Fundamental Diagram of Pedestrian Dynamics by Safety Interspace Model

TL;DR

This paper introduces a new safety interspace model based on NaSch to simulate pedestrian dynamics, accurately reproducing empirical fundamental diagrams and phenomena like stop-and-go waves.

Contribution

The paper extends the NaSch model with a safety interspace function and multi-grid space partition, specifically tailored for pedestrian flow simulation.

Findings

Successfully reproduces empirical fundamental diagrams.

Captures discontinuity areas in velocity-density curves.

Reproduces stop-and-go waves and phase separation.

Abstract

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.