Global stability conditions for rate control with arbitrary communication delays

Abstract

We adopt the optimization framework for the rate allocation problem proposed by Kelly and investigate the stability of the system with arbitrary communication delays between network elements. It is shown that there is a natural underlying discrete time system whose stability is directly related to the stability of the given system. We first present general stability conditions of the system with arbitrary delays, and then apply these results to establish the stability of the system with a family of popular utility and resource price functions. The exponential stability of the system with the given utility and resource price functions is established. We also investigate discretized models that better approximate the packet level dynamics of the system and show that similar stability conditions can be obtained. Numerical examples are provided to validate our analyses.