Mixing Microscopic and Macroscopic Representations of Traffic Flow: Hybrid Model Based on Lighthill–Whitham–Richards Theory

The hybrid traffic flow model, coupling a microscopic (vehicle-based) and a macroscopic (flow-based) representation of traffic flow, may be a useful tool to better understand the relationships between the various types of representation. It can also be a basis for implementing various model extensions, which may be easier with using one type of representation or the other. The hybrid model presented here combines a flow and a vehicular representation of the same model, which is the classical Lighthill–Whitham–Richards model. The use of a simple and unique model makes it possible to focus on the specific problems raised by translating boundary conditions from vehicular to flow formulation and conversely. This translation is made in order to ensure the conservation of flow and proper transmission of information both downstream and upstream and to minimize the perturbations induced by transitions between a continuous and a discrete representation of flow. The resulting model is shown to have good properties, particularly concerning congestion propagation and flow smoothing at the interfaces between the two models.