Stateless Near Optimal Flow Control with Poly-logarithmic Convergence

We design completely local, stateless, and self-stabilizing flow control mechanism to be executed by “greedy” agents associated with individual flow paths. Our mechanism is very natural and can be described in a single line: If a path has many “congested” edges, decrease the flow on the path by a small multiplicative factor, otherwise increase its flow by a small multiplicative factor. The mechanism does not require any initialization or coordination between the agents. We show that starting from an arbitrary feasible flow, the mechanism always maintains feasibility and reaches, after poly-logarithmic number of rounds, a 1 + approximation of the maximum throughput multicommodity flow. Moreover, the total number of rounds in which the solution is not 1 + approximate is also poly-logarithmic. Previous distributed solutions in our model either required a state since they used a primal-dual approach or had very slow (polynomial) convergence.