Exploring Areawide Dynamics of Pedestrian Crowds Three-Dimensional Approach

The main objectives of this paper are to evaluate existing measurement methods of pedestrian traffic flow and to propose a three-dimensional approach that extends Edie's definitions of fundamental traffic variables to multidirectional walking areas by using three-dimensional pedestrian trajectories. Pedestrian crowds have an areawide fundamental diagram that is similar to a network fundamental diagram of vehicular traffic. Pedestrian traffic in a multidirectional area exhibits hysteretic behavior similar to that of some other many-particle physical systems. Some of the underlying dynamics of bidirectional pedestrian streams are explored with empirical data. Pedestrian streams behave somewhat differently from ordinary fluids with regard to the viscosity concept in the models based on fluid dynamics. The velocity profile for both unidirectional and bidirectional pedestrian streams is hyperbolic (with higher values on the boundaries and lower values in the middle), opposite that of fluids. The formation and dissipation of self-organized pedestrian lanes also are explored. A modification to Helbing's social force model is proposed with regard to the attractive force between pedestrians.