  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.
