Nonreciprocal interactions in crowd dynamics: Investigating the impact of moving threats on pedestrian speed preferences

Abstract

Nonreciprocal interaction crowd systems, such as human–human, human–vehicle, and human–robot systems, often have serious impacts on pedestrian safety and social order. A more comprehensive understanding of these systems is needed to optimize system stability and efficiency. Despite the importance of these interactions, empirical research in this area remains limited. Thus, in our study we explore this underresearched area, focusing on scenarios where nonreciprocity plays a critical role, such as mass stabbings, which pose a substantial risk to public safety. We conducted the first experiments on this system and analysed high-accuracy data obtained from these experiments. Specifically, we conduct laboratory experiments on three scenarios: single exits, dual exits, and obscured chases. Then, we introduce an equation to describe the mechanism behind a direct threat zone, which significantly affects pedestrian behaviour. The extent of the direct threat zone is determined by the speed of the moving threat and the radius of danger occurrence. The equation can provide insights for different nonreciprocal interaction crowd systems, where the subjects of the nonreciprocal interactions can be a pedestrian, an autonomous robot or a vehicle. We further categorize potential threats into direct, adjacent, and rear-view zones, quantifying the level of threat for pedestrians. Our study revealed that a pedestrian’s desired velocity correlated positively with potential threat intensity, increasing until near the direct threat zone. An emerging steady state is observed when escape routes are blocked by moving threats. This deviation affects the density–velocity relationship, making it distinct from the general relationship. This deviation signifies unique pedestrian behaviour in the presence of moving threats. Additionally, the rate of change in the angle for pedestrian motion in various desired directions is synchronized. This indicates the emergence of collective intelligence in nonreciprocal interaction crowd systems. As a result, our study may constitute a pioneering step towards understanding nonreciprocal interactions in crowd systems through laboratory experiments. These findings may enhance pedestrian safety and inform not only government crowd management strategies but also individual self-protection measures.