Noise-induced stop-and-go traffic dynamics: Modelling and control

TL;DR

This paper tackles the problem of stop-and-go traffic waves arising from stochastic disturbances in a stable nonlinear car-following model. By injecting white Gaussian noise into the Adaptive Time Gap (ATG) framework and exploring both time-continuous and time-discrete formulations, it reveals a Kapitza-like nonlinear instability that drives a phase transition from laminar to oscillatory traffic, even when the deterministic system is unconditionally stable. A simple affine transformation of the dynamics is shown to counteract noise effects and dissipate waves, offering a potential control pathway with quantified trade-offs in acceleration and safety. The findings are supported by simulations that mirror classic experiments and demonstrate robustness to different noise types (white and Ornstein–Uhlenbeck), highlighting implications for ACC design and traffic stabilization strategies.

Abstract

This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following model, the study shows that minimal white Gaussian noise can destabilise the flow, leading to a phase transition from laminar to periodic dynamics through a nonlinear instability phenomenon, analogous to Kapitza's pendulum. Furthermore, a simple linear transformation of the model, which amplifies the response and introduces a positive acceleration bias, counteracts noise-induced effects and recovers the stability of uniform solutions. The findings are supported by simulations, offering new insights into the modelling and mitigation of oscillatory traffic dynamics.

Figures (8)

• Figure 1: Experimental trajectories of 22 vehicles on a single-lane circuit starting from a uniform configuration sugiyama2008traffic. After a while, a stop-and-go wave appears, causing the average speed to decrease and the standard deviation of the gap to increase.
• Figure 2: Replica of the experiment by Sugiyama et al. sugiyama2008traffic.
• Figure 3: Simulated trajectories of 22 vehicles on a 231-metre circuit as in the experiment by Sugiyama et al. sugiyama2008traffic using the stochastic ATG model \ref{['eq:SATGdiscrete']} where $\sigma=2.8$ m. The trajectories can be simulated online at: https://www.vzu.uni-wuppertal.de/fileadmin/site/vzu/Noise-Induced_Stop-and-Go_Modelling_and_Control.html?speed=0.7.
• Figure 4: Gap standard deviation for the 22 vehicles on the 231 m circuit (replica of the Sugiyama experiment) with the noisy ATG model \ref{['eq:SATG']} obtained from variation of the noise amplitude. The continuous lines are the averaged gap standard deviations of $K=100$ simulations, while the coloured areas are the min/max ranges. A phase transition arises from stable uniform solutions to stop-and-go dynamics as the noise amplitude increases. In addition, an optimal noise amplitude for the emergence of waves can be identified.
• Figure 5: Critical noise amplitude threshold according to the three main parameters of the ATG model (from left to right): $\ell$, $T$, and $\tau$. The system is unstable and waves propagate above the critical curve (red part) while the system is stable below it (blue part).