Bifurcation analysis of TCP-RED dynamics

The authors previously (2002) presented a first-order discrete-time dynamic model for a simplified TCP network with RED (random early detection) control, and numerically studied the nonlinear dynamics of the system. Here, a bifurcation analysis of a normalized version of this model is given, providing analytical justification for the previous results. Use of a normalized model is also useful from the point of view of simulation studies, in that fewer parameter combinations need to be considered. This system is used to analyze the operating point of TCP-RED and its stability with respect to various controller and system parameters. The existence of both typical (period doubling) and atypical (border collision) bifurcations with respect to certain parameters is demonstrated. An explicit stability condition in terms of system parameters is given and its implication for the dynamics of a network is discussed. Finally, a simple real time control example is considered in which the goal is delaying instability via small feedback adjustment of a system parameter.