Modeling the collective behavior of pedestrians with the spontaneous loose leader–follower structure in public spaces

Gaining insights into pedestrian flow patterns in public spaces can greatly benefit decision-making processes related to infrastructure planning. Interestingly, even pedestrians are unfamiliar with one another, they often follow others, drawing on positive information and engaging in a spontaneous collective behavior of pedestrians. To model this collective behavior, this paper proposed a social force-based technique characterized by a loosely defined leader–follower structure. First, a complex field-based phase transfer entropy (PTE) method was applied to measure the difference in information flow between pedestrians. Setting the detecting threshold with the 3 sigma principle, the radial basis function (RBF) was utilized to identify the leader in the collective. Integrating the PTE, RBF, and social force model (SFM), a comprehensive model (PTE-RBF-SFM) was developed to simulate collective behavior. Some bidirectional pedestrian flow data, collected from Fairground Düsseldorf, were used to validate the model in a real-world setting. The results showed that the proposed model provided more realistic trajectories than benchmark models, and the spontaneous leader–follower structure was found to change over time and stable with time interval prolonging.