulting processes compound Poisson cascades. We explain how to tune their correlation structure, as well as their scaling properties, and hint at how to go beyond scaling in form of pure power laws towards more general infinitely divisible scaling. Further, we point out that these cascades represent but the most simple and most intuitive case out of an entire array of infinitely divisible cascades allowing to construct general infinitely divisible processes with interesting scaling properties.
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    Multiscale Nature of Network Traffic
    (2002-05-01) Abry, Patrice; Baraniuk, Richard G.; Flandrin, Patrick; Riedi, Rudolf H.; Veitch, Darryl; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
    The complexity and richness of telecommunications traffic is such that one may despair to find any regularity or explanatory principles. Nonetheless, the discovery of scaling behavior in tele-traffic has provided hope that parsimonious models can be found. The statistics of scaling behavior present many challenges, especially in non-stationary environments. In this paper, we overview the state of the art in this area, focusing on the capabilities of the wavelet transform as a key tool for unravelling the mysteries of traffic statistics and dynamics.