TDGL and mKdV equations for an extended car-following model with the consideration of driver's memory

This paper presents an extended car-following model by taking driver's memory and the full velocity difference into the original optimal velocity model (OVM). The stability condition of this model is obtained by using linear stability theory. The TDGL equation and the mKdV equation are derived from nonlinear analysis. The energy consumption of new car-following models considering the driver's memory is discussed. Furthermore, the new car-following model is investigated in detail by numerical methods. Both analytical and simulation results show that the extended following car-following model will not only suppress the traffic congestion but also reduce energy consumption.