We intend to define a longitudinal car-following model based on the time gap between vehicles. A model of the interaction between a vehicle and theone in front is produced by adjusting the time gap to a targeted safety time that is a function of speed. The model is defined by an adaptive differential system, to which a consistent numerical scheme is associated. Introducing a reaction time, inducing a delay in the perception and processingof information about vehicles in interaction, alters the stability of thesystem through appearence of kinematic waves. A targeted safety time function plays an essential role in developing kinematic waves; by simulation,we will try to determine which domains and what types of parameters in the model are sources of instability. In some cases, introducing a reaction time can lead to collisions. A condition on the targeted safety time function can ensure there is no collision. Lastly, anticipatory strategies for offsetting the reaction time are defined and simulations make it possible to evaluate their effectiveness.
Abstract