Delayed Correlations in Inter-Domain Network Traffic

Abstract

To observe the evolution of network traffic correlations we analyze the eigenvalue spectra and eigenvectors statistics of delayed correlation matrices of network traffic counts time series. Delayed correlation matrix D is composed of the correlations between one variable in the multivariable time series and another at a time delay \tau . Inverse participation ratio (IPR) of eigenvectors of D deviates substantially from the IPR of eigenvectors of the equal time correlation matrix C. We relate this finding to the localization and discuss its importance for network congestion control. The time-lagged correlation pattern between network time series is preserved over a long time, up to 100\tau, where \tau=300 sec. The largest eigenvalue \lambda_{max} of D and the corresponding IPR oscillate with two characteristic periods of 3\tau and 6\tau . The existence of delayed correlations between network time series fits well into the long range dependence (LRD) property of the network traffic. The ability to monitor and control the long memory processes is crucial since they impact the network performance. Injecting the random traffic counts between non-randomly correlated time series, we were able to break the picture of periodicity of \lambda_{max}. In addition, we investigated influence of the periodic injections on both largest eigenvalue and the IPR, and addressed relevance of these indicators for the LRD and self-similarity of the network traffic.