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

Raphael Korbmacher; Parthib Khound; Antoine Tordeux; Frank Gronwald

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arXiv · 2512.04073

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

Raphael Korbmacher·Parthib Khound·Antoine Tordeux·Frank Gronwald

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Abstract

Stop-and-go waves in traffic flow are captivating collective phenomena with important safety and environmental consequences. While classical theories attribute these oscillations to linear instabilities caused by reaction delays and inertia, this study explores an alternative stochastic perspective. Using a linearly stable car-following model, we show that white Gaussian noise in the measurement of the inter-vehicle distance can destabilise the flow, inducing a phase transition to periodic stop-and-go dynamics via a nonlinear instability mechanism. Furthermore, we demonstrate that a simple linear transformation of the model, which amplifies the system response while introducing a positive acceleration bias, can counteract noise-induced effects and restores the stability of uniform traffic flow. These findings, supported by numerical simulations, aim to provide new insights into the modelling and control of oscillatory traffic dynamics.

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Raphael Korbmacher, Parthib Khound, Antoine Tordeux, Frank Gronwald. 2025-12-03. Noise-induced stop-and-go traffic dynamics: Modelling and control. https://arxiv.org/abs/2512.04073

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