Heavy-tailed distributions with applications to broadband communication systems traffic

In the 90's statistical studies of high-resolution traffic measurements in different communication networks scenarios (from LANs to WANs) have highlighted properties of long memory of actual traffic flows. Later the asymptotic self-similarity characteristic of measured aggregated traffic has been explained in terms of heavy-tailed, infinite variance phenomena at the level of individual network connections and of the interactions between the human user and the network.

These experimental evidences, in strong contrast with conventional Markovian models and light-tailed distributions, have a deep impact on analytical techniques as well as on simulation of real networks. For instance, one of the basic results is that if network traffic components have infinite variance (e.g. transmission time) then the corresponding limit variable has infinite expectation, that implies a drastic change of the simulation methodology (as far as sample generation and confidence interval estimation are concerned).

In spite of a great progress in this new area, many problems are still open and continue to attract attention of researchers.

In this work, we focus on the basic properties of heavy-tailed distributions and discuss their applicability to describe some important new features of the network traffic. Moreover, we also consider the related long-range dependence property of the network traffic.

Most of the work is a survey of the existing literature on this topic, and an important goal is to present the material in a unified way, taking into account the most recent contributions on international journals, suitable for advanced study on the general topic of network performance. Also it is assumed to present a comparison between different methods of estimation of Hurst parameter and their application to real-life network traffic.