A first-order discrete-time dynamic model for a simplified TCP network with RED control is introduced and its nonlinear dynamical behavior is analyzed. The results are used to consider automatic parameter tuning to improve dynamical behavior during congestion. It is argued that for this discrete time normalized feedback system, two controller parameters as opposed to three are enough to completely classify the dynamical behavior of the system. 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 algorithm is proposed for delaying the instability in the system and rendering the system stable. With the help of bifurcation diagrams it is demonstrated that the interaction between a RED gateway and TCP Reno connections can lead to chaotic behavior if the parameters are improperly selected. The analysis is validated through simulation.
References:
Priya Ranjan and Eyad H. Abed Nonlinear Instabilities in TCP-RED
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