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In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space…

Mathematical Physics · Physics 2009-07-02 Benedetto Piccoli , Andrea Tosin

A cellular automaton model of traffic flow taking into account velocity anticipation is introduced. The strength of anticipation can be varied which allows to describe different driving schemes. We find phase separation into a free-flow…

Statistical Mechanics · Physics 2007-05-23 M. E. Larraga , J. A. del Rio , A. Schadschneider

Pedestrian trajectory prediction is essential for collision avoidance in autonomous driving and robot navigation. However, predicting a pedestrian's trajectory in crowded environments is non-trivial as it is influenced by other pedestrians'…

Computer Vision and Pattern Recognition · Computer Science 2019-02-15 Sirin Haddad , Meiqing Wu , He Wei , Siew Kei Lam

We construct a two dimensional Cellular Automata based model for the description of pedestrian dynamics. Wide range of complicated pattern formation phenomena in pedestrian dynamics are described in the model, e.g. lane formation, jams in a…

Cellular Automata and Lattice Gases · Physics 2012-11-29 Quntao Zhuang

Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these…

Physics and Society · Physics 2018-02-14 Alexandre Nicolas , Ioannis Touloupas

Computer-based simulation of pedestrian dynamics reached meaningful results in the last decade, thanks to empirical evidences and acquired knowledge fitting fundamental diagram constraints and space utilization. Moreover, computational…

Multiagent Systems · Computer Science 2016-10-26 Luca Crociani , Daichi Yanagisawa , Giuseppe Vizzari , Katsuhiro Nishinari , Stefania Bandini

This article deals with the experimental study of pedestrian behaviours in some situations of one-dimensional traffic. Participants were pre-organized in a line, and asked to walk either in a straight line with a fast or slow leader, or to…

Physics and Society · Physics 2025-09-09 Cécile Appert-Rolland , Anne-Hélène Olivier , Julien Pettré

To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transportation authorities have implemented managed lane policies, which restrict certain freeway lanes to certain types of vehicles. It was…

Systems and Control · Computer Science 2018-11-16 Matthew A. Wright , Roberto Horowitz , Alex A. Kurzhanskiy

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

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

Accurate prediction of pedestrian trajectories is crucial for enhancing the safety of autonomous vehicles and reducing traffic fatalities involving pedestrians. While numerous studies have focused on modeling interactions among pedestrians…

Computer Vision and Pattern Recognition · Computer Science 2025-01-24 Mohammad Ali Rezaei , Fardin Ayar , Ehsan Javanmardi , Manabu Tsukada , Mahdi Javanmardi

The behavior of pedestrians shows certain regularities, which can be described by quantitative (partly stochastic) models. The models are based on the behavior of individual pedestrians, which depends on the pedestrian intentions and on the…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing

This paper presents a novel context-based approach for pedestrian motion prediction in crowded, urban intersections, with the additional flexibility of prediction in similar, but new, environments. Previously, Chen et. al. combined…

Machine Learning · Computer Science 2018-06-26 Golnaz Habibi , Nikita Jaipuria , Jonathan P. How

We investigate non-equilibrium lane formation in a generic model of a fluid with attractive interactions, that is, a two-dimensional Lennard-Jones (LJ) fluid composed of two particle species driven in opposite directions. Performing…

Soft Condensed Matter · Physics 2016-11-11 C. W. Wächtler , F. Kogler , S. H. L. Klapp

In this contribution first results of experiments on pedestrian flow through bottlenecks are presented and then compared to simulation results obtained with the Social Force Model in the Vissim simulation framework. Concerning the…

Multiagent Systems · Computer Science 2008-09-10 Tobias Kretz , Stefan Hengst , Peter Vortisch

This paper develops a general force-based pedestrian model named CosForce, in which cosine functions are employed to describe asymmetric interactions. These functions implicitly capture the mechanisms of anticipation and reaction. By…

Physics and Society · Physics 2025-09-15 Jinghui Wang , Wei Lv , Shuchao Cao , Chenglin Guo

Anticipating human actions in front of autonomous vehicles is a challenging task. Several papers have recently proposed model architectures to address this problem by combining multiple input features to predict pedestrian crossing actions.…

Computer Vision and Pattern Recognition · Computer Science 2023-05-30 Lina Achaji , Julien Moreau , François Aioun , François Charpillet

Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…

Physics and Society · Physics 2009-11-13 Anton Šurda

The ability to anticipate pedestrian motion changes is a critical capability for autonomous vehicles. In urban environments, pedestrians may enter the road area and create a high risk for driving, and it is important to identify these…

Computer Vision and Pattern Recognition · Computer Science 2023-05-26 Anthony Knittel , Morris Antonello , John Redford , Subramanian Ramamoorthy

In pedestrian dynamics, the internal drive that propels individuals toward their goals is typically captured by a single, fixed parameter, the desired walking speed. This simplification overlooks that motivation fluctuates in response to…

Physics and Society · Physics 2026-05-04 Ezel Üsten , Anna Sieben , Mohcine Chraibi , Armin Seyfried