Bandwidth sharing networks under a diffusion scaling

This paper considers networks operating under alpha-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 fluid limit is explicitly identified, for both the single-node network as well as the linear network. More specifically, a criterion is derived that indicates, for each specific class, whether or not it is essentially transmitting at peak rate. Knowing the equilibrium point of the fluid limit, the steady-state behavior under a diffusion scaling is determined. This allows an explicit characterization of the correlations between the number of flows of the various classes.