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Rate control protocols that utilise explicit feedback from routers are able to achieve fast convergence to an equilibrium which approximates processor-sharing on a single bottleneck link, and hence such protocols allow short flows to complete quickly. For a network, however, processor-sharing is not uniquely defined but corresponds with a choice of fairness criteria, and proportional fairness has a reasonable claim to be the network generalization of processor-sharing. In this paper, we develop a variant of RCP (rate control protocol) that achieves α-fairness when buffers are small, including proportional fairness as the case α = 1. At the level of theoretical abstraction treated, our model incorporates a general network topology, and heterogeneous propagation delays. For our variant of the RCP algorithm, we establish a simple decentralized sufficient condition for local stability. An outstanding question for explicit congestion control is whether the presence of feedback based on queue size is helpful or not, given the presence of feedback based on rate mismatch. We show that, for the variant of RCP considered here, feedback based on queue size may cause the queue to be less accurately controlled. A further outstanding question for explicit congestion control is the scale of the step-change in rate that is necessary at a resource to accommodate a new flow. We show that, for the variant of RCP considered here, this can be estimated from the aggregate flow through the resource, without knowledge of individual flow rates.

Stability and fairness of explicit congestion control with small buffers