Next Article in Journal
An Adaptive Routing-Forwarding Control Scheme Based on an Intelligent Fuzzy Decision-Making System for Opportunistic Social Networks
Next Article in Special Issue
Particle Methods Simulations by Kinetic Theory Models of Human Crowds Accounting for Stress Conditions
Previous Article in Journal
Orientation of Chiral Schiff Base Metal Complexes Involving Azo-Groups for Induced CD on Gold Nanoparticles by Polarized UV Light Irradiation
Previous Article in Special Issue
Forecasting Efficient Risk/Return Frontier for Equity Risk with a KTAP Approach—A Case Study in Milan Stock Exchange
Open AccessArticle

Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions

1
Departamento de Matemática Aplicada and Excellence Research Unit “Modeling Nature”, Universidad de Granada, 18071 Granada, Spain
2
Ecole Supérieure de Technologie d’Essaouira, Université Cadi Ayyad, BP. 383 Essaouira, Maroc
*
Author to whom correspondence should be addressed.
To the memory of Abdelghani Bellouquid.
Symmetry 2019, 11(9), 1093; https://doi.org/10.3390/sym11091093
Received: 29 July 2019 / Revised: 19 August 2019 / Accepted: 22 August 2019 / Published: 2 September 2019
This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to describe the quality of the driver-vehicle micro-system. We use methods coming from game theory to describe interactions at the microscopic scale, thus constructing new models within the framework of the Kinetic Theory of Active Particles; the resulting models incorporate some of the symmetries that are commonly found in the mathematical models of the kinetic theory of gases. Short-range interactions and mean field interactions are introduced and modeled to depict velocity changes related to passing phenomena. Our main goal is twofold: (i) to use continuum-velocity variables and (ii) to introduce a non-local acceleration term modeling mean field interactions, related to, for example, the presence of tollgates or traffic highlights. View Full-Text
Keywords: vehicular traffic; short- and long-range interactions; kinetic theory vehicular traffic; short- and long-range interactions; kinetic theory
Show Figures

Figure 1

MDPI and ACS Style

Calvo, J.; Nieto, J.; Zagour, M. Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions. Symmetry 2019, 11, 1093.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop