Convergence Complexity of Optimistic Rate-Based Flow-Control Algorithms

Abstract

This paper studies basic properties of rate-based flow-control algorithms and of the max-min fairness criteria. For the algorithms we suggest a new approach for their modeling and analysis, which may be considered more “optimistic” and realistic than traditional approaches. Three variations of the approach are presented, and their rate of convergence to the optimal max-min fairness solution is analyzed. In addition, we introduce and analyze approximate rate-based flow-control algorithms. We show that under certain conditions the approximate algorithms may converge faster. However, we show that the resulting flows may be substantially different from the flows dictated by the max-min fairness. We further demonstrate that the max-min fairness solution can be very sensitive to small changes, i.e., there are configurations in which an addition or deletion of a session with rate δ may change the allocation of another session by Ω(δ·2n/2), but by no more thanO(δ·2n). This implies that the max-min fairness criteria may provide a bad estimate of how far a set of flow allocations is from the optimal allocation.