Stabilization of traffic flow based on multi-anticipative intelligent driver model

This paper extends the intelligent driver model (IDM) with a multi-anticipative behavior and a reaction delay to describe the motion of the dynamical traffic flow. In the approach, the acceleration and deceleration manipulations of drivers depend on the velocity of the subject vehicle n, the netto gaps and velocity differences between vehicle n and a range of the preceding vehicles from n-1 to n-m. We analyze the linear stability of the multi-anticipative intelligent driver model (MIDM) by introducing a small disturbance into the homogeneous traffic flow on a single lane with open boundaries. The induced neutral stability curve in the phase diagrams reflects the multi-anticipative behavior and shows that the stable region is a result of the collective effects of the desired time gap, the reaction time, the maximum acceleration, the maximum anticipative vehicles, the homogeneous velocity and netto gap, and so on. The traffic congestions can be suppressed by introducing the multi-anticipative interactions. The results of numerical simulation coincide with the theoretical linear stability analysis.