Gradient bandwidth allocations

Abstract

We look at bandwidth-sharing networks where bandwidth allocations are not known to maximize a priori any utility function. Instead, we only require the allocation functions to be 0-homogeneous and concave, which are desirable properties in many situations. We show that a certain gradient condition is necessary and sufficient for such allocations to solve an optimization problem leading to important corollaries such as deriving the stability set of these 0-homogeneous concave allocation.