A Theoretical Study of Internet Congestion Control: Equilibrium and Dynamics

Citation

Wang, Jiantao (2006) A Theoretical Study of Internet Congestion Control: Equilibrium and Dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4DQ0-GA49. https://resolver.caltech.edu/CaltechETD:etd-11122005-082753

Abstract

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 are 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 are present. We also introduce a discrete-time model for FAST TCP that fully captures the effect of 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 of whether a fairer allocation is 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.

At the end, two other related projects are briefly described.

Thesis Files