Abstract:We investigated the mixed traffic flow with human-driving and autonomous cars. A new mathematical model with adjustable sensitivity and smooth factor was proposed to describe the autonomous car’s moving behavior in which smooth factor is used to balance the front and back headway in a flow. A lemma and a theorem were proved to support the stability criteria in traffic flow. A series of simulations were carried out to analyze the mixed traffic flow. The fundamental diagrams were obtained from the numerical simulation results. The varying sensitivity and smooth factor of autonomous cars affect traffic flux, which exhibits opposite varying tendency with increasing parameters before and after the critical density. Moreover, the sensitivity of sensors and smooth factors play an important role in stabilizing the mixed traffic flow and suppressing the traffic jam.