A general class of car-following models is analyzed where the longitudinal acceleration of a vehicle is determined by a nonlinear function of the distance to the vehicle in front, their velocity difference, and the vehicle’s own velocity. The driver’s response to these stimuli includes the driver reaction time that appears as a time delay in governing differential equations. The linear stability of the uniform flow is analyzed for human-driven and computer-controlled (robotic) vehicles. It is shown that the stability conditions are equivalent when considering ring-road and platoon configurations. It is proven that time delays result in novel high-frequency oscillations that manifest themselves as short-wavelength traveling waves. The theoretical results are illustrated using an optimal velocity model where the nonlinear behavior is also revealed by numerical simulations. The results may lead to better understanding of multi-vehicle dynamics and allow one to design cooperative autonomous cruise control algorithms.

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