Steps Toward the Fundamental Diagram — Empirical Results and Modelling

The empirical relation between density and velocity (fundamental diagram) of pedestrian movement is not completely analyzed, particularly with regard to the ‘microscopic’ causes which determine the relation at medium and high densities. The simplest system for the investigation of this dependency is the single-file movement. We present experimental results for this system and discuss the following observations. The data show a linear relation between the velocity and the inverse of the density, which can be regarded as the required length of one pedestrian to move. Furthermore we compare the results for the single-lane movement with literature data for the movement in a plane. This comparison shows an unexpected conformance between the fundamental diagrams, indicating that lateral interference has negligible influence on the velocity-density relation. For the modelling we treat pedestrians as self-driven objects moving in a continuous space. On the basis of a modified social force model we analyze qualitatively the influence of various approaches for the interactions of pedestrians on the resulting velocity-density relation. The one-dimensional system allows focusing on the role of the required length and remote force. We found that the reproduction of the typical form of the fundamental diagram is possible if the model increases the required length of a person with increasing current velocity. Furthermore we demonstrate the influence of a remote force on the velocity-density relation.