Lyapunov-Based Crowd Stability Analysis for Asymmetric Pedestrian Merging Layout at T-Shaped Street Junction

In emergencies close to a T-shaped street junction (TSJ), pedestrian overcrowding and trampling are typical unstable situations triggered by external disturbances, potentially leading to serious casualties during crowd movement. It is significant to analyze the pedestrian flow stability to achieve safe and efficient crowd evacuation. To analyze the stability of crowd flow, this study uses the two-dimensional Aw-Rascle dynamic-flow model to build the pedestrian merging dynamics at a TSJ area. Then the principle of the Lyapunov stability criterion in modern control theory is employed to analyze the stability of the pedestrian crowd. A novel stability criterion for an asymmetric pedestrian merging layout at a TSJ is then proposed. When the crowd acceleration in the local area exceeds the critical acceleration, the crowd will evolve to an unstable state. To validate this criterion, numerical simulations of a case study of a crowd stampede with serious casualties (1703 victims reported) occurring at a TSJ area in Mecca, Saudi Arabia, during the Hajj in 2015 is implemented. To build stable acceleration regimes, this paper tunes the key parameters of the number of pedestrians, width ratio of main street to branch street, and pedestrian drop-off location along the street 223, and discusses the stable ranges of acceleration to satisfy the pedestrian stability criterion. This criterion and the experimental results can supply new information to control pedestrian flow and keep it stable.