An Extension of LWR Model Considering Slope and Heterogeneous Drivers

The LWR model's proposition has played an important part in the traffic flow study history. In this paper, we advance an extension model from the origin LWR model. The model takes slope and heterogeneous drivers into account according to an increased speed caused by gravity. We separate heterogeneous drivers with different free flow speed on the flat road and take their interaction into consideration. Numerical simulation is then done and traffic flow status can be shown clearly which confirms the effectiveness of this model.