Global Asymptotic Stability Analysis of FAST TCP Using Nonlinear Small Gain Theorem

We investigate the global asymptotic stability of FAST TCP based on a continuous-time model for FAST TCP network in which all of cross traffics, time-varying network feedback delays, and queuing delay dynamics at link are taken into consideration. We recognize the dynamic interaction between FAST TCP source and link as a feedback interconnection of two input-to-state stable(ISS) subsystems. Then, applying the Razumikhin-type nonlinear small gain theorem, we prove that FAST TCP network is inherently ISS and globally asymptotically stable without any specific conditions on the tuning parameter α or update gain γ for FAST TCP operation. The ISS property of FAST TCP guarantees the robustness to disturbances, and the approach using the small gain theorem provides a guideline to design a globally stable and robust congestion control algorithm. The simulation results demonstrate the validity of the global asymptotic stability of FAST TCP.