An Improved Speed-Density Relationship Model for Pedestrian Flow

The speed-density relationship performs as a basis to realize the behavior of a complex system such as vehicular or pedestrian traffic flow. Based on the speed-density relationship, the relationships between other pedestrian characteristics such as speed-flow, flow-density and speed-pedestrian module could be derived. Compared to vehicular flow, very little research has been done to develop a general model to describe pedestrian speed-density relationship. The widely used exponential speed-density models, the Underwood model and the Drake model show that the maximum flow is obtained at jam density, which is illogical because at jam density the movement is very limited and the speed will be at its minimum level. In this study, we propose an improved deterministic speed-density model for pedestrian flow which is an important contribution in the field of pedestrian studies. The proposed model shows that the maximum flow occurs at a density which is less than the jam density and thus, overcoming the limitations of the existing models. The validity of the model is empirically verified by primary and secondary datasets. The results showed that the proposed model can describe the speed-density relationship for all the datasets that were collected for different scenarios such as indoor and outdoor facilities. This model can be used as a general speed-density relationship.