Abstract
Today the most cities in the world face different problems caused by vehicular traffic due to the increasing number of vehicles on road, such as traffic congestion, environmental pollution, excessive noise, increased accidents on the road, etc. Therefore it is important to represent the phenomenon by applying models so as to find better traffic flow patterns in a given city. In this work we introduce a simple macroscopic model to describe traffic flow in traffic congestion and we obtain the equation that relates the characteristic behavior between traffic flow and traffic density, known in the literature as fundamental relationship. Finally, we find an analytical solution for optimal flow passing vehicles on a congested road section.
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