A new car following model based on weighted average velocity field

In real traffic, the motion status of forward moving vehicles play an important role in influencing the following vehicle’s motion behaviour. Nowadays, autonomous and electric vehicles have been incorporated with car-following mode when the control process is more complicated and more meaningful. As a result, researchers are studying car-following control strategies for vehicles to attain stability in traffic. Based on this, we propose a new car following model considering weighted average velocity field to describe the average effect of multi-vehicle interaction on the whole road. The weighted average velocity field can be regarded as the weighted average of velocities of finite number of vehicles preceding the objective vehicle with more weightage to more preceding vehicle. The stability condition is derived through stability analysis. Subsequently, the modified Korteweg–de Vries (mKdV) equation is formulated to unveil traffic congestion in the form of the kink-antikink density wave. Theoretical findings indicate that the weighted average velocity field yields larger stability regions compared to the average velocity field. Numerical simulations were conducted, and the results obtained demonstrate that the weighted average effect of multi-vehicle interactions play a crucial role in suppressing traffic jams faster than a simple average.