In driving a vehicle, drivers respond to the changes of both the headway and the relative velocity to the vehicle in front. In this paper a new car-following model including these maneuvers is proposed. The acceleration of the model becomes infinite (has a singularity) when the distance between two vehicles is zero, and the asymmetry between the acceleration and the deceleration is incorporated in a nonlinear way. The model is simple but contains enough features of driving for reproducing real vehicle traffic. From the linear stability analysis, we confirm that the model shows the metastable homogeneous flow around the critical density, beyond which a traffic jam emerges. Moreover, we perform experiments to verify this model. From the data it is shown that the acceleration of a vehicle has a positive correlation with the relative velocity.

In this paper, we have proposed a new compressible fluid model for the one-dimensional traffic flow taking into account a variation of the reaction time of drivers, which is based on the actual measurements. The model is a generalization of the Payne model by introducing a densitydependent function of reaction time. The linear stability analysis of this new model shows the instability of homogeneous flow around a critical density of vehicles, which is observed in real traffic flow. Moreover, the condition of the nonlinear saturation of density against small perturbation is theoretically derived from the reduction perturbation method.

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