The Car Following Model with Relative Speed in Front on the Three-Lane Road

An improved car following model on one road with three lanes is presented in this paper, which considers the relative velocity in front on the main lane and the left and the right adjacent lanes. The stability criterion and neutral stability curve are obtained by linear stability theory. The nonlinear stability analysis is investigated further to get the solution of the modified Korteweg-de Vries (mKdV) equation and get the three areas of stability, metastability, and unstability. The new LRVD model (left and right lane velocity difference model) with bigger stable area can stabilize middle lane traffic flow better, which is proved by the linear theory, nonlinear theory, and the simulation. The LRVD model shows if drivers on the middle lane pay more attention to more cars in front on the two side lanes on the three-lane road, the middle lane traffic flow is certain to be more stable in real life. On the complex three-lane road, if intelligent traffic management system based on the huge traffic data for drivers is applied in real life, it is very helpful to ensure traffic safety, which is also the trend of transportation development in future.