Study on security features of freeway traffic flow with cellular automata model—Taking the number of overtake as an example

•Influence of overtaking frequency on freeway traffic flow.•Control rules containing passing lane under various conditions.•Quantitative relationship between vehicle density and mixing ratio.

On the basis of the multi-lane cellular automata model, considering the influence of vehicle lane-changing frequency on highway traffic safety, taking the overtaking ratio as the main indicator of traffic safety level, we propose two kinds of three-lane cellular automata traffic flow models under two different lane control conditions, and make computer simulation with the two models respectively, and analyze the relationship between mixing ratio of different vehicles, density, and overtaking ratio. The results of numerical experiments show that different lane control conditions and mixing ratios have significant influences.