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

TL;DR

This paper presents a stochastic model explaining how minimal noise can induce stop-and-go waves in traffic, and proposes a control method to mitigate these oscillations, with implications for traffic safety and efficiency.

Contribution

It introduces a novel stochastic approach to model noise-induced traffic waves and proposes a simple linear transformation to counteract these effects, enhancing traffic flow stability.

Findings

Minimal white Gaussian noise can destabilize traffic flow.

A linear transformation can restore stability to uniform traffic flow.

Simulations support the effectiveness of the proposed control method.

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.