Stability and string stability of car-following models with reaction-time delay
Abstract
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 non rational 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, partial string stability).
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