Abstract

We review two models of optimal transport where congestion effects during the transport can possibly by taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fields with given divergence. The second one is the model by Carlier et al., which is in turn a continuous reformulation of Wardrop's model on graphs. We discuss the extensions of these models to their natural functional analytic setting and show that they are indeed equivalent, by using Smirnov's decomposition theorem for normal 1-currents.