White and relaxed noises in optimal velocity models for pedestrian flow with stop-and-go waves

A class of microscopic stochastic models is proposed to describe 1D pedestrian trajectories obtained in laboratory experiments. The class contains continuous first-order models that are based on statistically calibrated optimal velocity functions. More specifically, we consider a model with an additive white noise and another one where the noise is determined by the inertial Ornstein–Uhlenbeck process. Simulation results show that both stochastic models give a good description of the characteristic relation between speed and spacing (fundamental diagram) and its variability. However, only the inertial noise model can reproduce the observed stop-and-go waves, bimodal speed distributions, and non-zero speed or spacing autocorrelations. This allows us to identify minimal microscopic stochastic mechanisms for the emergence of stable traffic waves. (paper)