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Convergence results for synchronised communication networks

We present a simplified model of a network of TCP-like sources that compete for a shared bandwidth. We show that: (i) networks of communicating devices operating AIMD congestion control algorithms may be modelled as a positive linear system; (ii) such networks possess a unique stationary point; and (iii) this stationary point is stable. Using these results we establish conditions for the fair co-existence of traffic in networks employing heterogeneous AIMD algorithms, and present convergence rates to equilibria for such networks.