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Related papers: Two-dimensional LWR model for lane-free traffic

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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

Vehicle trajectories can offer the most precise and detailed depiction of traffic flow and serve as a critical component in traffic management and control applications. Various technologies have been applied to reconstruct vehicle…

Optimization and Control · Mathematics 2023-06-12 Xuejian Chen , Guoyang Qin , Toru Seo , Ye Tian , Jian Sun

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

This work studies two-dimensional fixed-flux Rayleigh-B\'enard convection with periodic boundary conditions in both horizontal and vertical directions and analyzes its dynamics using numerical continuation, secondary instability analysis…

Fluid Dynamics · Physics 2023-12-12 Chang Liu , Manjul Sharma , Keith Julien , Edgar Knobloch

Urban road transport is a major civilisational and economic challenge, affecting the quality of life and economic activity. Addressing these challenges requires a multidisciplinary approach and sustainable urban planning strategies to…

Analysis of PDEs · Mathematics 2026-05-20 Mauritz N. Cartier van Dissel , Paweł Gora , Dragoş Manea

In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic for junctions with diverging lanes. We consider cases with and without directional preferences and present corresponding kinetic coupling…

Analysis of PDEs · Mathematics 2020-04-01 Raul Borsche , Axel Klar

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

We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing , Ansgar Hennecke , Vladimir Shvetsov , Martin Treiber

We consider the optical properties of Lindquist-Wheeler (LW) models of the Universe. These models consist of lattices constructed from regularly arranged discrete masses. They are akin to the Wigner-Seitz construction of solid state…

Cosmology and Nongalactic Astrophysics · Physics 2013-05-30 Timothy Clifton , Pedro G. Ferreira , Kane O'Donnell

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average…

Statistical Mechanics · Physics 2009-10-31 Martin Treiber , Ansgar Hennecke , Dirk Helbing

We investigate pattern formation in a driven mixture of two repulsive particles by introducing a Field-based Lattice Model (FLM), a hybrid model that combines aspects of the driven Widom-Rowlison lattice gas (DWRLG) and its statistical…

Statistical Mechanics · Physics 2025-12-08 G. E. Freire Oliveira , R. Dickman , M. O. Lavrentovich , R. K. P. Zia

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

Systems and Control · Electrical Eng. & Systems 2026-03-11 Wuping Xin

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…

Numerical Analysis · Mathematics 2018-10-18 Michael Herty , Andrea Tosin , Giuseppe Visconti , Mattia Zanella

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

Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each…

Probability · Mathematics 2007-05-23 Omer Angel , Alexander E Holroyd , James B Martin

In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are…

Numerical Analysis · Mathematics 2024-01-03 M. Pereira , B. Kulcsár , Gy. Lipták , M. Kovács , G. Szederkényi

Most autonomous-vehicles (AVs) driving strategies are designed and analyzed at the vehicle level, yet their aggregate impact on macroscopic traffic flow is still not understood, particularly the flow heterogeneity that emerges when AVs…

Systems and Control · Electrical Eng. & Systems 2025-08-14 Chenguang Zhao , Huan Yu

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars…

Dynamical Systems · Mathematics 2015-03-27 J. A. Conejero , M. Murillo Arcila , J. B. Seoane-Sepúlveda

The relation between flow and density is an essential quantitative characteristic to describe the efficiency of traffic systems. We have performed experiments with single-file motion of bicycles and compare the results with previous studies…

We provide a model to understand how adverse weather conditions modify traffic flow dynamic. We first prove that the microscopic Free Flow Speed of the vehicles is changed and then provide a rule to model this change. For this, we consider…