Probabilistic dynamics of small groups in crowd flows

Chiel van der Laan; Alessandro Corbetta

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arXiv · 2511.13181

Probabilistic dynamics of small groups in crowd flows

Chiel van der Laan·Alessandro Corbetta

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Abstract

Pedestrians in crowds frequently move as part of small groups, constituting up to 70% of individuals. Dyads (groups of two) are most frequent. Understanding quantitatively the dynamics of dyads walking in crowds is therefore an essential building block towards a fundamental comprehension of crowd behavior as a whole, and mandatory for accurate crowd dynamics models. Unavoidably, due to the non-deterministic behavior of pedestrians, characterizations of the dynamics must be probabilistic. In this work, we analyse the dynamics of over 6M dyads: a statistical ensemble of unprecedented resolution within a multi-year real-life pedestrian trajectory measurement campaign (21M trajectories, from Eindhoven Station, NL). We provide phenomenological models for dyad behavior depending on the surrounding crowd state. We present a thorough collection of fundamental diagrams that probabilistically relate both dyad velocity and formation to the state of the surrounding crowd (density, relative velocity). Depending on the surrounding crowd, dyads adjust interpersonal distance and may shift in formation, possibly moving from abreast states (which favors social interaction) to in-file (which favors navigating dense crowds). To quantitatively investigate formation changes, we introduce a scalar indicator, which we dub Orientation Log-Odds (OLO), that quantifies the relative log-likelihood of abreast versus in-file formations. Conceptually, the OLO quantifies the energy difference between abreast and in-file configurations under a Boltzmann-like assumption. We model how OLO depends on the crowd state, showcasing that its derivative is a product of two velocity-density fundamental diagrams. Together, these results provide a statistically robust, data-driven description of dyad configuration dynamics in real-world crowds, establishing a foundation towards new predictive, group-aware crowd models.

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Chiel van der Laan, Alessandro Corbetta. 2025-11-17. Probabilistic dynamics of small groups in crowd flows. https://arxiv.org/abs/2511.13181

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