Monotone iterative simulation of the multilane traffic dispersion model

In this study, the multilane traffic flow is modeled as a nonlinear Poisson equation in a two-dimensional space. The model is derived from the interaction among vehicles and the assumption that vehicles will tend toward the equilibrium state under a given traffic condition. A monotone iterative scheme for the nonlinear model, which is a finite difference approximation of the model, is presented. The convergency is also discussed herein. At last, a numerical example is employed to explain the model.