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Pedestrian behavior has much more complicated characteristics in a dense crowd and thus attracts the widespread interest of scientists and engineers. However, even successful modeling approaches such as pedestrian models based on particle…

Multiagent Systems · Computer Science 2014-04-11 Qi Xu , Baohua Mao , Xujie Feng , Jia Feng

It is suggested that the motion of pedestrians can be described as if they would be subject to `social forces'. These `forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal…

Statistical Mechanics · Physics 2009-10-31 Dirk Helbing , Peter Molnar

For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction…

Physics and Society · Physics 2007-05-23 Armin Seyfried , Bernhard Steffen , Thomas Lippert

This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…

Physics and Society · Physics 2015-01-14 Nicola Bellomo , Stefano Berrone , Livio Gibelli , Alexandre Pieri

Pedestrian routing choices play a crucial role in shaping collective crowd dynamics, yet the influence of interactions among unfamiliar individuals remains poorly understood. In this study, we analyze real-world pedestrian behavior at a…

Physics and Society · Physics 2026-03-25 Ziqi Wang , Alessandro Gabbana , Federico Toschi

In shared space environments, urban space is shared among different types of road users, who frequently interact with each other to negotiate priority and coordinate their trajectories. Instead of traffic rules, interactions among them are…

Multiagent Systems · Computer Science 2022-03-01 Suhair Ahmed , Fatema T. Johora , Jörg P. Müller

Dense pedestrian crowds may pose significant safety risks, yet their underlying dynamics remain insufficiently understood to reliably prevent accidents. In these environments, physical interactions and contact forces fundamentally shape the…

Physics and Society · Physics 2025-05-12 Thomas Chatagnon , Antoine Tordeux , Mohcine Chraibi

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

The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages for studying related problems. In general, microscopic models…

Adaptation and Self-Organizing Systems · Physics 2026-01-27 Liangze Yang , Hui Yu , Jie Du

In this paper, we present a computational modeling approach for the dynamics of human crowds, where the spreading of an emotion (specifically fear) has an influence on the pedestrians' behavior. Our approach is based on the methods of the…

Physics and Society · Physics 2021-02-19 Daewa Kim , Kaylie O'Connell , William Ott , Annalisa Quaini

Understanding the movement behaviours of individuals and the way they react to the external world is a key component of any problem that involves the modelling of human dynamics at a physical level. In particular, it is crucial to capture…

Computer Vision and Pattern Recognition · Computer Science 2025-12-09 Gabriele Galatolo , Mirco Nanni

This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the…

Mathematical Physics · Physics 2010-09-07 Emiliano Cristiani , Benedetto Piccoli , Andrea Tosin

This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…

Multiagent Systems · Computer Science 2026-01-07 Péter Molnár

In this paper a comparison between first order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number $N$ of pedestrians. The novelty is the fact of considering massive agents, namely…

Analysis of PDEs · Mathematics 2016-03-22 Alessandro Corbetta , Andrea Tosin

In this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers. At the same time, we introduce a new family of macroscopic models, which make…

Optimization and Control · Mathematics 2015-04-22 Emiliano Cristiani , Fabio S. Priuli , Andrea Tosin

In an emergency situation, imitation of strategies of neighbours can lead to an order-disorder phase transition, where spatial clusters of pedestrians adopt the same strategy. We assume that there are two strategies, cooperating and…

Physics and Society · Physics 2013-03-12 P. Gawronski , K. Malarz , M. J. Krawczyk , J. Malinowski , A. Kupczak , W. Sikora , K. Kulakowski , J. Was , J. Kantelhardt

This article focuses on different aspects of pedestrian (crowd) modeling and simulation. The review includes: various modeling criteria, such as granularity, techniques, and factors involved in modeling pedestrian behavior, and different…

Robotics · Computer Science 2021-02-08 Amir Rasouli

With the increasing size and frequency of mass events, the study of crowd disasters and the simulation of pedestrian flows have become important research areas. Yet, even successful modeling approaches such as those inspired by Newtonian…

Physics and Society · Physics 2015-05-28 Mehdi Moussaid , Dirk Helbing , Guy Theraulaz

People tend to walk in groups, and interactions with those groups have a significant impact on crowd behavior and pedestrian traffic dynamics. Social norms can be seen as unwritten rules regulating people interactions in social settings.…

Physics and Society · Physics 2025-10-31 Saleh Albeaik , Faisal Alsallum , Mohamad Alrished

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