Modeling and Analysis of Heavy-tailed Distributions via Classical Teletraac Methods

We propose a new methodology for modeling and analyzing heavy-tailed distributions, such as the Pareto distribution, in communication networks. The basis of our approach is a tting algorithm which approximates a heavy-tailed distribution by a hyperexponential distribution. This algorithm possesses several key properties. First, the approximation can be achieved within any desired degree of accuracy. Second, the tted hyperexponential distribution depends only on a few parameters. Third, only a small number of exponentials are required in order to obtain an accurate approximation over many time scales. Once equipped with a tted hyperexponential distribution, we have an integrated framework for analyzing queueing systems with heavy-tailed distributions. We consider the GI=G=1 queue with Pareto distributed service time and show how our approach allows to derive both quantitative numerical results and asymptotic closed-form results. This derivation shows that classical teletraac methods can be employed for the analysis of heavy-tailed distributions.