A decay model for the fundamental diagram of pedestrian movement

Pedestrian dynamics has many significant applications, such as the evacuation and the design and optimization of pedestrian facilities. The most important characteristic of pedestrian dynamics is the fundamental diagram, which indicates the relationship between density, velocity and flow of pedestrians. The fundamental diagram varies for different facilities like corridors, stairs or ramps, and it also depends on whether the pedestrian flow is unidirectional or bidirectional. However, the general model for the fundamental diagram is unknown. Here we use a decay model to quantify the relationship between the walking speed and density. The concept ‘maximum density’, which was thought previously as the density where pedestrians hardly move, is corrected to the density where the ‘turbulent’ crowd conditions arise. The decay characteristic of pedestrian movement is found, which is seldom studied before. The decay model agrees well with empirical results, and it can interpret the disagreement of different fundamental diagrams quantitatively.