Stop-and-go waves induced by correlated noise in pedestrian models without inertia

Stop-and-go waves are commonly observed in traffic and pedestrian flows.In most microscopic traffic models,they occur through a phase transition and instability of the homogeneous solution after fine tuning of parameters.Inertia effects are believed to play an important role in this mechanism.In this article,we present a novel explanation for stop-and-go waves based on stochastic effects in the absence of inertia.The model used is a first order optimal velocity(OV)model including an additive stochastic noise.A power spectral analysis for single-file pedestrian trajectories highlights the existence of Brownian speed residuals.We use the Ornstein-Uhlenbeck process to describe such a correlated noise.The introduction of this specific colored noise in the first order OV model allows describing realistic stop-and-go behavior without requiring instabilities or phase transitions,the homogeneous configurations being systematically stochastically stable.We compare the stochastic model to deterministic unstable OV models and analyze individual speed autocorrelation to describe the nature of the waves in stationary states.We apply the approach to pedestrian single-file motion and compare simulation results to real pedestrian trajectories.The simulation results are quantitatively very similar to the real trajectories.We discuss plausible values for the model parameters and their meaning.