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We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…

Discrete Mathematics · Computer Science 2010-02-05 Andrea Clementi , Angelo Monti , Riccardo Silvestri

The lateral position of vehicles within their lane is a decisive factor for the range of vision of vehicle sensors. This, in turn, is crucial for a vehicle's ability to perceive its environment and gain a high situational awareness by…

Robotics · Computer Science 2024-05-28 Nicole Neis , Juergen Beyerer

In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…

Mathematical Physics · Physics 2014-03-25 Luisa Fermo , Andrea Tosin

By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…

Other Condensed Matter · Physics 2007-05-23 Peter Wagner

On the basis of assumptions about the behavior of driver-vehicle units concerning acceleration, deceleration, overtaking, and lane-changing maneuvers, a gas-kinetic traffic model for uni-directional multi-lane freeways is constructed.…

Statistical Mechanics · Physics 2015-06-25 Dirk Helbing

In [7], Berthelin, Degond, Delitala and Rascle introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model consists of a Pressureless Gas Dynamics system under a maximal constraint on the density…

Analysis of PDEs · Mathematics 2012-08-08 Florent Berthelin , Damien Broizat

We develop a Markovian traffic equilibrium model for ride-hailing in which vehicles, whether empty or hired, make sequential order-acceptance and link-choice decisions over a traffic network to maximize total discounted return in an…

Computer Science and Game Theory · Computer Science 2026-04-24 Song Gao , Hanyu Cheng , Chiwei Yan , Guocheng Jiang

We present here a real-time control model for the train dynamics in a linear metro line system. The model describes the train dynamics taking into account average passenger arrival rates on platforms, including control laws for train dwell…

Optimization and Control · Mathematics 2018-10-30 Florian Schanzenbacher , Nadir Farhi , Fabien Leurent , Gérard Gabriel

Based on the classical traffic model by Greenberg, a linear differential equation, we analyze it by means of varying the critical velocity $v_o$ that appears in it as a parameter. In order to make such analysis we have obtained a solution…

Dynamical Systems · Mathematics 2017-12-06 Oscar A. Rosas-Jaimes , Luis A. Quezada-Téllez , Guillermo Fernández-Anaya

We present in this article traffic flow and control models for the train dynamics in metro lines. The first model, written in the max-plus algebra, takes into account minimum running, dwell and safety time constraints, without any control…

Optimization and Control · Mathematics 2018-01-09 Nadir Farhi , Cyril Nguyen Van Phu , Habib Haj-Salem , Jean-Patrick Lebacque

We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…

Analysis of PDEs · Mathematics 2024-09-04 P Cardaliaguet

In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…

Optimization and Control · Mathematics 2025-04-02 Dawson Do , Hossein Nick Zinat Matin , Masuma Mollika Miti , Maria Laura Delle Monache

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

Systems and Control · Electrical Eng. & Systems 2026-03-11 Wuping Xin

We investigate the behaviour of an original traffic model. The model considers a single multi-lane street, populated by autonomous vehicles directed from either end to the other. Lanes have no intrinsic directionality, and the vehicles are…

Computational Physics · Physics 2007-05-23 Federico Polito , Fergal Dalton

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…

Analysis of PDEs · Mathematics 2007-05-23 G. M. Coclite , B. Piccoli

We propose three models for the traffic of vehicles within a network formed by sites (cities, car-rental agencies, parking lots, etc.) and connected by two-way arteries (roads, highways), that allow forecasting the vehicular flux in a…

Physics and Society · Physics 2017-10-25 Dino Otero , Diógenes Galetti , Salomon S. Mizrahi

In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…

Soft Condensed Matter · Physics 2007-05-23 M. E. Larraga , J. A. del Rio

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

We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the…

Condensed Matter · Physics 2009-10-22 Kai Nagel , Hans J. Herrmann

In recent years statistical physicists have developed {\it discrete} "particle-hopping" models of vehicular traffic, usually formulated in terms of {\it cellular automata}, which are similar to the microscopic models of interacting charged…

Statistical Mechanics · Physics 2007-05-23 Debashish Chowdhury , Ludger Santen , Andreas Schadschneider