An extended continuum mixed traffic model

With the development of vehicle technology, the number of vehicles equipped with the adaptive cruise control (ACC) system is increasing, and it is more and more common for ACC vehicles to drive with regular vehicles. In this work, we proposed a mixed traffic model with regular vehicles and ACC vehicles via the transformation of micro-model and macro-model. The linear stability analysis tells that the permeability of ACC vehicles has an important influence on the traffic system. Meanwhile, through the nonlinear analysis, the KdV–Burgers equation describing the density wave is obtained. Besides, the results of numerical simulations are consistent with the theory, which indicates that the increase in ACC vehicles is conducive to the stability of the transportation system.