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This paper presents Phantom, a simple constant space algorithm for rate based flow control. As shown by our simulations, it converges fast to a fair rate allocation while generating a moderate queue length. While our approach can be easily implemented in ATM switches for managing ABR traffic, it is also suitable for flow control in TCP router based networks. Both the introduced overhead and the required modifications in TCP flow control systems are minimal. The implementation of this approach in TCP guarantees fairness and provides a unifying interconnection between TCP routers and ATM networks. The new algorithm easily inter-operates with current TCP flow control mechanisms and thus can be gradually introduced into installed based TCP networks.

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 mod cling 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 tlows 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 8 may change the allocation of another session by Cl(c$ .2~), but by no more than 0(6 .2W).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.