Modeling and analysis of power-tail distributions via classical teletraffic methods

  • Authors:

  • David Starobinski;Moshe Sidi

  • Affiliations:

  • Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA Email: staro@eecs.berkeley.edu;Department of Electrical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel Email: moshe@ee.technion.ac.il

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2000

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Abstract

We propose a new methodology for modeling and analyzing power-tail distributions, such as the Pareto distribution, in communication networks. The basis of our approach is a fitting algorithm which approximates a power-tail 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 fitted 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 fitted hyperexponential distribution, we have an integrated framework for analyzing queueing systems with power-tail 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 teletraffic methods can be employed for the analysis of power-tail distributions.