Convergence to fractional Brownian motion and to the Telecom process : the integral representation approach

It has become common practice to use heavy-tailed distributions in order to describe the variations in time and space of network traffic workloads. The asymptotic behavior of these workloads is complex; different limit processes emerge depending on the specifies of the work arrival structure and the nature of the asymptotic scaling. We focus on two variants of the infinite source Poisson model and provide a coherent and unified presentation of the scaling theory by using integral representations. This allows us to understand physically why the various limit processes arise