Phase Plane Analysis and Design for TCP Congestion Control

This paper describes a phase-plane method for providing an interpretation of various TCP flow control mechanisms. By using the phase-plane analysis, the stability and dynamical switching behaviors of TCP congestion control protocols are studied. By analyzing the mathematical models of the TCP congestion avoidance algorithms, the equilibrium condition and the dynamical behavior can be characterized within the phase plane. Furthermore, two types of design frameworks for the TCP window size adjustment are proposed and analyzed. These two protocols, called Vegas-like TCP type I and Vegas-like TCP type II, are designed based on the vector field of a dynamical system and inherit the idea from the standard TCP-Vegas protocol that uses RTT (round-trip-time) as a congestion measure. Type I gives a change in the number of switching dynamics of the vector field, while type II keeps the same number of switching dynamics of the vector field as TCP-Vegas but with a different style in each of switching dynamics. Finally, the performance of the proposed scheme is compared with the standard TCP-Vegas by the simulation study in the network simulator, ns-2.