Traffic flow models are usually categorized into microscopic models which individually consider vehicles, and macroscopic ones which use density to characterize the traffic. However, models from different categories could lead to very close solutions. Furthermore, previous works have shown that the nature of the underlying behavioral rule is much more important than the traffic representation to define model properties. This paper will illustrate this point in the LWR framework. The first aim is to demonstrate that the car-following models based on Newell's optimal velocity approach correspond to the numerical resolution of the LWR model in Lagrangian coordinates. Note that the LWR model is usually solved using an Eulerian grid. The choice between an individual and a continuous representation of traffic is only then a choice between two discretization forms of the same model. The second aim of the paper is to formulate boundary conditions for coupling together both discretizations, following previous works on hybrid modeling. Point interfaces (located at discrete points in space) are proposed generalizing the demand and supply concept. Simulation results are then presented. That shows that the wave's propagation at the interfaces level is consistent with the LWR solutions. The interfaces do not induce perturbations when changing the flow representation and appear to be transparent for the model solutions. Furthermore, the proposed hybrid model is compatible with the major extensions of the LWR model developed over the past few years (bounded acceleration, intersections modeling, multi-lanes representation).
Abstract