| This dissertation deals with congestion control of the Internet based on analytical frameworks of convex optimization and control theory.; The development of congestion control protocols is first reviewed, with focus on their implicit negative feedback principle. A survey is then presented of recent analytical approaches to the problem, based on utility optimization and control system technology. In particular, we review two sets of algorithms ("dual" and "primal-dual") which exhibit the following equilibrium features: highly efficient usage of resource, high quality of service such as low delays, and fair rate allocation ("primal-dual" only), together with the local stability of this equilibrium, which is scalable with respect to delays, capacities, and network topology.; The global stability with time delays of these two sets of congestion control algorithms is extensively studied. We apply a variety of approaches, concentrating for the most part on single bottleneck networks. For the "dual" algorithm with homogeneous delays, the Small-Gain theorem is applied to the nonlinear delay system by decomposing it into two blocks with time delays encapsulated into one block, and nonlinearities into the other. A Lyapunov-Razumikhin argument is used for the stability analysis with heterogeneous data flows. For the "primal-dual" algorithm, perturbation analysis is extended to study the multi-state system by taking the fast scale dynamics as a growth limited perturbation. For general topologies, the trajectories of both systems are shown to be ultimately bounded independently of stability conditions. Focusing again on single bottleneck systems, these bounding arguments are then extended through iteration to obtain tighter results on global stability of both systems.; Implementation issues at packet level are investigated for the "primal-dual" algorithm. Through comprehensive analysis on stability, robustness and speed of response, the parameters can be successfully configured. The effects of elements such as utility functions on the dynamic properties can also be predicted. A feedback communication scheme is implemented, which transmits the float prices through statistical marking of ECN bits. Pseudo codes for the controllers are given, and possible solutions to reduce the computing overhead are discussed. Design objectives both for equilibrium and dynamics are validated through extensive simulations. Another implementation without ECN support, in which queueing delays act as feedback signals, is also studied through simulations. |
