  Several large scale networks, such as the backbone of the Internet, have been
observed to behave like convex Riemannian manifolds of negative curvature. In
particular, this paradigm explains the observed existence, for networks of this
type, of a "congestion core" through which a surprising large fraction of the
traffic transits, while this phenomenon cannot be detected by purely local
criteria. In this practical situation, it is important to estimate and predict
the size and location of this congestion core. In this article we reverse the
point of view and, motivated by the physical problem, we study congestion
phenomena in the purely theoretical framework of convex Riemannian manifolds of
negative curvature. In particular, we introduce a novel method of fair-division
algorithm to estimate the size and impact of the congestion core in this
context.
