A Theoretical Study of Internet Congestion Control: Equilibrium and                                              Dynamics

Jiantao Wang, Control and Dynamical Systems, California Institute of Technology

In the last several years, significant progress has been made in modelling the Internet congestion control using theories from convex optimization and feedback control. In this dissertation, the equilibrium and dynamics of various congestion control schemes are rigorously studied using these mathematical frameworks.

First, we study the dynamics of TCP/AQM systems. We demonstrate that the dynamics of queue and average window in Reno/RED networks is determined predominantly by the protocol stability, not by AIMD probing nor noise traffic. Our study shows that Reno/RED becomes unstable when delay increases, and more strikingly when link capacity increases. Therefore, TCP Reno is ill suited for the future high-speed network, which has motivated the design of FAST TCP. Using a continuous-time model, we prove that FAST TCP is globally stable without feedback delays, and provide a sufficient condition for local stability when feedback delays present. We also introduce a discrete-time model for FAST TCP that fully captures the effect of {\em self-clocking}, and derive the local stability condition for general networks with feedback delays.                                                                                      
                                                                                                                                
Second, the equilibrium properties (i.e., fairness, throughput and capacity) of TCP/AQM systems are studied using the utility maximization framework. We quantitatively capture the variations in network throughput with changes in link capacity and allocation fairness. We clarify the open conjecture whether a fairer allocation is {\em always} more efficient. The effects of changes in routing are studied using a joint optimization problem over both source rates and their routes. We investigate whether minimal-cost routing with proper link costs can solve this joint optimization problem in a distributed way. We also identify the tradeoff between achievable utility and routing stability.