Towards a mathematical model for stability in pedestrian flows

Abstract

It is suggested that flows of pedestrians on curved paths, such as the recirculating flow that occur around the Kaaba in Mecca, continually strat-ify themselves according to tolerance of crowd density with those pedestrians who are more tolerant of high densities taking a path of shorter length. Such stratification occurs over a distance, referred to here as the "stratification dis-tance scale" and is generally of the order of the radius of curvature of the flow. Once stratified a pedestrian crowd flows smoothly around an obstacle with a distance scale greater than the stratification distance scale. However, flow past a smaller obstacle with a distance scale less than the stratification dist..