COMPARISON OF NUMERICAL METHODS TO SOLVE TRAFFIC FLOW MODEL

Abstract

Traffic congestion has a significant impact on economic activity throughout much of the world. In our country there is a higher density of population and activities require more efficient infrastructure development. But building new infrastructure, it is long term and expensive solution. A short term solution to improve the traffic management to rationalize the use of existing infrastructure. Optimizing the flow at intersections would result in reduced congestion. In order to maximize the use of existing infrastructure, the influences of the different factors on the intersection flow have to be quantified. This can be done by modeling. Our objective on this study is by developing reasonable model try to find a better numerical method by performing numerical simulation. First we discus Lighthill and Whitham Richards (LWR)traffic flow model that lead to the PDE linear advection equation . By making velocity constant we present the discritization of liner advection equation in order to compute the numerical and exact solutions of the PDEs using three methods; First order Upwind, Lax Fredric and Lax Wendroff. From the simulation results we found that Lax-Wondroff scheme is the best method relative to the other methods. Finally we give the clue for further study of this research that any one who interested .