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Related papers: A Mixed ODE-PDE Model for Vehicular Traffic

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A simple algorithm for constructing an effective traffic model is presented. The algorithm uses statistically well-defined quantities extracted from the flow-density plot, and the resulting effective model naturally captures and predicts…

Adaptation and Self-Organizing Systems · Physics 2014-12-16 Bo Yang , Christopher Monterola

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

This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…

Classical Analysis and ODEs · Mathematics 2023-12-05 Matteo Piu , Gabriella Puppo

We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…

Statistical Mechanics · Physics 2007-05-23 Elad Tomer , Leonid Safonov , Nilly Madar , Shlomo Havlin

In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…

Numerical Analysis · Mathematics 2017-02-22 Gabriella Puppo , Matteo Semplice , Andrea Tosin , Giuseppe Visconti

In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental…

Numerical Analysis · Mathematics 2015-03-20 Raul Borsche , Mark Kimathi , Axel Klar

By means of microscopic simulations we show that non-instantaneous adaptation of the driving behaviour to the traffic situation together with the conventional measurement method of flow-density data can explain the observed…

Statistical Mechanics · Physics 2009-11-10 Martin Treiber , Dirk Helbing

In this paper we propose a multiscale traffic model, based on the family of Generic Second Order Models, which integrates multiple trajectory data into the velocity function. This combination of a second order macroscopic model with…

Numerical Analysis · Mathematics 2022-07-29 Caterina Balzotti , Maya Briani

In this paper we propose a new modeling technique for vehicular traffic flow, designed for capturing at a macroscopic level some effects, due to the microscopic granularity of the flow of cars, which would be lost with a purely continuous…

Mathematical Physics · Physics 2014-03-25 Emiliano Cristiani , Benedetto Piccoli , Andrea Tosin

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

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [20], where a two-dimensional model for a single class of vehicles is proposed, we extend the…

Numerical Analysis · Mathematics 2020-11-04 Caterina Balzotti , Simone Göttlich

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

Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…

Optimization and Control · Mathematics 2023-02-06 Amoolya Tirumalai , John S. Baras

The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…

Physics and Society · Physics 2015-04-10 Tal Cohen , Rohan Abeyaratne

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…

Mathematical Physics · Physics 2014-04-08 Cécile Appert-Rolland , Pierre Degond , Sébastien Motsch

We present a traffic model that extends the linear car-following model as well as the min-plus traffic model (a model based on the min-plus algebra). A discrete-time car-dynamics describing the traffic on a 1-lane road without passing is…

Optimization and Control · Mathematics 2011-08-19 Nadir Farhi

We study the global existence of solutions of a discrete (ODE based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We propose an adaptation of this model so that a macroscopic…

Analysis of PDEs · Mathematics 2021-02-18 Jan Haskovec , Lisa Maria Kreusser , Peter Markowich

This paper is concerned with highway traffic estimation using traffic sensing data, in a Lagrangian-based modeling framework. We consider the Lighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956) in…

Analysis of PDEs · Mathematics 2012-11-21 Ke Han , Tao Yao , Terry L. Friesz

In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of…

Dynamical Systems · Mathematics 2009-09-29 Wenlong Jin

We present a macroscopic traffic flow model that extends existing fluid-like models by an additional term containing the second derivative of the safe velocity. Two qualitatively different shapes of the safe velocity are explored: a…

Statistical Mechanics · Physics 2009-11-07 S. Rosswog , P. Wagner