Random Matrix Theory Approach To Traffic Dynamics Of Complex Computer Networks
University of Louisville
University of Lousiville
Last modified: May 31, 2007
We study traffic dynamics of complex computer network using traffic count data recorded by monitoring software at the University of Louisville. Our analysis of system's correlations is based on the Random Matrix Theory (RMT) extensively used in physics, engineering and, more recently, in finance.
To describe "awareness" of the network's structural constituents about each other, we look at the equal-time cross-correlation matrix C. One of the possible analytical approaches is the study of eigenvalues and eigenvectors of C. The eigenvalues have direct connection to spectrum of physical systems, while eigenvectors describe the excitation/signal/information propagation inside the system.
In this paper, however, we focus on the more integrative characteristic of the complex network dynamics. Similarly to spectral analysis of engineering complex structures, we compute the so-called resolvent for the matrix C, and address its statistics. The spectrum of the cross-correlation matrix splits into three parts. The majority of the eigenvalues of C fall within the bounds predicted by the RMT for the eigenvalues of random correlation matrices. They constitute the central part of the spectrum. The other two, left and right parts of the spectrum display systematic deviations from the RMT predictions. This is reflected in the qualitative and quantitative statistical behavior of the resolvent.
Thus, our goal is to utilize the differences between three parts of the spectrum to establish the profile of healthy dynamics of the complex network.