Equilibria of a Class of Transport Equations Arising in Congestion Control

This paper studies a class of transport equations arising from stochastic models in congestion control. This class contains two cases of loss point process models: the rate-independent Poisson case where the packet loss rate is independent of the throughput of the flow and the rate-dependent case where the point process of losses has an intensity which is a function of the instantaneous rate. This class of equations covers both the case of persistent and of non-persistent flows. We give a direct proof of the fact that there is a unique density solving the associated differential equation and we provide a closed form expression for this density and for its mean value.