The convergence properties of distributed maxmin fair rate allocation algorithms

We introduce a new conceptual framework to investigate the underlying structure of network bottlenecks in maxmin fair flow control. It is shown that a network has a hierarchical structure with regard to its bottlenecks. The number, H, of network bottleneck levels is proved to be no greater than the number, K, of network bottleneck rates. It is also shown that H can be much smaller than K. We propose a new computational model of maxmin fair rate allocation based on the structural property of network bottlenecks. It is shown that in comparison with a widely used computational model, this one provides a better description of the convergence processes of a class of distributed maxmin fair rate allocation (DMFRA) algorithms. As a natural outcome, we also obtain new and tighter upper bounds on the convergence time of these algorithms.