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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

We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of different dimensions, with exchange boundary conditions.…

Analysis of PDEs · Mathematics 2025-05-07 Matthieu Alfaro , Romain Ducasse , Samuel Tréton

We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized…

Analysis of PDEs · Mathematics 2010-07-01 Mauro Garavello , Paola Goatin

The vehicular flow in the urban street canyon is considered. The classical field description is used in the modelling of the vehicular movement and of gaseous mixture in generic urban street canyon. The dynamical variables include vehicular…

Disordered Systems and Neural Networks · Physics 2007-05-23 Maciej M. Duras

Lane changing is one of the most common maneuvers on motorways. Although, macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in one…

Numerical Analysis · Mathematics 2019-03-20 Michael Herty , Salissou Moutari , Giuseppe Visconti

In this paper we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space-…

Systems and Control · Electrical Eng. & Systems 2021-01-26 Denis Nikitin , Carlos Canudas-de-Wit , Paolo Frasca

Traffic congestion, a daily frustration for millions and a multi-billion dollar drain on economies, has long resisted deep physical understanding. While simple theoretical models of traffic flow have suggested connections to critical…

Chaotic Dynamics · Physics 2025-07-15 Garyoung Lee , Aryaman Jha , Kurt Wiesenfeld , Jorge Laval

Auto manufacturers and research groups are working on autonomous driving for long period and achieved significant progress. Autonomous vehicles (AV) are expected to transform road traffic reduction from current conditions, avoiding…

Robotics · Computer Science 2024-05-28 Ragav V , Jesher Joshua M , Syed Ibrahim S P

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…

Mathematical Physics · Physics 2014-04-08 Cécile Appert-Rolland , Pierre Degond , Sébastien Motsch

Recent breakthroughs in autonomous driving have been propelled by advances in robust world modeling, fundamentally transforming how vehicles interpret dynamic scenes and execute safe decision-making. World models have emerged as a linchpin…

Robotics · Computer Science 2025-09-11 Tuo Feng , Wenguan Wang , Yi Yang

We investigate a driven two-channel system where particles on different lanes mutually obstruct each others motion extending an earlier model by Popkov and Peschel [1]. This obstruction may occur in biological contexts due to steric…

Biological Physics · Physics 2015-03-13 Anna Melbinger , Tobias Reichenbach , Thomas Franosch , Erwin Frey

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

Numerical Analysis · Mathematics 2021-09-09 Mildred Aduamoah , Benjamin D. Goddard , John W. Pearson , Jonna C. Roden

Autonomous Vehicles are currently being tested in a variety of scenarios. As we move towards Autonomous Vehicles, how should intersections look? To answer that question, we break down an intersection management into the different conundrums…

Robotics · Computer Science 2018-09-10 Shravan Krishnan , Govind Aadithya R , Rahul Ramakrishnan , Vijay Arvindh , Sivanathan K

For a foreseeable future, autonomous vehicles (AVs) will operate in traffic together with human-driven vehicles. Their planning and control systems need extensive testing, including early-stage testing in simulations where the interactions…

Robotics · Computer Science 2020-07-21 Ran Tian , Nan Li , Ilya Kolmanovsky , Yildiray Yildiz , Anouck Girard

This paper focuses on the speed planning problem for connected and automated vehicles (CAVs) communicating to traffic lights. The uncertainty of traffic signal timing for signalized intersections on the road is considered. The eco-driving…

Optimization and Control · Mathematics 2019-04-11 Chao Sun , Jacopo Guanetti , Francesco Borrelli , Scott Moura

We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a…

Analysis of PDEs · Mathematics 2017-12-20 Wen Shen , Karim Shikh-Khalil

Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…

Statistical Mechanics · Physics 2009-08-13 Anton Šurda

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established…

patt-sol · Physics 2009-10-30 K. Nakanishi , K. Itoh , Y. Igarashi , M. Bando

A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…

Other Condensed Matter · Physics 2009-11-10 K. Thomas Waldeer

In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to…

Numerical Analysis · Mathematics 2025-02-21 N. Garcia-Chan , L. J. Alvarez-Vazquez , A. Martinez , M. E. Vazquez-Mendez