A model of crowd behavior and movement in the jamarat system, which is a critical bottleneck during the hajj, the muslims' annual pilgrimage to makkah, saudi arabia, is described. The model consists of a set of partial differential equations that are solved numerically following a discretization of time and space. Mathematical relations are defined for three fundamental processes: (a) radial movement, (b) lateral movement, and (c) stoning process. These relations are developed and calibrated using actual measurements taken at the site. As a result, a bidirectional speed-concentration model is developed to describe radial movement, revealing that the impedance to movement from facility users going in the same direction is about twice that from those going in the opposite direction. The overall model isapplied to the evaluation of possible design and control strategiesaimed at improving the efficiency and throughput of the system. This paper appears in transportation research record no. 1320, Freeway operations, highway capacity, and traffic flow 1991.
Abstract