A nonlinear integral operator encountered in the bandwidth sharing of a star-shaped network

We consider a symmetrical star-shaped network, in which bandwidth is shared among the active connections according to the “min” policy. Starting from a chaos propagation hypothesis, valid when the system is large enough, one can write equilibrium equations for an arbitrary link of the network. This paper describes an approach based on functional analysis of nonlinear integral operators, which allows to characterize quantitatively the behaviour of the network under heavy load conditions.