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Related papers: The Aw-Rascle traffic model with locally constrain…

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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…

Analysis of PDEs · Mathematics 2015-10-16 Paola Goatin , Francesco Rossi

In this study, we analyse the famous Aw-Rascle system in which the difference between the actual and the desired velocities (the offset function) is a gradient of a singular function of the density. This leads to a dissipation in the…

Analysis of PDEs · Mathematics 2022-09-27 N Chaudhuri , L Navoret , Charlotte Perrin , E Zatorska

Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental…

Physics and Society · Physics 2009-11-11 Florian Siebel , Wolfram Mauser

The two phase model for vehicular traffic flows recently appeared in \cite{goatin2006aw} and \cite{BenyahiaRosini01} is endowed with a point constraint on the flow to allow for the modelling of phenomena such as the effects of toll booths…

Analysis of PDEs · Mathematics 2016-05-27 Massimiliano D. Rosini , Benyahia Mohamed Ramiz

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

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

We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a transport equation. The evolution of the car density is…

Analysis of PDEs · Mathematics 2025-05-16 Elio Marconi , Laura V. Spinolo

We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the…

Numerical Analysis · Mathematics 2013-05-17 Jeffrey K. Wiens , John M. Stockie , JF Williams

We study the Aw-Rascle system in a one-dimensional domain with periodic boundary conditions, where the offset function is replaced by the gradient of the function $\rho_{n}^{\gamma}$, where $\gamma \to \infty$. The resulting system…

Analysis of PDEs · Mathematics 2024-04-29 Muhammed Ali Mehmood

In [7], Berthelin, Degond, Delitala and Rascle introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model consists of a Pressureless Gas Dynamics system under a maximal constraint on the density…

Analysis of PDEs · Mathematics 2012-08-08 Florent Berthelin , Damien Broizat

In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…

Numerical Analysis · Mathematics 2016-06-17 Maya Briani , Emiliano Cristiani

We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters.…

Numerical Analysis · Mathematics 2022-09-08 Jan Friedrich , Simone Göttlich , Maximilian Osztfalk

Daganzo's criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277-286 (1995)] and Aw and Rascle's proposal how to overcome them [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916-938 (2000)] have…

Physics and Society · Physics 2009-06-14 Dirk Helbing , Anders Johansson

We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars…

Statistical Mechanics · Physics 2008-11-26 H. -W. Lee , V. Popkov , D. Kim

This paper presents scalable traffic stability analysis for both pure autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic flow models. Human vehicles are modeled by a non-equilibrium traffic flow model, i.e.,…

Optimization and Control · Mathematics 2024-09-23 Kuang Huang , Xuan Di , Qiang Du , Xi Chen

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…

Analysis of PDEs · Mathematics 2007-05-23 G. M. Coclite , B. Piccoli

We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a…

Analysis of PDEs · Mathematics 2022-08-05 Nilasis Chaudhuri , Eduard Feireisl , Ewelina Zatorska

We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a road with rough conditions. We approximate the problem through an upwind-type numerical…

Analysis of PDEs · Mathematics 2023-01-30 Felisia Angela Chiarello , Harold Deivi Contreras , Luis Miguel Villada

We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…

Probability · Mathematics 2019-12-13 Simone Göttlich , Stephan Knapp

In this paper, we derive second order hydrodynamic traffic models from kinetic-controlled equations for driver-assist vehicles. At the vehicle level we take into account two main control strategies synthesising the action of adaptive cruise…

Statistical Mechanics · Physics 2021-12-30 Giacomo Dimarco , Andrea Tosin , Mattia Zanella