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This paper concerns the design of distributed algorithms for sharing network bandwidth resources among contending flows. The classical fairness notion is the so-called max-min fairness; Kelly (see Europ. Trans. Telecom. vol.8 p.33-37, 1997) has previously introduced the alternative proportional fairness criterion; we introduce a third criterion, which is naturally interpreted in terms of the delays experienced by ongoing transfers. We prove that fixed size window control can achieve fair bandwidth sharing according to any of these criteria, provided scheduling at each link is performed in an appropriate manner. We next consider a distributed random scheme where each traffic source varies its sending rate randomly, based on binary feedback information from the network. We show how to select the source behaviour so as to achieve an equilibrium distribution concentrated around the considered fair rate allocations …