A dynamical traffic flow model for a cognitive drivers' sensitivity in Lagrangian scope

A new microscopic traffic flow model is established based on heterogeneous driver's sensitivity; in this new model, the driver's sensitivity is defined as being dependent on the headway distances to the preceding vehicle, similar to Bando’s optimal velocity function. We introduce the formulation of this cognitive driver's sensitivity utilizing a modified form of Bando’s optimal velocity function. A simple methodology, which is used for improving Bando’s optimal velocity function, has been implemented for developing the cognitive driver’s sensitivity function, which establishes a correlation between the flow field’s density and human drivers' responses. The model is highly advanced for introducing a human-driven traffic flow field considering the driver’s mental behavioral activity. Using the linear stability condition, we elucidate a neutral stability condition. A series of numerical simulations indicates how the present model describes dynamics that differ from the conventional model, which assumes a constant driver's sensitivity.