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Related papers: A Space-time Nonlocal Traffic Flow Model: Relaxati…

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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 consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $\rho$ ahead. The averaging kernel is of exponential type: $w_\varepsilon(s)=\varepsilon ^{-1}…

Analysis of PDEs · Mathematics 2020-05-20 Alberto Bressan , Wen Shen

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

This paper presents a new spatial-temporal nonlocal traffic flow model formulated to overcome the boundedness limitations inherent in classical local formulations. The model introduces an adaptive kernel that captures both spatial and…

Numerical Analysis · Mathematics 2026-03-30 Animesh Biswas , Archie Huang , Shaurya Agarwal , Christopher Housholder

In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in literature, but it is also able to describe new dynamics mainly…

Analysis of PDEs · Mathematics 2023-04-25 Jan Friedrich , Simone Göttlich , Alexander Keimer , Lukas Pflug

This paper considers numerical discretization of a nonlocal conservation law modeling vehicular traffic flows involving nonlocal inter-vehicle interactions. The nonlocal model involves an integral over the range measured by a horizon…

Numerical Analysis · Mathematics 2023-01-04 Kuang Huang , Qiang Du

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

While macroscopic models for single or multi-lane traffic flow are well established, these models are not applicable to the dynamics and characteristics of disordered traffic which is characterized by widely different types of vehicles and…

Physics and Society · Physics 2023-10-27 Shrey Agrawal , Venkatesan Kanagaraj , Martin Treiber

We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model…

Analysis of PDEs · Mathematics 2024-05-08 Helge Holden , Nils Henrik Risebro

In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are…

Numerical Analysis · Mathematics 2024-07-04 Timo Böhme , Simone Göttlich , Andreas Neuenkirch

In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential…

Analysis of PDEs · Mathematics 2024-01-09 Giuseppe M. Coclite , Kenneth H. Karlsen , Nils Henrik Risebro

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

The emerging connected and automated vehicle technologies allow vehicles to perceive and process traffic information in a wide spatial range. Modeling nonlocal interactions between connected vehicles and analyzing their impact on traffic…

Analysis of PDEs · Mathematics 2023-07-06 Kuang Huang , Qiang Du

In this paper, an extension of a linear control design for hyperbolic linear partial differential equations is presented for a first-order traffic flow model. Starting from the Lighthill-Whitham-Richards (LWR) model, variable speed limit…

Systems and Control · Electrical Eng. & Systems 2024-03-06 Brian Block , Stephanie Stockar

Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…

Numerical Analysis · Mathematics 2023-06-01 Raul Borsche , Axel Klar

In this paper, we study a nonlocal extension of the Aw-Rascle-Zhang traffic model, where the pressure-like term is modeled as a convolution between vehicle density and a kernel function. This formulation captures nonlocal driver…

Analysis of PDEs · Mathematics 2026-02-10 Debora Amadori , Felisia Angela Chiarello , Gianmarco Cipollone

We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $\rho$ ahead. The averaging kernel is of exponential type: $w_\varepsilon(s)=\varepsilon^{-1}…

Analysis of PDEs · Mathematics 2020-11-12 Alberto Bressan , Wen Shen

Using a nonlocal macroscopic LWR-type traffic flow model, we present an approach to control the nonlocal velocity towards a given equilibrium velocity. Therefore, we present a Lyapunov function measuring the $L^2$ distance between these…

Optimization and Control · Mathematics 2022-10-06 Jan Friedrich

The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…

Optimization and Control · Mathematics 2017-07-10 Iasson Karafyllis , Nikolaos Bekiaris-Liberis , Markos Papageorgiou

Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize traffic congestion. As the number of traffic sensors is naturally constrained by budgetary requirements, real-time estimation of traffic…

Systems and Control · Computer Science 2019-11-12 Sebastian A. Nugroho , Ahmad F. Taha , Christian Claudel
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