Converging to approximated max-min flow fairness in logarithmic time

Max-min is a frequently praised criterion for flow control despite its limitations. In practice, the fast rate of changes in the connection layout in modern networks makes it hard for any flow control algorithm to converge to an optimal point. In such an environment, it might be better to trade accuracy with speed. We present algorithms that relax the optimality criterion of the max-min flow fairness but achieve a fast convergence time that is logarithmic in the link bandwidth and not a function of the number of active connections (or sessions). The relaxation we use requires rates to be increased or decreased by a certain factor, 1+ε, or in other words, assigned rates can only be a natural power of some basic bandwidth 1+ε. Under this criterion, the quiescent time of our flow control algorithms is log_1+ε B, where B is the maximum link bandwidth in minimum allocation units. This is a great improvement over the super-linear quiescent time of known algorithms both exact and approximated