An adaptive time gap car-following model

We intend to define a continuous car-following model exclusively based on the time gap. A model of the interaction between a vehicle and its predecessor is produced by adjusting the time gap to a targeted safety time that is a function of speed. The model is defined by a differential system, to which a consistent numerical scheme is associated. The parameters of the model are statistically estimated by maximum likelihood. In order to reproduce a heterogeneous traffic flow, vehicles are differentiated by type, and to recreate asymmetric longitudinal behavior, acceleration phases are distinguished from deceleration phases. Introducing a reaction time, inducing a delay in the perception and processing of information about vehicles in interaction, can alter the stability of the flux through appearance of kinematic waves. By simulation, the types and domains of parameters which are asymptotically unstable are identified. The results reveal that, in the model, the statistically estimated parameters form is strongly factor of instability.