A Note on the Fairness of Additive Increase and Multiplicative Decrease

Some recent papers [KMT97, MR98] have shown that congestion control based on additive increase and multiplicative decrease tends to share bandwidth according to proportional fairness. Proportional fairness is a form of fairness which distributes bandwidth with a bias in favour of flows using a smaller number of hops, this is in contrast with max-min fairness, which gives absolute priority to small flows. We revisit those results by using the modelling framework based on the ordinary differential equation method in [LJU77, KC78]. We find that for the case of small increments and constant round trip times, and in the regime of rare negative feedback, the proportional fairness result can only very approximately reflect the real rate allocation when we assume that the feedback received by sources is independent of their sending rates. In the case where sources receive feedback proportionally to their sending rates, and still for sources with identical round trip times, this is no longer true and the fairness provided is different. We show, by simulation on some examples, that even for larger increments, the average rate convergence is in agreement with our results. Finally, we establish that in the event of rate proportional feedback, our results maintain consistency with the well-known derivations relating TCP throughput as a function of loss ratio. However, this does not hold for the rate independent case, which we consider further validation ofthe assumption of rate dependent feedback.


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