Numerical Resolution of the LWR Method for First Order Traffic Flow Model

Congestion in Moroccan roads especially in urban areas is increasing and gaining in scale more and more nowadays, it can be induced by roads perforated, absence of traffic signs, behaviors of drivers, overcapacity of roads, illegal parking etc. Also, disproportional traffic lights cycle in a junction also serves as cause of congestion. One of the most innovative solutions is to build an intelligent transportation system (ITS) to collect data in real time and adjust the cycle time of traffic lights in every road intersection, provide alternative paths and predict when and where congestion will occur. Having a numerical model that give reliable solutions in real time using accurate data is essential. In this perspective, we use the LWR macroscopic model to model traffic flow and we adapt numerical resolution methods of Lax-Friedrichs and Godunov Schemes to test their accuracy and adaptability for traffic situations.