Use of Simulation and Random Matrix Theory to Identify the State of Network Traffic

The traffic behavior of the University of Louisville network with the interconnected backbone routers and the number of Virtual Local Area Network (VLAN) subnets is investigated using the Random Matrix Theory (RMT) approach. We employ the system of equal interval time series of traffic counts at all router to router and router to subnet connections as a representation of the inter-domain traffic. The cross-correlation matrix C of the real and simulated traffic rate changes between different traffic time series is calculated and tested against null- hypothesis of random interactions. The majority of the eigenvalues lambda_i of matrix C fall within the bounds predicted by the RMT for the eigenvalues of random correlation matrices. The inverse participation ratio (IPR) of congested traffic shows the higher level of localization (fewer number of randomly interacting network nodes). In other words, the IPR level signifies the start of congestion or correlated traffic. Hence, the RMT based model for multiple input multiple output (MIMO) system widely accepted in wireless communication domain is quite applicable for analysis and modeling of traffic dynamics of wired systems. In particular, the IPR of the RMT predicted boundaries in real traffic can be used as a congestion indicator in network congestion control mechanisms.