Hybrid Control of Bifurcation and Chaos in Dynamic Model of Compound TCP under RED

Compound TCP(CTCP) is a practical congestion control algorithm for high-speed and long delay networks. In this paper we address the problem of bifurcation and chaos analysis and its control of a nonlinear congestion control model with CTCP connections and random early detection (RED) gateway. First, we briefly analyze the nonlinear dynamics of the CTCP network with respect to system parameters. Then a hybrid control strategy using both state feedback and parameter perturbation is employed to control the bifurcation and stabilize the chaotic orbits embedded in this discrete-time dynamic system of CTCP/RED. Theoretical analysis show that the controlled system can achieve a stable average queue size in an extended range of parameters and even completely eliminates the chaotic behavior in a particular range of parameters. Therefore it is possible to decrease the sensitivity of RED parameters. Finally, numerical simulations are provided to show the effectiveness of the theoretical results.