Pointwise Hölder exponent estimation in data network traffic

TL;DRAbstract

We present an algorithm able to estimate the pointwise Holder exponent of any function. This algorithm is based on a study of the wavelet decomposition of the function and is motivated by the existence of an effective characterization of the function's local Holder exponent through size estimates of the wavelet coefficients. The algorithm can be applied to all kind of singularities (e.g., oscillating or nonoscillating, isolated or not). We discuss the consistency of the results we have obtained and the problem of its implementation for sampled functions of finite length. We also show how such estimates of the local regularity can also lead to a more general statistical analysis of functions, using the multifractal spectrum. Our motivating application is the estimation of local "burstiness" in data network traffic. Considerable work is devoted to summarizing the statistical nature of bursts in network traffic and we present an algorithm to pinpoint local irreg

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