Large Scale Cross-Correlations in Internet Traffic

TL;DR

This paper applies random matrix theory to analyze cross-correlations in Internet traffic, revealing universal properties and network-specific correlations, and identifying active centers influencing traffic dynamics.

Contribution

It introduces a novel application of RMT to large-scale Internet traffic data, uncovering universal correlation properties and identifying key active centers in the network.

Findings

Eigenvalue distribution matches RMT predictions

Large eigenvalues indicate genuine network correlations

Active centers exchange information with many routers

Abstract

The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network `Renater'. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues--up to a rescaling which exhibits a typical correlation time of the order 10 minutes--and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between connections. The study of the most correlated connections reveals the existence of `active centers' which are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the WWW traffic.