Dynamic Optimal Transport on Networks

Abstract

We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter κ, has to be paid for interchanging mass between edges and vertices. We show existence of minimisers using duality and discuss the relationship of the model to other metrics such as Fisher–Rao and the classical Wasserstein metric. Finally, we examine the limiting behaviour of the model in terms of the parameter κ.