Noise-Induced Stop-and-Go Dynamics in Pedestrian Single-file Motion

Schadschneider, Andreas; Tordeux, Antoine · 2020 · Crossref

DOI: 10.17815/cd.2020.70

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Summary

This paper addresses the phenomenon of stop-and-go waves in single-file pedestrian motion, proposing a novel explanation based on stochastic effects rather than the traditional inertia-based mechanisms used in vehicular traffic modeling. While stop-and-go dynamics are commonly attributed to instability and phase transitions in deterministic models requiring fine-tuned parameters, the authors argue that pedestrian dynamics lack pronounced inertia and mechanical delays. Consequently, empirical evidence for phase transitions in pedestrian flow is scarce. The study aims to demonstrate that stop-and-go behavior can arise naturally from colored noise inherent in human cognition and response, without requiring system instability. The authors develop a stochastic first-order microscopic model described by a Langevin equation. The model consists of a deterministic optimal velocity function for convection and a noise term modeled as an Ornstein-Uhlenbeck process, representing colored noise with an exponentially decreasing time-correlation function. Statistical analysis of empirical pedestrian speed time-series confirms the presence of Brownian noise, characterized by a power spectral density proportional to $1/f^2$. Simulations were conducted using an explicit Euler-Maruyama scheme with parameters calibrated to empirical data: a time gap of 1 second, agent size of 0.3 meters, noise volatility $\alpha = 0.1 \, \text{ms}^{-3/2}$, and noise relaxation time $\beta = 5 \, \text{s}$. The simulations compared the stochastic model against unstable deterministic optimal velocity models and empirical trajectory data from experiments involving 28, 45, and 62 participants. The results show that the stochastic model successfully reproduces realistic stop-and-go dynamics. In semi-congested and congested states, the simulations generated backward-propagating waves with frequencies matching those of the deterministic unstable models and empirical data. The frequency of these waves depended solely on the number of agents and the time gap, while the noise parameters influenced the amplitude and stability of the waves. Specifically, larger noise relaxation times ($\beta$) produced stable waves with large amplitudes, whereas smaller values led to transient, white-noise-like fluctuations. Free-flow states remained homogeneous in both simulations and experiments. The stochastic approach accurately captured the empirical trajectories without the need for the fine-tuning required by instability-based models. The significance of this work lies in providing an alternative mechanism for stop-and-go formation in pedestrian flows that aligns better with the physical reality of human movement. By attributing oscillations to colored noise rather than inertial instability, the model avoids the unrealistic constraints of reaction times exceeding physical time gaps. The identified noise relaxation time of approximately 5 seconds reflects the mean period of stochastic deviations from equilibrium, offering a more plausible interpretation of pedestrian behavior than the 0.5–1 second reaction times typical of inertial traffic models. This approach enhances the realism of pedestrian dynamics simulations and provides a framework for interpreting empirical data through the lens of stochastic perturbations.

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• pedestrian behavior perception