Multi-class continuum traffic flow models

Traffic flow modelling has developed rapidly over the last two decades. In many applications, the models are combined with measured data concerning the current traffic state and with fast computational methods. Because of this combination it has become possible to make accurate and useful short term predictions about the evolution of the traffic state. The predictions can be used to inform and advise road users, for example about alternative routes. Furthermore, the predictions can be used to control traffic in an efficient way in order to prevent or reduce delays. The predictions are in particular useful in the case of exceptional circumstances such as an accident, extreme weather conditions or festivities. In such cases historical data is less useful and routes that are optimal under normal circumstances are not optimal anymore.

The main contribution of this dissertation is the development and analysis of a new traffic flow model and accompanying numerical methods. This model, Fastlane, takes into account the differences between types of vehicles (for example passenger cars and trucks) and driving styles. Furthermore, the model is well suited to make useful short term predictions for the traffic state on a network of main roads. This is due to the development of efficient numerical methods.

In the dissertation first the literature review is discussed. The literature review is largely based on a newly developed genealogy of traffic flow models. This model tree shows how such models have developed since their introduction in the 1930’s. It is followed by the model development and analysis. The model includes multiple classes which express the heterogeneity between vehicles and drivers. We then make a short side step to discuss the Lagrangian coordinate system that has proven useful in the model analysis. Furthermore, the Lagrangian coordinate system is subsequently applied in numerical methods for homogeneous roads and networks of inhomogeneous roads. Finally, we present recommendations for both practice and science.

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