We present a model of a network of synchronised sources operating additive increase multiplicative decrease (AIMD) congestion control algorithms. We show: (i) that networks of such devices in the presence of a drop-tail bottleneck buffer may be modelled as a positive linear system; (ii) that such networks possess a unique stationary point; and (iii) that this stationary point is globally exponentially stable. We use these results to establish conditions for the fair co-existence of traffic in networks employing heterogeneous AIMD algorithms and to design a new protocol for operation over high-speed and long-distance links. (c) 2004 Published by Elsevier Ltd.