Bandwidth-sharing networks under a diffusion scaling

This paper considers networks operating under α-fair bandwidth sharing. When imposing a peak rate (i.e., an upper bound on the users' transmission rates, which could be thought of as access rates), the equilibrium point of the uid limit is explicitly identi ed, for both the single-node network as well as the linear network. More speci cally, a criterion is derived that indicates, for each speci c class, whether or not it is essentially transmitting at peak rate. Knowing the equilibrium point of the uid limit, the steady-state behavior under a diffusion scaling is determined. This allows an explicit characterization of the correlations between the number of ows of the various classes.