Convergence complexity of optimistic rate based flow control algorithms

This paper studies basic properties of rate based flowcontrol 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 an 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 than the flows according to 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 · 2 n/2), but by no more than O(δ · 2ⁿ). This implies that it might be hard to locally estimate in a given state how close a session is to its max-min fair allocation.