Stochastic Headway Dependent Velocity Model for 1d Pedestrian Dynamics at High Densities

Phase separation into a jammed phase and a free-flow phase is a well understood feature observed in vehicular traffic. Experiments have shown a similar behavior for pedestrians, though the situation is more complicated. The two separate phases in single-file pedestrian movement are a jammed high-density phase and a phase of medium to high density with slowly moving pedestrians. We propose a one-dimensional Stochastic Headway Dependent Velocity Model (SHDV) which is continuous in space but discrete in time. The velocity of each agent depends on its headway and on its velocity. The SHDV model can qualitatively reproduce the experimentally observed phase separation at high densities and the observed velocity distribution. The SHDV model provides a deeper understanding of the basic mechanism that leads to the unusual kind of phase separation observed in the experiments.