Modeling Spatial Dependence on Pedestrian Fundamental Diagram by Harmonic Spatial Filtering

Abstract

In this study, we propose a method of modeling spatial dependence on pedestrian fundamental diagrams. A fundamental relationship between density and speed of pedestrian flow is useful with regard to evaluating the level of service in pedestrian facilities. However, this relationship always depends on the position although there is typically a lack of a priori knowledge regarding the position of bottlenecks, i.e., the position to be evaluated. Therefore, we propose an approach to use data obtained at entire area in a facility. We assume that the difference of fundamental diagrams at any position in a facility could be regarded as a fluctuation. This fluctuation over positions is modeled as a spatial dependence structure. The harmonic spatial filtering approach is employed to estimate the fundamental diagram and spatial fluctuation pattern simultaneously. We show that the regression accuracy of the proposed method is better than that of a non-spatial model. Furthermore, we interpret the estimated spatial fluctuation pattern over the entire experimental area, which might be useful in facility design.