Solutions of the 2D Macroscopic Motor Vehicle Traffic Flow Model

The study developed heterogeneous motor vehicle traffic flow models focussing on two dimensional heterogeneity and multi - lane road heterogeneity aspects. It established the 2 - ensemble traffic composition formulation using vehicle heterogeneity characteristics in two dimensions. Lighthill - Whitham and Richards motor vehicle traffic model, investigated how homogeneous vehicles travels in a one dimensional, single lane road; without curvatures. The study shows that that when vehicles are few, traffic density is lower, the flux is also lower; the velocity is high as there is maximum vehicle - road interaction. As the number of vehicles increases such that many vehicles passes the fifth nodal point at a relatively high velocity and density; the flow rate is high. At maximum density called jam density, vehicles cannot move; the flux is lower. Graphical representation of the traffic flow variables with respect to the distance covered on the highway is done using MATLAB. The information obtained from the study is very useful to civil engineers, mechanical engineers, town planners, computer programmers and upcoming mathematicians not forgetting drivers and riders.