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Related papers: Second-order traffic flow models on networks

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A recently introduced scheme for networked conservation laws is analyzed in various experiments. The scheme makes use of a novel relaxation approach that governs the coupling conditions of the network and does not require a solution of the…

Numerical Analysis · Mathematics 2022-10-10 Niklas Kolbe

We propose a bound-preserving Runge-Kutta (RK) discontinuous Galerkin (DG) method as an efficient, effective and compact numerical approach for numerical simulation of traffic flow problems on networks, with arbitrary high order accuracy.…

Numerical Analysis · Mathematics 2014-07-14 Suncica Canic , Benedetto Piccoli , Jing-Mei Qiu , Tan Ren

An extended multi-class Aw-Rascle (AR) model with pressure term described as a function of area occupancy defined in form of proportional densities is presented. Two vehicle classes that is; cars and motorcycles are considered based on an…

Analysis of PDEs · Mathematics 2024-05-16 Nanyondo Josephine , Henry Kasumba

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 addresses the problem of traffic state estimation (TSE) in the presence of heterogeneous sensors which include both fixed and moving sensors. Traditional fixed sensors are expensive and cannot be installed throughout the highway.…

Systems and Control · Electrical Eng. & Systems 2024-07-04 Suyash C. Vishnoi , Sebastian A. Nugroho , Ahmad F. Taha , Christian G. Claudel

We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely, we introduce deterministic particle schemes for the Hughes…

Numerical Analysis · Mathematics 2016-11-03 Marco Di Francesco , Simone Fagioli , Massimiliano D. Rosini , Giovanni Russo

Based on a Boltzmann-like traffic equation for aggressive drivers we construct in this paper a second-order continuum traffic model which is similar to the Navier-Stokes equations for viscous fluids by applying two well-known methods of…

Mathematical Physics · Physics 2010-12-01 W. Marques , A. R. Mendez

A uni-directional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of car i.e. slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg (Na-Sch) model of traffic flow,…

Statistical Mechanics · Physics 2007-05-23 M. Ebrahim Fouladvand

This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…

Analysis of PDEs · Mathematics 2020-07-09 Elie Bretin , Simon Masnou , Arnaud Sengers , Garry Terii

The societal impact of traffic is a long-standing and complex problem. We focus on the estimation of ozone production due to vehicular traffic. For this, we couple a system of conservation laws for vehicular traffic, an emission model, and…

Numerical Analysis · Mathematics 2020-10-27 Caterina Balzotti , Maya Briani , Barbara De Filippo , Benedetto Piccoli

We study vehicular traffic on a road with multiple lanes and dense, unidirectional traffic following the traditional Lighthill-Whitham-Richards model where the velocity in each lane depends only on the density in the same lane. The model…

Analysis of PDEs · Mathematics 2018-12-05 Helge Holden , Nils Henrik Risebro

We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman equations on networks. The scheme is explicit and stable under some technical conditions. We prove a convergence theorem and some error…

Numerical Analysis · Mathematics 2018-04-26 Elisabetta Carlini , Adriano Festa , Nicolas Forcadel

This paper investigates the well-posedness of contact discontinuity solutions and the vanishing pressure limit for the Aw-Rascle traffic flow model with general pressure functions. The well-posedness problem is formulated as a free boundary…

Analysis of PDEs · Mathematics 2025-06-10 Zijie Deng , Wenjian Peng , Tian-Yi Wang , Haoran Zhang

We propose a semidiscrete scheme for approximation of entropy solutions of one-dimensional scalar conservation laws with nonnegative initial data. The scheme is based on the concept of particle paths for conservation laws and can be…

Analysis of PDEs · Mathematics 2025-04-16 Magnus C. Ørke

Physical solutions to the widely used Aw-Rascle-Zhang (ARZ) traffic model and the adapted pressure (AP) ARZ model should satisfy the positivity of density, the minimum and maximum principles with respect to the velocity $v$ and other…

Numerical Analysis · Mathematics 2024-09-25 Wei Chen , Shumo Cui , Kailiang Wu , Tao Xiong

We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For an arbitrary large class of initial data and the periodic domain, we prove the existence of global-in-time measure-valued solutions.…

Analysis of PDEs · Mathematics 2023-02-24 Nilasis Chaudhuri , Piotr Gwiazda , Ewelina Zatorska

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

Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…

Numerical Analysis · Mathematics 2025-07-01 Shaoshuai Chu , Alexander Kurganov , Saeed Mohammadian , Zuduo Zheng

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

In this article, we propose a second-order central scheme of the Nessyahu-Tadmor-type for a class of scalar conservation laws with discontinuous flux and present its convergence analysis. Since solutions to problems with discontinuous flux…

Numerical Analysis · Mathematics 2025-03-25 Nikhil Manoj , Sudarshan Kumar K
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