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

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In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends…

Analysis of PDEs · Mathematics 2024-05-06 Abraham Sylla

We show the convergence of the zero relaxation limit in systems of $2 \times 2$ hyperbolic conservation laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation…

Analysis of PDEs · Mathematics 2018-11-01 James M. Scott , M. Paul Laiu , Cory D. Hauck

In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the…

Numerical Analysis · Mathematics 2020-03-30 Simone Göttlich , Elisa Iacomini , Thomas Jung

A novel continuum model has been developed to address the vehicle size heterogeneity in mixed traffic. By incorporating the principle of vehicle area conservation, a new set of traffic flow variables centered on the concept of vehicle area…

Analysis of PDEs · Mathematics 2026-04-27 Nandan Maiti , Bhargava Rama Chilukuri

We develop backstepping state feedback control to stabilize a moving shockwave in a freeway segment under bilateral boundary actuations of traffic flow. A moving shockwave, consisting of light traffic upstream of the shockwave and heavy…

Optimization and Control · Mathematics 2019-04-10 Huan Yu , Mamadou Diagne , Liguo Zhang , Miroslav Krstic

The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…

Numerical Analysis · Mathematics 2023-08-21 Michael Herty , Niklas Kolbe

A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of…

Networking and Internet Architecture · Computer Science 2012-08-07 Corentin Briat , Emre Altug Yavuz , Gunnar Karlsson

We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…

Analysis of PDEs · Mathematics 2022-04-26 Tej-Eddine Ghoul , Nader Masmoudi , Eliot Pacherie

The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…

Optimization and Control · Mathematics 2018-02-26 Iasson Karafyllis , Markos Papageorgiou

The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid…

Plasma Physics · Physics 2013-07-02 Alexander V. Milovanov , Jens Juul Rasmussen

This paper develops boundary feedback control laws in order to damp out traffic oscillations in the congested regime of the linearized two-class Aw-Rascle (AR) traffic model. The macroscopic second-order two-class AR traffic model consists…

Optimization and Control · Mathematics 2019-05-17 Mark Burkhardt , Huan Yu , Miroslav Krstic

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 derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance…

Networking and Internet Architecture · Computer Science 2016-11-18 C. Briat , E. A. Yavuz , H. Hjalmarsson , K. H. Johansson , U. T. Jönsson , G. Karlsson , H. Sandberg

When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…

High Energy Physics - Theory · Physics 2014-11-21 Stanislaw D. Glazek

We consider the Gibbs representation over space-time of non-equilibrium dynamics of Hamiltonian systems defined on a lattice with local interactions. We first write the corresponding action functional as a sum of local terms, defining a…

Mathematical Physics · Physics 2009-11-11 Raphael Lefevere

A rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemotaxis, respectively. It relies on a novel reformulation of the…

Analysis of PDEs · Mathematics 2019-11-27 Maria Krasnianski , Kevin Painter , Christina Surulescu , Anna Zhigun

In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…

Optimization and Control · Mathematics 2025-04-02 Dawson Do , Hossein Nick Zinat Matin , Masuma Mollika Miti , Maria Laura Delle Monache

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

Traffic control is at the core of research in transportation engineering because it is one of the best practices for reducing traffic congestion. It has been shown in recent years that the traffic control problem involving…

Optimization and Control · Mathematics 2021-05-10 Hao Liu , Christian Claudel , Randy Machemehl

Transportation departments take actions to manage traffic flow and reduce travel times based on estimated current and projected traffic conditions. Travel time estimates and forecasts require information on traffic density which are…

Applications · Statistics 2016-02-01 Nicholas Polson , Vadim Sokolov