Stability and String Stability of Car-Following Models with Reaction-Time Delay.

We investigate the transfer function emanating from the linearization of a car-following model for human drivers when taking into account their reaction time, which is known to be a cause of the stop-and-go traffic phenomenon. This leads to a nonrational transfer function, implying nontrivial stability conditions which are explicitly given. They are in particular satisfied whenever string stability holds. We also show how this reaction time can introduce a partial string stability, where the transfer function modulus remains smaller than 1 up to some critical frequency. We explore conditions in the parameter space discriminating between 3 different regimes (stability, string stability, and partial string stability).