First-Order Pedestrian Traffic Flow Theory

Abstract

This paper discusses the validity of first-order traffic flow theory for the description of two-dimensional pedestrian flow operations in the case of an oversaturated bottleneck in front of which a large high-density region has formed. The paper shows how observations of density, speed, and flow that have been collected from laboratory walking experiments can be interpreted from the viewpoint of first-order theory. It is observed that pedestrians present at the same cross section inside of the congested region may encounter different flow conditions. This mainly depends on the lateral position of the pedestrian with respect to the center of the congested region. In the lateral center, high densities and low speeds are observed. However, on the boundary of the congested region, pedestrians may walk in nearly free-flow conditions and literally walk around this congested region. Visualization of these data in the flow– density plane results in a large scatter of points that have similar flows (bottleneck capacity) but different densities. This can be explained by noticing that observations of congestion of pedestrian traffic over the total width of the cross section do not belong to a single fundamental diagram but belong to a set of different fundamental diagrams. This observation has consequences for estimation of the fundamental diagram describing pedestrian traffic.