A continuous model of transportation revisited
Abstract
We review two models of optimal transport, where congestion effects during the transport can be possibly 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. (SIAM J Control Optim 47: 1330-1350, 2008), which in turn is the 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 decomposition theorem for normal 1-currents.
Keywords
Cite
@article{arxiv.1211.6677,
title = {A continuous model of transportation revisited},
author = {Lorenzo Brasco and Mircea Petrache},
journal= {arXiv preprint arXiv:1211.6677},
year = {2013}
}
Comments
26 pages. Theorem A.20 of v1 was not correct: we removed it and replaced it with the counterexample A.18 in v2. We also made some improvements to the wording and corrected some typos