Second-Order Model and Capacity Drop at Merge

This study deals with the modeling of merge sections from a macroscopic point of view. It is well known that the first-order macroscopic model is not able to reproduce the capacity drop, that is, the fact that the maximal throughput just downstream of a merge is lower after the onset of congestion than just before. Second-order models, such as the one proposed recently by Bastin and Haut, claim to be able to reproduce this observed feature. The ability of this second-order model, chosen for its generality, to reproduce the capacity drop was studied by using numerical investigations. Definitions of the capacity drop are reviewed and some of the experimental observations are reported. The latest attempts to model the capacity drop are presented. Then the chosen model is presented briefly, and its numerical resolution is detailed. The study's main contribution can then be developed. From numerical experiments, it is shown that the studied approach allows the definition of a new framework for capacity drop modeling. Its limitations are also explored.