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Fitting mixtures of exponentials to long-tail distributions to analyze network performance models

Traffic measurements from communication networks have shown that many quantities characterizing network performance have long-tail probability distributions, i.e., with tails that decay more slowly than exponentially. Long-tail distributions can have a dramatic effect upon performance, but it is often difficult to describe this effect in detail, because performance models with component long-tail distributions tend to be difficult to analyze. We address this problem by developing an algorithm for approximating a long-tail distribution by a finite mixture of exponentials. The fitting algorithm is recursive over time scales. At each stage, an exponential component is fit in the largest remaining time scale and then the fitted exponential component is subtracted from the distribution. Even though a mixture of exponentials has an exponential tail, it can match a long-tail distribution in the regions of primary interest when there are enough exponential components.