Dynamics of delayed car-following models: human vs. robotic drivers

Summary. Ag eneral class of car-following models is studied with different driver reaction time configurations. In particular the stability of traffic flow is investigated in case of human-driven vehicles and computer-controlled (robotic) cars. It isshown that in both cases, time delays can change the frequency of arising oscillations and, consequently, the wavelength of the emerging traveling waves, leading to high-frequency / short-wavelength oscillations. Furthermore, interacting the with the nonlinearities inthe system, time delays can make the dynamics excitable, such that waves may be triggered when the uniform flow is linearly stable. Finally, low-frequency and high-frequency oscillations can interact at the nonlinear level leading to very complex dynamics. Modeling car following Car following has been studied for six decades and there exis ta bout ah undred different models which can reproduce traffic behavior for chosen sets of driver parameters. Still ,n o fundamental modeling principles has been established to guide scientists and engineers how to construct car-following models and what kind of qualitative requirements these models must satisfy. In order to change this tendency, a new direction has been identified in transportation science: instead of studying the dynamics of individual models quantitatively, the qualitative dynamics of classes of models shall be studied [1, 3]. Such investigations are useful for classifying the existing models and can also provide guidance for future models. Here, we investigate a class of models where each driver monitors the kinematic properties of the driver ahead and reacts to such stimuli with reaction time delays. These models can describe the behavior of human drivers fairly accurately, and may also be applied when programmingAutonomousCruise Control (ACC) devices (that consist of a radar sensor and an on board computer and can actuate the vehicle based on information collected about the environment). To obtain tractable models, usually identical vehicles areconsidered, so the acceleration of theith vehicle is given by ˙ v i (t )= f ! h i (t!!), ˙ h i (t!"),v i (t!#) " ,