Mathematical Modeling of pedestrian flow through the obstacle bottleneck

Abstract

For pedestrians in walking facilities, their movements are often obstructed by bottlenecks where the walkable widths are geometrically reduced. In previous research, to reproduce the influence of bottlenecks on pedestrian movements, agent-based simulation models have been widely applied. However, their high reliability on modeling rules and parameters requires calibration at the microscopic level, which makes them difficult to apply from an engineering perspective. Here, we applied a mathematical approach, which estimates the egress efficiency based on the density-flow rate fundamental diagram, to reproduce the egress time of pedestrians in our field experiments. Both the obstacle and the exit were considered bottlenecks in our experiments. It was indicated that with the same width, the obstacle bottleneck acted as an ‘ineffective’ bottleneck that did not affect the egress time when it was near the exit bottleneck, whereas acted as an ‘effective’ bottleneck when it was distant from the exit bottleneck. To reproduce this phenomenon, we applied a mathematical approach that abstracts the walking scenario as a scheme with the bottlenecks as links and different regions as nodes. As a result, the egress times under different layouts were reproduced successfully by introducing the density-flow rate fundamental diagram into the scheme. Furthermore, a reasonable range of the obstacle size and obstacle-exit width, under which condition the egress time is constant, was estimated. This study can be applied to estimate the egress time of the walking facilities by considering the fundamentals of pedestrian flows from a mathematical perspective, thus helping in the actual design of bottlenecks that could ensure efficient and safe pedestrian egress in walking facilities.