On the superposition of heterogeneous traffic at large time scales

TL;DR

This paper investigates the distributional behavior of aggregated network traffic over large time scales, explaining why Gaussian models are prevalent and identifying the conditions under which different stochastic processes approximate traffic.

Contribution

It provides new limit theorems for finite streams of independent traffic sources, clarifying the conditions for Gaussian approximation and the role of aggregation.

Findings

Gaussian approximation holds under sufficient vertical aggregation.

Traffic with different session initiation intensities can be modeled by fBm or stable Levy motion.

The paper quantifies the amount of aggregation needed for Gaussian behavior.

Abstract

Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail, Mikosch et al. (Ann Appl Probab, 12:23-68, 2002) and Kaj and Taqqu (Progress Probab, 60:383-427, 2008) have shown that traffic at large time scales can be approximated by either fractional Brownian motion (fBm) or stable Levy motion. We study distributional properties of cumulative traffic that consists of a finite number of independent streams and give an explanation of why Gaussian examples abound in practice but not stable Levy motion. We offer an explanation of how much vertical aggregation is needed for the Gaussian approximation to hold. Our results are expressed as limit theorems for a sequence of cumulative traffic processes whose session initiation intensities satisfy growth rates similar to those used in Mikosch et al. (Ann Appl Probab, 12:23-68, 2002).