<![CDATA[This paper addresses the discovery of an interesting property in car-following processes, which was not reported in the existing literatures. A hybrid order behavior is supported by both experimental data and theoretical simulations. To demonstrate this behavior, the first order and the second order car-following behaviors are defined. Then, by comparing the first and the second order car-following behaviors in the existing analystic models and the real traffic context, this paper finds that a significant amount of the second order car-following processes in real traffic context do not match the existing models and structural mismatches are observed. The popularity and significance of such cases suggest the existence of unmodelled dynamics in the existing methods, that is, the car following behavior should be determined by more factors than the immediate proceeding vehicle. Therefore, the existing car-following models must be improved to accommodate these factors. This forms one of the main values of this paper. This paper then defines the hybrid order car-following behavior and prompts to associate this behavior with the concerned unmodelled dynamics (mismatches between the actual traffic data and the simulation from models). The neural network is employed to model such dynamics. The idea of the proposed hybrid order behavior matches the fact that the car-following behavior is determined by multiple vehicles driving in front of the subject car instead of only the immediate proceeding one. This is valuable because it provides guidance on the improvement of existing car-following models. The neural network model validates that the consideration of multiple vehicles improves the accuracy of car-following modelling.]]>
