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 been considered in modeling pedestrian dynamics. 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 Seyfried’s field experiments at the Research Centre Jülich, and use its empirical data to validate our SR model. We compare the SR model with the standard LG model. We tested different probabilities of slow reaction _ps$p_s$ in the SR model and found the simulation data of _ps=0.3$p_s=0.3$ fit the empirical data best. The RMS error of the mean velocity of the SR model is smaller than that of the standard LG model. In the range of _ps=0.1–0.3$p_s=0.1–0.3$, our fundamental diagram between velocity and density by simulation coincides with field experiments. The distribution of individual velocity in the fundamental diagram in the SR model agrees with the empirical data better than that of the standard LG model. In addition, we observe stop-and-go waves and phase separation in pedestrian flow by simulation. We reproduced the phenomena of uneven distribution of interspaces by the SR model while the standard LG model did not. 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.