In the classical Monge-Kantorovich problem, the transportation cost only
depends on the amount of mass sent from sources to destinations and not on the
paths followed by this mass. Thus, it does not allow for congestion effects.
Using the notion of traffic intensity, we propose a variant taking into account
congestion. This leads to an optimization problem posed on a set of probability
measures on a suitable paths space. We establish existence of minimizers and
give a characterization. As an application, we obtain existence and variational
characterization of equilibria of Wardrop type in a continuous space setting
