Abstract-This work develops a discrete-time dynamical feedback system model for a simplified TCP network with RED control and provides a nonlinear analysis that can help in understanding observed parametric sensitivities. The model describes network dynamics over large parameter variations. The dynamical model is used to analyze the TCP-RED operating point and its stability with respect to various RED controller and system parameters. Bifurcations are shown to occur as system parameters are varied. These bifurcations, which involve the emergence of oscillatory and/or chaotic behavior, shed light on the parametric sensitivity observed in practice. The bifurcations arise due to the presence of a nonlinearity in the TCP throughput characteristic as a function of drop probability at the gateway. Among the bifurcations observed in the system are period doubling and border collision bifurcations. The bifurcations are studied analytically, numerically, and experimentally.

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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.

Abstract-This work develops a discrete-time dynamical feedback system model for a simplified TCP network with RED control and provides a nonlinear analysis that can help in understanding observed parametric sensitivities. The model describes network dynamics over large parameter variations. The dynamical model is used to analyze the TCP-RED operating point and its stability with respect to various RED controller and system parameters. Bifurcations are shown to occur as system parameters are varied. These bifurcations, which involve the emergence of oscillatory and/or chaotic behavior, shed light on the parametric sensitivity observed in practice. The bifurcations arise due to the presence of a nonlinearity in the TCP throughput characteristic as a function of drop probability at the gateway. Among the bifurcations observed in the system are period doubling and border collision bifurcations. The bifurcations are studied analytically, numerically, and experimentally.