Convergence complexity of optimistic rate-based flow-control algorithms

This paper studies basic properties of rate-based flow-control algorithms a nd of the max-min fairness criteria. For the algorithms we suggest a new ap proach for their modeling and analysis, which may be considered more "optim istic" and realistic than traditional approaches. Three variations of the a pproach are presented, and their rate of convergence to the optimal max-min fairness solution is analyzed. In addition, we introduce and analyze appro ximate rate-based now-control algorithms. We show that under certain condit ions 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 s olution can be very sensitive to small changes, i.e., there are configurati ons in which an addition or deletion of a session with rate delta may chang e the allocation of another session by Omega(delta . 2(n/2)), but by no mor e than O(delta . 2(n)). This implies that the max-min fairness criteria may provide a bad estimate of how far a set of now allocations is from the opt imal allocation. (C) 1999 Academic Press.