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In this paper, we present a new approach that generalizes the existing second-order hydrodynamic traffic models. In the proposed approach, we use the expression for the relative velocity of disturbances propagation in traffic flow. We show…

We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with…

Analysis of PDEs · Mathematics 2025-03-04 Dario Mazzoleni , Emanuela Radici , Filippo Riva

A macroscopic model-based approach for estimation of the traffic state, specifically of the (total) density and flow of vehicles, is developed for the case of "mixed" traffic, i.e., traffic comprising both ordinary and connected vehicles.…

Optimization and Control · Mathematics 2015-04-28 Nikolaos Bekiaris-Liberis , Claudio Roncoli , Markos Papageorgiou

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

The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which…

Analysis of PDEs · Mathematics 2019-07-05 Pierre Cardaliaguet , Nicolas Forcadel

Traffic congestion is one of the most notable problems arising in worldwide urban areas, importantly compromising human mobility and air quality. Current technologies to sense real-time data about cities, and its open distribution for…

Physics and Society · Physics 2016-12-30 Albert Solé-Ribalta , Sergio Gómez , Alex Arenas

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

Probability · Mathematics 2021-02-11 Michel Mandjes , Jaap Storm

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of…

Statistical Mechanics · Physics 2009-11-07 H. K. Lee , H. -W. Lee , D. Kim

Macroscopic transport modelling aims to predict traffic flows after proposed public policy interventions, such as a new road or railway section or a temporary road closure. As such, it is a vital step in infrastructure planning and…

Machine Learning · Computer Science 2026-05-12 Peter Vanya , Katarína Šimková , Rastislav Farkaš

The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of…

Analysis of PDEs · Mathematics 2023-12-04 Matteo Piu , Michael Herty , Gabriella Puppo

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

This paper deals with the modeling and mathematical analysis of vehicular traffic phenomena according to a kinetic theory approach, where the microscopic state of vehicles is described by: (i) position, (ii) velocity, as a continuous…

Analysis of PDEs · Mathematics 2021-03-26 J. Calvo , J. Nieto , M. Zagour

Mobile sensing enabled by GPS or smart phones has become an increasingly important source of traffic data. For sufficient coverage of the traffic stream, it is important to maintain a reasonable penetration rate of probe vehicles. From the…

Analysis of PDEs · Mathematics 2016-03-29 Benedetto Piccoli , Ke Han , Terry L. Friesz , Tao Yao , Junqing Tang

The present paper proposes a stochastic model of the traffic flow. This model has a discrete set of states and the continuous time. The model is a generalization of the discrete stochastis model that has been considered in a previous paper…

Other Condensed Matter · Physics 2007-05-23 A. P. Buslaev , A. G. Tatashev , M. V. Yashina

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

In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is…

Numerical Analysis · Mathematics 2016-12-14 Antoine Tordeux , Guillaume Costeseque , Michael Herty , Armin Seyfried

Transportation is a major contributor to CO2 emissions, making it essential to optimize traffic networks to reduce energy-related emissions. This paper presents a novel approach to traffic network control using Differentiable Predictive…

Systems and Control · Electrical Eng. & Systems 2024-06-18 Renukanandan Tumu , Wenceslao Shaw Cortez , Ján Drgoňa , Draguna L. Vrabie , Sonja Glavaski

This study addresses the challenge of estimating traffic states for road links. We propose an innovative approach that leverages partial trajectory data captured by camera-equipped probe vehicles traveling in the opposite lane. The…

Signal Processing · Electrical Eng. & Systems 2025-10-02 Tanay Rastogi , Michele D. Simoni , Anders Karlström

In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have…

Machine Learning · Computer Science 2024-12-06 Maya Briani , Emiliano Cristiani , Elia Onofri

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