PHASE-PLANE ANALYSIS OF SWITCHING DYNAMICS OF TCP FLOW CONTROL ALGORITHMS

H.-T. Lee,∗ F.-L. Lian,∗∗ and T.-C. Fong∗∗

Keywords

Phaseplane analysis, switching dynamics, transmission control pro tocol, congestion avoidance

Abstract

A phase-plane method for providing an interpretation of various transmission control protocol (TCP) flow control mechanisms has been proposed in this paper. The dynamical switching behaviours and stability of TCP congestion control protocols are discussed by using the phase-plane analysis. Via analyzing the mathematical models of the TCP congestion avoidance algorithms, the dynamical behaviour and equilibrium condition 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 dynamical systems and inherit the idea from the standard TCP-Vegas protocol that uses round-trip time as a congestion measure. Type I gives a change in the number of switching dynamics of the vector field, on the other hand, 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 validated and compared with the standard TCP-Vegas by the simulation study in the network simulator, ns-2.

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