GOATIN , Paola

Comment les mathématiques contribuent-elles à la gestion du trafic routier et piéton ? Paola Goatin l'explique dans cet épisode du podcast audio.

International audience

The paper presents a review of the main analytical results available on the traffic flow model with phase transitions described in [10]. We also introduce a forthcoming existence result on road networks [14].

Building on previous theoretical findings, we conduct a numerical study on the boundary stabilization of Generic Second Order Macroscopic traffic models in Lagrangian coordinates. These consist in 2 × 2 nonlinear hyperbolic systems of balance equations with a relaxation-type source term, which is not required to satisfy the sub-characteristic...

International audience

This survey offers a unified up-to-date presentation of macroscopic models of traffic flow, pointing out their main characteristics and possible drawbacks. The presentation is completed by several pictures illustrating the models' features. Some open problems and future research directions are also given to inspire the reader.

Ce mémoire présente une partie de mon activité de recherche postérieure à la thèse, soutenue en 2000. Plus particulièrement, je décris ici les résultats obtenus à partir de 2004, en tant que Maître de Conférences à l'Institut des Sciences de l'Ingénieur de Toulon et du Var et membre de l'actuel Institut de mathématiques de Toulon et du Var.

In the present work, we consider a System Optimum Dynamic Traffic Assignment optimization problem on road networks employing time-varying partial traffic flow control. Depending on the network performance, trajectory control between the relative origin and destination nodes is applied to a variable fraction ("compliant") of the demand. Network...

We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is obtained recasting the problem in the space of probability measures equipped with the $\infty$-Wasserstein...

In the present work, we address a pseudo-System Optimum Dynamic Traffic Assignment optimization problem on road networks relying on trajectory control over a portion of the flows and limited knowledge on user response. The fractions of controlled flow moving between each origin-destination couple are defined as "compliant", while the remaining...

We present a Lax–Friedrichs type scheme to compute the solutions of a class of non-local and non-linear systems of conservation laws in several space dimensions. The convergence of the approximate solutions is proved by providing suitable L 1 , L ∞ and BV uniform bounds. To illustrate the performances of the scheme, we consider an application...

We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both in the speed law and in the number of lanes. This allows to describe a number of realistic situations....

We rigorously prove the convergence of the micro-macro limit for particle approximations of the Aw-Rascle-Zhang equations with a maximal density constraint. The lack of BV bounds on the density variable is supplied by a compensated compactness argument.