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Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…

Analysis of PDEs · Mathematics 2026-04-03 Ansgar Jüngel , Cordula Reisch , Sara Xhahysa

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner's three-phase traffic theory…

Physics and Society · Physics 2011-08-25 Martin Treiber , Arne Kesting , Dirk Helbing

We propose a microscopic traffic model where the update velocity is determined by the deceleration capacity and response time. It is found that there is a class of collisions that cannot be distinguished by simply comparing the stop…

Statistical Mechanics · Physics 2015-05-15 Hyun Keun Lee , Jeenu Kim , Youngho Kim , Choong-Ki Lee

We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined…

Analysis of PDEs · Mathematics 2020-02-10 M. Herty , G. Puppo , G. Visconti

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

A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is…

Statistical Mechanics · Physics 2009-11-11 J. Kaupuzs , R. Mahnke , R. J. Harris

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

In this paper, we reveal the relationship between entropy rate and the congestion in complex network and solve it analytically for special cases. Finding maximizing entropy rate will lead to an improvement of traffic efficiency, we propose…

Physics and Society · Physics 2017-09-15 Yuhang Fan , Hanyuan Liu , Shibo He

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 present a phase diagram of the different kinds of congested traffic that are triggered by disturbances when passing ramps or other spatial inhomogeneities of a freeway. The simulation results obtained by the nonlocal, gas-kinetic-based…

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

Recently, hysteretic transitions to `synchronized traffic' with high values of both density and traffic flow were observed on German freeways [B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. We propose a macroscopic traffic…

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

Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…

Statistical Mechanics · Physics 2009-08-13 Anton Šurda

We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…

We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…

Numerical Analysis · Mathematics 2017-03-09 Anke Böttcher , Herbert Egger

We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…

High Energy Physics - Lattice · Physics 2016-08-14 José A. Cuesta , Froilán C. Martínez , Juan M. Molera , Angel Sánchez Escuela

This article deals with macroscopic traffic flow models on a road network. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws.…

Numerical Analysis · Mathematics 2018-04-23 Oliver Kolb , Guillaume Costeseque , Paola Goatin , Simone Göttlich

Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…

Systems and Control · Electrical Eng. & Systems 2021-06-09 Renátó Besenczi , Norbert Bátfai , Péter Jeszenszky , Roland Major , Fanny Monori , Márton Ispány

We consider a modified Nagel-Schreckenberg (NS) model in which drivers do not decelerate if their speed is smaller than the headway (number of empty sites to the car ahead). (In the original NS model, such a reduction in speed occurs with…

Statistical Mechanics · Physics 2017-02-15 M. L. L. Iannini , Ronald Dickman

In this paper, we propose a control design methodology for a linearized continuum traffic model in the congested regime. The continuum traffic flow on a highway is modeled using a linearized quasilinear hyperbolic partial differential…

Optimization and Control · Mathematics 2019-11-11 Stephen Chen , Huan Yu , Miroslav Krstic

We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers'…

Statistical Mechanics · Physics 2015-06-24 A. De Martino , M. Marsili , R. Mulet