Exploring areawide dynamics of pedestrian crowds: Three-dimensional approach

The main objective of this paper is to evaluate the existing measurement methods of pedestrian traffic flow and propose a three-dimensional approach, extending Edie's definitions of fundamental traffic variables to multi-directional walking areas using three-dimensional pedestrian trajectories. It is found that similar to the notion of the Network Fundamental Diagram (NFD) of vehicular traffic, pedestrian crowds have an area-wide fundamental diagram. It is also shown that pedestrian traffic in a multidirectional area, exhibits hysteretic behavior similar to some other many-particle physical systems. Moreover, this paper explores some of the underlying dynamics of bidirectional pedestrian streams using empirical data. We show that pedestrian streams behave somewhat differently from ordinary fluids with regard to the viscosity concept in the models based on fluid dynamics. It is found that the velocity profile for both unidirectional and bidirectional pedestrian streams is hyperbolic with higher values on the boundaries and lower values in the middle, in opposite of the velocity profile of fluids. This paper also explores the formation and dissipation of self-organized pedestrian lanes. Thus, a modification to Helbing's social force model is proposed with regard to the attractive force between pedestrians.