Representation of Positive Alpha-Stable Network Traffic Through Levy Mixtures
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Aspects of network traffic, among other impulsive time series, can be more accurately represented using the family of stable distributions. Simple, closed form solutions for stable distributions do not exist, other than special cases. Mixtures of one of these special cases, the L´evy (or Pearson V) distribution, can be used to provide a closed-form approximation of positive -stable (P S) distributions. We show that for a specific network traffic trace, accurate closed-form approximations of a P S time series can be obtained with only four mixture components. Additionally, we provide an algorithm for creating L´evy Mixture Approximations (LMAs) and demonstrate that non-linear methods can improve model accuracy while constraining the number of components and computational cost. This approach provides a computationally-tractable, accurate model for non-Gaussian, positive (or negative) time series such as network traffic. This model is in a form that is less costly for follow-on processing and detection, potentially facilitating real-time applications.
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