Related papers: A continuous model of transportation revisited
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…
We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
Urban mobility forecast and analysis can be addressed through grid-based and graph-based models. However, graph-based representations have the advantage of more realistically depicting the mobility networks and being more robust since they…
Traffic prediction is a flourishing research field due to its importance in human mobility in the urban space. Despite this, existing studies only focus on short-term prediction of up to few hours in advance, with most being up to one hour…
We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book…
A Markovian model of the evolution of intermittent connections of various classes in a communication network is established and investigated. Any connection evolves in a way which depends only on its class and the state of the network, in…
Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method.…
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…
The papers describes an easy approach, based on a classical construction by Dacorogna and Moser, to prove that optimal vector fields in some minimal flow problem linked to optimal transport models (congested traffic, branched transport,…
We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…
The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Brenier's theorem and the Kantorovich-Rubinstein formula are…
In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational…
Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths…
We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $\epsilon$-regularity result for optimal transport maps…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
We propose a discrete transport equation on graphs which connects distributions on both vertices and edges. We then derive a discrete analogue of the Benamou-Brenier formulation for Wasserstein-$1$ distance on a graph and as a result…
Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based $L^1$-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that…