An extended continuum model accounting for the driver's timid and aggressive attributions

Considering the driver's timid and aggressive behaviors simultaneously, a new continuum model is put forwarded in this paper. By applying the linear stability theory, we presented the analysis of new model's linear stability. Through nonlinear analysis, the KdV–Burgers equation is derived to describe density wave near the neutral stability line. Numerical results verify that aggressive driving is better than timid act because the aggressive driver will adjust his speed timely according to the leading car's speed. The key improvement of this new model is that the timid driving deteriorates traffic stability while the aggressive driving will enhance traffic stability. The relationship of energy consumption between the aggressive and timid driving is also studied. Numerical results show that aggressive driver behavior can not only suppress the traffic congestion but also reduce the energy consumption. - Highlights: • A new continuum model is developed with the consideration of the driver's timid and aggressive behaviors simultaneously. • Applying the linear stability theory, the new model's linear stability is obtained. • Through nonlinear analysis, the KdV–Burgers equation is derived. • The energy consumption for this model is studied.