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Autonomous vehicles (AVs) allow new ways of regulating the traffic flow on road networks. Most of available results in this direction are based on microscopic approaches, where ODEs describe the evolution of regular cars and AVs. In this…

Analysis of PDEs · Mathematics 2020-04-21 Mauro Garavello , Paola Goatin , Thibault Liard , Benedetto Piccoli

One-directional traffic on two-lanes is modeled in the framework of a spring-block type model. A fraction $q$ of the cars are allowed to change lanes, following simple dynamical rules, while the other cars keep their initial lane. The…

Physics and Society · Physics 2015-06-05 Ferenc Jarai-Szabo , Zoltan Neda

We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit for all ranges of traffic data. Moreover, the…

Analysis of PDEs · Mathematics 2017-10-18 Raul Borsche , Axel Klar

On the basis of assumptions about the behavior of driver-vehicle units concerning acceleration, deceleration, overtaking, and lane-changing maneuvers, a gas-kinetic traffic model for uni-directional multi-lane freeways is constructed.…

Statistical Mechanics · Physics 2015-06-25 Dirk Helbing

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

Probability · Mathematics 2021-02-11 Michel Mandjes , Jaap Storm

A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg-de Vries (mKdV) equation within the unstable regime. Steady travelling wave solutions to this…

Dynamical Systems · Mathematics 2016-08-12 Laura Hattam

This paper is concerned with one-dimensional 2 x 2 systems of conservation laws with a flux f=f(x, U) that is discontinuous with respect to the spatial variable. No monotonicity assumption is imposed on the mapping x \to f(x,U). We…

Analysis of PDEs · Mathematics 2026-03-23 Felisia Angela Chiarello , Simone Fagioli , Massimiliano Daniele Rosini

The goal of this work is to provide a viable solution based on reinforcement learning for traffic signal control problems. Although the state-of-the-art reinforcement learning approaches have yielded great success in a variety of domains,…

Machine Learning · Computer Science 2020-05-20 Yueh-Hua Wu , I-Hau Yeh , David Hu , Hong-Yuan Mark Liao

We study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and…

Statistical Mechanics · Physics 2021-09-06 Felisia Angela Chiarello , Benedetto Piccoli , Andrea Tosin

Traffic breakdown, as one of the most puzzling traffic flow phenomena, is characterized by sharply decreasing speed, abruptly increasing density and in particular suddenly plummeting capacity. In order to clarify its root mechanisms and…

Physics and Society · Physics 2017-04-04 Zuojun Wang , Junfang Tian , Rui Jiang , Xiaopeng Li , Shou Feng Ma

The paper investigates the use of low-diffusion (contact-discontinuity-resolving [Liou M.S.: {\em J. Comp. Phys.} {\bf 160} (2000) 623--648]) approximate Riemann solvers for the convective part of the Reynolds-averaged Navier-Stokes…

Computational Physics · Physics 2016-07-01 N. Ben Nasr , G. A. Gerolymos , I. Vallet

One of the most difficult jobs in remote sensing is dealing with traffic bottlenecks at airports. This fact has been confirmed by several studies attempting to resolve this issue. Among a wide range of approaches employed the most…

Image and Video Processing · Electrical Eng. & Systems 2021-08-26 WT Al-Shaibani , Mustafa Helvaci , Ibraheem Shayea , Azizul Azizan

This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…

Mathematical Physics · Physics 2015-06-15 Chun-Xiu Wu , Peng Zhang , S. C. Wong , Keechoo Choi

The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…

Analysis of PDEs · Mathematics 2007-05-23 Francois James , Simona Mancini , Francois Bouchut

The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional that ranks the outcomes of different driving strategies is…

Soft Condensed Matter · Physics 2007-05-23 Ihor Lubashevsky , Peter Wagner , Reinhard Mahnke

User equilibrium is a central concept for studying transportation networks, and one can view it as the result of a dynamical process of drivers' route choice behavior. In this paper, based on a definition of O-D First-In-First-Out…

Dynamical Systems · Mathematics 2007-11-20 Wen-Long Jin

We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…

Optimization and Control · Mathematics 2021-04-23 Dongchan Lee , Konstantin Turitsyn , Jean-Jacques Slotine

This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic…

Analysis of PDEs · Mathematics 2019-10-25 Arnaud Ducrot , Zhihua Liu , Pierre Magal

Predicting traffic conditions has been recently explored as a way to relieve traffic congestion. Several pioneering approaches have been proposed based on traffic observations of the target location as well as its adjacent regions, but they…

Artificial Intelligence · Computer Science 2023-08-22 Xingyi Cheng , Ruiqing Zhang , Jie Zhou , Wei Xu

We develop structure preserving schemes for a class of nonlinear mobility continuity equation. When the mobility is a concave function, this equation admits a form of gradient flow with respect to a Wasserstein-like transport metric. Our…

Numerical Analysis · Mathematics 2025-10-21 Jose A. Carrillo , Li Wang , Chaozhen Wei