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Related papers: Second-order traffic flow models on networks

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A conservative flux postprocessing algorithm is presented for both steady-state and dynamic flow models. The postprocessed flux is shown to have the same convergence order as the original flux. An arbitrary flux approximation is projected…

Numerical Analysis · Mathematics 2017-10-20 Lars H. Odsæter , Mary F. Wheeler , Trond Kvamsdal , Mats G. Larson

This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…

Analysis of PDEs · Mathematics 2026-04-29 Akbota Senkebayeva

The traffic modelling often keeps the mesoscopic scale in the theoretical sphere because the integro-differential nature of its equations. In the present work we suggest to use the lattice Boltzmann method to overcome these difficulties. In…

Physics and Society · Physics 2018-10-01 Romain Noël , Laurent Navarro , Guy Courbebaisse

Jamitons are self-sustained traveling wave solutions that arise in certain second-order macroscopic models of vehicular traffic. A necessary condition for a jamiton to appear is that the local traffic density breaks the so-called…

Analysis of PDEs · Mathematics 2024-12-06 Raimund Bürger , Claudio Muñoz , Sebastián Tapia

Our aim in this paper is to establish a theoretical fundamental diagram for a multi-class traffic flow from a gas-kinetic-like traffic model. We start with a multi-class generalization of the Prigogine-Herman-Boltzmann equation to construct…

Statistical Mechanics · Physics 2019-09-04 A. R. Mendez , W. Marques , R. M. Velasco

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

We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…

Analysis of PDEs · Mathematics 2024-09-04 P Cardaliaguet

In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is…

Numerical Analysis · Mathematics 2016-12-14 Antoine Tordeux , Guillaume Costeseque , Michael Herty , Armin Seyfried

The one-dimensional Aw-Rascle (AR) system has become a cornerstone of macroscopic models for single-lane vehicular traffic. A possible generalization of this model to a multi-dimensional setting is the so-called dissipative AR model, which…

Analysis of PDEs · Mathematics 2025-02-24 Ewelina Zatorska

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…

Systems and Control · Computer Science 2015-05-25 Samuel Coogan , Murat Arcak

We study the stability of Riemann solutions to pressureless Euler equations with Coulomb-like friction under the nonlinear approximation of flux functions with one parameter. The approximated system can be seen as the generalized Chaplygin…

Analysis of PDEs · Mathematics 2017-06-28 Qingling Zhang

We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two…

Statistical Mechanics · Physics 2009-10-31 Vladislav Popkov , Ingo Peschel

We investigate two models for traffic flow with modified acceleration ('slow-to-start') rules. Even in the simplest case $v_{max}=1$ these rules break the 'particle-hole` symmetry of the model. We determine the fundamental diagram…

Statistical Mechanics · Physics 2009-10-30 Andreas Schadschneider , Michael Schreckenberg

We consider traffic flows described by conservation laws. We study a 2:1 junction (with two incoming roads and one outgoing road) or a 1:2 junction (with one incoming road and two outgoing roads). At the mesoscopic level, the priority law…

Analysis of PDEs · Mathematics 2023-11-21 Pierre Cardaliaguet , Nicolas Forcadel , Regis Monneau

While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…

Statistical Mechanics · Physics 2009-11-10 Dirk Helbing

We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…

Analysis of PDEs · Mathematics 2018-09-11 Wen Shen

Despite the success of classical traffic flow (e.g., second-order macroscopic) models and data-driven (e.g., Machine Learning - ML) approaches in traffic state estimation, those approaches either require great efforts for parameter…

Machine Learning · Statistics 2022-03-22 Yun Yuan , Zhao Zhang , Xianfeng Terry Yang

In this paper, we investigate traffic signal control in a network of interconnected intersections, aiming to balance lane-level vehicle densities through optimal green-time allocation. We develop a two-lane traffic flow model that…

Systems and Control · Electrical Eng. & Systems 2025-12-09 Xinfeng Ru , Ting Bai , Weiguo Xia , Andreas A. Malikopoulos

The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…

Analysis of PDEs · Mathematics 2022-10-26 Chao Zhang , Lifeng Wang

In this paper, we introduce a unified framework for studying various cloud traffic management problems, ranging from geographical load balancing to backbone traffic engineering. We first abstract these real-world problems as a…

Networking and Internet Architecture · Computer Science 2016-02-04 Chen Feng , Hong Xu , Baochun Li