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

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