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Adaptive cruise control (ACC) vehicles are proving to be the first generation of driver-assist enabled vehicles. In order to study the impacts of ACC vehicles on string stability and traffic flow characteristics, accurately calibrating microscopic car following models is crucial to simulate inter-vehicle dynamics. While many car following models have been used to simulate car following behavior, a single, continuous function may not describe both acceleration and braking realistically. We propose an asymmetric model which is based on the symmetric optimal velocity relative velocity (OVRV) model and switch parameters under different conditions to realize and reproduce car following dynamics of ACC vehicles. We conduct an analytical string stability analysis and the string stability criterion is derived. The calibration and simulation results show that the proposed asymmetric ACC model reduces model spacing error by up to 38% compared with the symmetric OVRV model. Compared with other commonly used asymmetric car following models in the transportation community, the proposed asymmetric ACC model can reduce spacing error by 44.8%. Furthermore, we validate the derived string stability criterion with a numerical test simulating with a string of vehicles. We conclude that an asymmetric car following model shows more accurate performance in the capture of ACC car following behavior. [ABSTRACT FROM AUTHOR]