Macroscopic modeling for traffic flow on three-lane highways

In this paper, a macroscopic traffic flow model for three-lane highways is proposed. The model is an extension of the speed gradient model by taking into account the lane changing. The new source and sink terms of lane change rate are added into the continuity equations and the speed dynamic equations to describe the lane-changing behavior. The result of the steady state analysis shows that our model can describe the lane usage inversion phenomenon. The numerical results demonstrate that the present model effectively reproduces several traffic phenomena observed in real traffic such as shock and rarefaction waves, stop-and-go waves and local clusters.