Related papers: A continuous model of transportation revisited
We revisit the classic problem of determining optimal routes in a graph for transporting two given distributions defined on its nodes, originally studied by Wardrop and Beckmann in the 1950s. The global congestion profile at any given time…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
We propose a model of optimal parallel transport between vector fields on a connection graph, which consists of a weighted graph along with a map from its edges to an orthogonal group. Inspired by the well-known equivalence of 1-Wasserstein…
In this paper, urban traffic is modeled using dual graph representation of urban transportation network where roads are mapped to nodes and intersections are mapped to links. The proposed model considers both the navigation of vehicles on…
We adapt the problem of continuous congested optimal transport to the Heisenberg group, equipped with a sub-Riemannian metric. Originally introduced in the Euclidean setting by Carlier, Jimenez, and Santambrogio as a path-dependent variant…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…
We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove…
The congestion formation on a urban road network is one of the key issue for the development of a sustainable mobility in the future smart cities. In this work we propose a reductionist approach studying the stationary states of a simple…
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…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
Congestion in transport networks is a topic of theoretical interest and practical importance. In this paper we study the flow of vehicles in urban street networks. In particular, we use a cellular automata model to simulate the motion of…
The effects of real-time provision of travel-time information on the behaviour of drivers are considered. The model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015] is extended to consider uncertainty in the response of a…
Beckmann's problem in optimal transport minimizes the total squared flux in a continuous transport problem from a source to a target distribution. In this article, the regularity theory for solutions to Beckmann's problem in optimal…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
A model for 1D traffic flow is developed, which is discrete in space and time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go traffic. Due to…
In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…