Delayed Correlations in Inter-Domain Network Traffic

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 (τ ) is composed of the correlations between one variable in the multivariable time series and another at a time delay τ . We determined, that inverse participation ratio (IPR) of eigenvectors of D (τ ) deviates substantially from that of eigenvectors of the equal time correlation matrix. The largest eigenvalue λmax of D (τ ) and the corresponding IPR oscillate with two characteristic periods of 3τ and 6τ . Found delayed correlations between network time series fits well into the long range dependence (LRD) property of the network traffic. Injecting the random traffic counts between non-randomly correlated time series, we were able to break the picture of periodicity of λmax. 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. CATEGORIES AND SUBJECT DESCRIPTORS C.2.3 [Computer-Communication Networks]: Network Operations GENERAL TERMS Measurement, Experimentation