Asymptotic stability of constant time headway driving strategy with multiple driver reaction delays

This paper addresses the asymptotic stability of a continuous-time deterministic car-following model with respect to different driving strategies. More precisely, the model takes into account a constant time headway driving behavior as well as the presence of multiple decision-making and actuation delays in describing the drivers´ actions. The stability analysis of the corresponding derived models is challenging and we will focus on characterizing the stability regions in the delay parameter space. Such a problem depicts some interesting properties in terms of delays that simplify the overall analysis leading to some simple frequency-sweeping based algorithms as well as to various practical interpretations of the results in terms of drivers´ behaviors. Illustrative examples complete the presentation.