A Force-Based Model to Reproduce Stop-and-Go Waves in Pedestrian Dynamics

Abstract

Stop-and-go waves in single-file movement are a phenomenon that is ob- served empirically in pedestrian dynamics. It manifests itself by the co-existence of two phases: moving and stopping pedestrians. We show analytically based on a simplified one-dimensional scenario that under some conditions the system can have instable homogeneous solutions. Hence, oscillations in the trajectories and in- stabilities emerge during simulations. To our knowledge there exists no force-based model which is collision- and oscillation-free and meanwhile can reproduce phase separation. We develop a new force-based model for pedestrian dynamics able to reproduce qualitatively the phenomenon of phase separation. We investigate analytically the stability condition of the model and define regimes of parameter values where phase separation can be observed. We show by means of simulations that the predefined conditions lead in fact to the expected behavior and validate our model with respect to empirical findings.