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The NaSch model is a classical one-dimensional cellular automata (CA) modelof freeway traffic. However, it is not suitable for simulating pedestriandynamics due to the kinetic difference between vehicles and pedestrians. Basedon NaSch model, we proposed a new safety interspace model to investigate thesingle-file pedestrian stream. We simulated and reproduced Seyfried'sexperiment in 2006 quantitatively and use the empirical data to validate ourmodel. We defined the safety interspace as a linear function of currentvelocity and introduced a normal distributed random variable to describe therandomness of spatial cognition. Meanwhile, we extended NaSch model in spacepartition from single-grid mode to multi-gird mode to increase spatialresolution. It was found that through three model perimeters with appropriatevalues, the new model could reproduce faithfully the typical form of thefundamental diagram from empirical data. The velocity-density curve insimulation could indicate the discontinuity areas in fundamental diagramobserved from empirical data. In addition, we reproduced the stop-and-go wavesand phase separation into a stopping area and an area where pedestrians walkslowly at high density.

Fundamental Diagram of Pedestrian Dynamics by Safety Interspace Model