Nonlinear stability analysis for a class of TCP/AQM networks

Recent work has shown the benefit of using proportional feedback in TCP/AQM (transmission control protocol/active queue management) networks. By proportional feedback we mean the marking probability is proportional to the instantaneous queue length. Our earlier work (2001) relied on linearization of nonlinear fluid-flow models of TCP. In this work we address these nonlinearities directly and establish some stability results when the marking is proportional. In the case of delay-free marking, we show the system's equilibrium point to be asymptotically stable for all proportional gains. In the more realistic case of delayed feedback, we establish local asymptotic stability and quantify a region of attraction.