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

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This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across…

Systems and Control · Computer Science 2019-06-20 Matthew A. Wright , Roberto Horowitz

In this work, we propose an alternative stochastic model for the fundamental diagram of traffic flow with minimal number of parameters. Our approach is based on a mesoscopic viewpoint of the traffic system in terms of the dynamics of…

Physics and Society · Physics 2016-02-23 Adriano Francisco Siqueira , Carlos Jose Todero Peixoto , Chen Wu , Wei-Liang Qian

This paper examines the optimal velocity follow-the-leader dynamics, a microscopic traffic model, and explores different aspects of the dynamical model, with particular emphasis on collision analysis. More precisely, we present a rigorous…

Optimization and Control · Mathematics 2023-09-22 Hossein Nick Zinat Matin , Maria Laura Delle Monache

Traffic safety at intersections is studied quantitatively using methods from Statistical Mechanics on the basis of simple microscopic traffic flow models. In order to determine a relationship between traffic flow and the number of crashes,…

Statistical Mechanics · Physics 2023-11-17 Andreas Leich , Ronald Nippold , Andreas Schadschneider , Peter Wagner

We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending…

Analysis of PDEs · Mathematics 2018-12-19 Giacomo Albi , Mattia Bongini , Francesco Rossi , Francesco Solombrino

We present in this article an algebraic approach to model and simulate road traffic networks. By defining a set of road traffic systems and adequate concatenating operators in that set, we show that large regular road networks can be easily…

Optimization and Control · Mathematics 2014-06-27 Nadir Farhi , Habib Haj-Salem , Jean-Patrick Lebacque

Microscopic traffic models describe how cars interact with their neighbors in an uninterrupted traffic flow and are frequently used for reference in advanced vehicle control design. In this paper, we propose a novel mechanical system…

Systems and Control · Computer Science 2019-03-12 Zhaojian Li , Firas Khasawneh , Xiang Yin , Aoxue Li , Ziyou Song

Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a…

Physics and Society · Physics 2012-10-29 Florian Knorr , Michael Schreckenberg

The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of the first order Lighthill-Whitham-Richards (LWR) model, possessing a family of fundamental diagram curves, rather than a single one. We investigate to which extent…

Physics and Society · Physics 2013-06-12 Shimao Fan , Benjamin Seibold

This study proposes a hybrid model based on Transformers, named MSCMHMST, aimed at addressing key challenges in traffic flow prediction. Traditional single-method approaches show limitations in traffic prediction tasks, whereas hybrid…

Machine Learning · Computer Science 2025-03-19 Weiyang Geng , Yiming Pan , Zhecong Xing , Dongyu Liu , Rui Liu , Yuan Zhu

Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…

Statistical Mechanics · Physics 2007-05-23 Kai Nagel , Christopher Kayatz , Peter Wagner

Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…

Physics and Society · Physics 2023-10-10 Nour Khoudari , Rabie Ramadan , Megan Ross , Benjamin Seibold

We propose an efficient method for reconstructing traffic density with low penetration rate of probe vehicles. Specifically, we rely on measuring only the initial and final positions of a small number of cars which are generated using…

Dynamical Systems · Mathematics 2026-02-13 Nail Baloul , Amaury Hayat , Thibault Liard , Pierre Lissy

This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with the…

Analysis of PDEs · Mathematics 2021-10-22 Xiaoqian Gong , Benedetto Piccoli , Giuseppe Visconti

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…

We show that all existing deterministic microscopic traffic models with identical drivers (including both two-phase and three-phase models) can be understood as special cases from a master model by expansion around well-defined ground…

Adaptation and Self-Organizing Systems · Physics 2015-10-07 Bo Yang , Christopher Monterola

Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks)…

Optimization and Control · Mathematics 2025-10-17 Maria Teresa Chiri , Christopher Denaro , Xiaoqian Gong , Benedetto Piccoli

We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…

Probability · Mathematics 2011-10-24 V. A. Malyshev , A. A. Zamyatin

We propose a microscopic decision model for route choice based on discrete choice theory. The correlation of overlapping routes is included in the random portions of the utility explicitly. For computational efficiency, we restrict the…

Physics and Society · Physics 2018-11-29 Markus Rausch , Martin Treiber , Stefan Lämmer

We consider a strongly coupled ODE-PDE system representing moving bottlenecks immersed in vehicular traffic. The PDE consists of a scalar conservation law modeling the traffic flow evolution and the ODE models the trajectory of a slow…

Analysis of PDEs · Mathematics 2018-01-16 Thibault Liard , Benedetto Piccoli