Perturbation and stability analysis of the multi-anticipative intelligent driver model. (English) Zbl 1195.90020

Summary: This paper discusses three kinds of IDM car-following models that consider both the multi-anticipative behaviors and the reaction delays of drivers. Here, the multi-anticipation comes from two ways:
(1) the driver is capable of evaluating the dynamics of several preceding vehicles, and
(2) the autonomous vehicles can obtain the velocity and distance information of several preceding vehicles via inter-vehicle communications.
We study the stability of homogeneous traffic flow. The linear stability analysis indicates that the stable region will generally be enlarged by the multi-anticipative behaviors and reduced by the reaction delays. The temporal amplification and the spatial divergence of velocities for local perturbation are also studied, where the results further prove this conclusion. Simulation results also show that the multi-anticipative behaviors near the bottleneck will lead to a quicker backwards propagation of oscillations.


90B20 Traffic problems in operations research
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