A new multi-anticipative car-following model with consideration of the desired following distance

We propose in this paper an extension of the multi-anticipative optimal velocity car-following model to consider explicitly the desired following distance. The model on the following vehicle's acceleration is formulated as a linear function of the optimal velocity and the desired distance, with reaction-time delay in elements. The linear stability condition of the model is derived. The results demonstrate that the stability of traffic flow is improved by introducing the desired following distance, increasing the time gap in the desired following distance or decreasing the reaction-time delay. The simulation results show that by taking into account the desired following distance as well as the optimal velocity, the multi-anticipative model allows longer reaction-time delay in achieving stable traffic flows.