Time Delayed Feedback Control of Internet Congestion Control Model with Compound TCP under RED

This paper is concerned with controlling of chaotic behavior in Internet congestion control model with Compound TCP under RED. Compound TCP (CTCP) is currently the default transport layer protocol in the Windows operating system. Firstly, this paper briefly analyzes the nonlinear dynamics of the CTCP under RED network with respect to system parameters. Bifurcation is shown to occur when parameters cross through the critical values. Then, in order to widen the stability domain of the system, the Time Delayed Feedback Control (TDFC) is added to the system. With the purpose of better reflecting the effect of TDFC, the paper analyzes the fixed point of congestion control system by theoretical analysis. By appropriately selecting the time delay feedback gain, the bifurcation is successfully delayed and the chaotic orbits are stabilized to the fixed point which indicates the performance of congestion control system is improved significantly. Finally, numerical simulations are provided to show the effectiveness of the theoretical results.