Characteristic Timescales: Analyzing End-to-end Delay in Networks under High Loads

We develop a theory of network behavior under high load conditions and rapidly changing traffic demand matrices, using techniques from spectral graph theory and the physics of dynamical systems. We focus on the mean end-to-end delay as the performance metric and show that at high loads, there is a “characteristic timescale” of the network that determines the mean end-to-end delay. We show how this timescale can be analytically determined for a given network and validate our theory using simulations. We envisage that such a characterization can be used to compare network performance among various topologies, and can potentially lead to new network optimization techniques.