Universalities in Fundamental Diagrams of Cars, Bicycles, and Pedestrians

Since the pioneering work of Greenshields, the fundamental diagram is used to characterize and describe the performance of traffic systems. During the last years the discussion and growing database revealed the influence of human factors, traffic types, or ways of measurements on this relation. The manifoldness of influences is important and relevant for applications but moves the discussion away from the main feature characterizing the transport properties of traffic systems. The authors focus again on the main feature by comparing the fundamental diagram of cars, bicycles, and pedestrians moving in a row in a course with periodic boundaries. The underlying data are collected by three experiments, performed under well-controlled laboratory conditions. In all experiments the setup, in combination with technical equipment or methods of computer vision, allowed the authors to determine the trajectories with high precision. The trajectories visualized by space-time diagrams show three different states of motion (free-flow state, jammed state, and stop-and-go waves) in all these systems. Obviously the values of speed, density, and flow of these three systems cover different ranges. However, after a simple rescaling of the velocity by the free speed and of the density by the length of the agents, the fundamental diagrams conform regarding the position and height of the capacity. This indicates that the similarities between the systems go deeper than expected and offers the possibility of a universal model for heterogeneous traffic systems.