Fundamental Diagram of Pedestrian Dynamics by Safety Interspace Model
  The NaSch model is a classical one-dimensional cellular automata (CA) model of freeway traffic. However, it is not suitable for simulating pedestrian dynamics due to the kinetic difference between vehicles and pedestrians. Based on NaSch model, we proposed a new safety interspace model to investigate the single-file pedestrian stream. We simulated and reproduced Seyfried's experiment in 2006 quantitatively and use the empirical data to validate our model. We defined the safety interspace as a linear function of current velocity and introduced a normal distributed random variable to describe the randomness of spatial cognition. Meanwhile, we extended NaSch model in space partition from single-grid mode to multi-gird mode to increase spatial resolution. It was found that through three model perimeters with appropriate values, the new model could reproduce faithfully the typical form of the fundamental diagram from empirical data. The velocity-density curve in simulation could indicate the discontinuity areas in fundamental diagram observed from empirical data. In addition, we reproduced the stop-and-go waves and phase separation into a stopping area and an area where pedestrians walk slowly at high density. 
Jun Fang, Zheng Qin, Zhengcai Lu, Fengfei Zhao
physics.soc-ph nlin.CG