Modelling the Behavior of Human Crowds as Coupled Active-passive Dynamics of Interacting Particle Systems

Thoa Thieu () and Roderick Melnik ()
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Thoa Thieu: The University of Texas Rio Grande Valley
Roderick Melnik: Wilfrid Laurier University

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 1, 1-22

Abstract: Abstract The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model reliably such human crowd systems with complex social interactions, stochastic tools play an important role for the setting of mathematical formulations of the problems. In this work, using the description based on an exclusion principle, we study a statistical-mechanics-based lattice gas model for active-passive population dynamics with an application to human crowd behaviors. We provide representative numerical examples for the evacuation dynamics of human crowds, where the main focus in our considerations is given to an interacting particle system of active and passive human groups. Furthermore, our numerical results show that the communication between active and passive humans strongly influences the evacuation time of the whole population even when a local “faster-is-slower” phenomenon is taken into account. To provide an additional inside into the problem, a stationary state of our model is analyzed via current representations and heat map techniques. Finally, future extensions of the proposed models are discussed in the context of coupled data-driven modelling of human crowds and traffic flows, vital for the design strategies in developing intelligent transportation systems.

Keywords: Crowd dynamics; Collective behavior; Social group interactions; Faster-is-slower; Particles current; Kinetic Monte Carlo and Markov chains; Occupation numbers; Evacuation dynamics; Simple exclusion dynamics; Lattice Boltzmann and lattice gas cellular automata methods; Social networks; 70L99; 82-10; 82C20; 91C05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10139-9

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