  Based on the Nagel-Schreckenberg (NS) model with periodic boundary
conditions, we proposed the NSOS model by adding the overtaking strategy (OS).
In our model, overtaking vehicles are randomly selected with probability $q$ at
each time step, and the successful overtaking is determined by their
velocities. We observed that (i) traffic jams still occur in the NSOS model;
(ii) OS increases the traffic flow in the regime where the densities exceed the
maximum flow density. We also studied the phase transition (from free flow
phase to jammed phase) of the NSOS model by analyzing the overtaking success
rate, order parameter, relaxation time and correlation function, respectively.
It was shown that the NSOS model differs from the NS model mainly in the jammed
regime, and the influence of OS on the transition density is dominated by the
braking probability $p$
