Speed and Velocity Variance: An approach to analyzing crowd congestion dynamics

Crowd dynamics, particularly in high-density scenarios, pose significant challenges for congestion analysis and risk mitigation. This study introduces novel metrics, speed and velocity variances, to evaluate crowd congestion. By approximating individuals to special particles, speed/velocity variance quantifies movement irregularity, offering a unique perspective on congestion levels. The proposed concept was applied on experimental data from a T-shaped merging corridor. Experimental analyses with varying densities and turning angles demonstrate speed/velocity variance effectiveness in capturing localized disruptions and pre-collision risks. The findings highlight speed/velocity variance's sensitivity to both individual and group dynamics, providing a higher resolution compared to traditional metrics such as density and the recently proposed congestion number. Moreover, speed/velocity variance's dependency on turning angles and crowd size underscores its potential for real-time monitoring and enhanced predictive capabilities in complex scenarios.