The fundamental Diagram of Pedestrian Model with Slow Reaction
  The slow-to-start models are a classical cellular automata model in simulating vehicle traffic. However, to our knowledge, the slow-to-start effect has not considered in modeling pedestrian dynamic. We verify the similar behavior between pedestrian and vehicle, and propose an new lattice gas (LG) model called the slow reaction (SR) model to describe the pedestrian's delayed reaction in single-file movement. We simulate and reproduce the Seyfried's field experiments at the research centre Julich, and use its empirical data to validate our SR model. We compare the SR model with the standard LG model. We test different probability of slow reaction ps in SR model and found the simulation data of ps=0.3 fit the empirical data best. The RMS error of mean velocity of SR model is smaller than that of standard LG model. In the range of ps=0.1~0.3, our fundamental diagram between velocity and density by simulation coincides with field experiments. The distribution of individual velocity in fundamental diagram in SR model agrees with the empirical data better than that of standard LG model. In addition, we observe the stop-and-go waves and phase separation in pedestrian flow by simulation. We reproduced the phenomena of uneven distribution of interspaces by SR model while the standard LG model did not implement. The SR model can reproduce the evolution of spatio-temporal structures of pedestrian flow with higher fidelity to Seyfried's experiments than the standard LG model. 
Jun Fang, Zheng Qin, Hao Hu, Zhaohui Xu, Huan Li
physics.soc-ph