American Institute of Mathematical Sciences

September  2011, 6(3): 465-483. doi: 10.3934/nhm.2011.6.465

Towards a mathematical model for stability in pedestrian flows

 1 Department of Infrastructure Engineering, University of Melbourne, Parkville, Victoria 3010, Australia, Australia

Received  December 2010 Revised  June 2011 Published  August 2011

It is suggested that flows of pedestrians on curved paths, such as the recirculating flow that occur around the Kaaba in Mecca, continually stratify 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 distance 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 distance scale, leads to some temporary breakdown in this stratification, with the flow developing patches of turbulent-like behavior with different pedestrian types responding differently to the obstacle. The flow between the nearby Safa and Marwa Hills is poorly stratified because of the lack of curvature of the flow between the Hills even though the flow is recirculating. At the start of each turning point by each Hill, the change in curvature leads to turbulence-like behavior as the stratification reforms, after its breakdown between the Hills, for the flow around the Hills.
Citation: Abdul M. Kamareddine, Roger L. Hughes. Towards a mathematical model for stability in pedestrian flows. Networks & Heterogeneous Media, 2011, 6 (3) : 465-483. doi: 10.3934/nhm.2011.6.465
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