Macroscopic View: Crowd Evacuation Dynamics at T-Shaped Street Junctions Using a Modified Aw-Rascle Traffic Flow Model

This study investigates a dynamic flow model for crowd evacuation at T-shaped street junctions (TSJs) from a macroscopic view. The Aw-Rascle traffic flow model is modified by constructing an impact matrix in the street intersection area to practically describe the crowd convergence mechanism at a TSJ. For coherence, this modified model is proved to be anisotropic, similar to the original Aw-Rascle traffic flow model. To describe real scenarios with higher crowd density and lower speeds during organized pilgrimages, the initial Gaussian distribution of the crowd is improved to a higher-order smoothing function. To validate the modified Aw-Rascle traffic flow model, we reconstruct the drastic stampede that occurred at the TSJ of streets 204 and 223 during the 2015 Mecca pilgrimage. Further, the main environmental parameters that potentially lead to a stampede are discussed with numerical simulations. A valuable suggestion is that the street width ratio should be extended from 1.1 to 1.4 to prevent stampedes, matching the expansion engineering of street 204 reported by BBC News. An interesting phenomenon is that the closer the bus unloading location on street 223 is to the TSJ center, the lower the maximum crowd density and the safer the pedestrians will be. With this modified Aw-Rascle flow model at TSJs, this paper provides strategic and technical suggestions for future crowd flow control to reduce the risk of crowd stampedes.