Impact of headway uncertainty on traffic flow: Asymptotic and local stability analysis of car-following model

In car-following behavior, a vehicle’s motion is primarily influenced by the headway and velocity of the preceding vehicle. However, uncertainties in these parameters arising from poor road surface quality, malfunctioning sensors, adverse weather conditions, and driver variability can significantly affect traffic flow dynamics. This study proposes an extended car-following model based on the “Full Velocity Difference” (FVD) model, which incorporates headway and velocity uncertainties along with a cooperative driving mechanism. Control theory is employed to derive both local and asymptotic stability criteria, allowing an investigation into the influence of uncertainties on traffic behavior. Through linear stability analysis and nonlinear analysis, the model’s neutral stability condition is obtained, along with the derivation of the associated Burgers and “modified Korteweg–de Vries” (mKdV) equations. The proposed model outperforms the existing models in the literature with respect to the size of the stability region. Numerical simulations demonstrate that headway and velocity uncertainties notably affect vehicle startup behavior and the stability of traffic flow. Additionally, power spectrum theory is used to analyze spectral entropy, offering deeper insights into the impact of uncertainty on traffic dynamics through simulation.