A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities

Abstract

On freeways, congestion always leads to capacity drop. This means the queue discharge rate is lower than the pre-queue capacity. Our recent research findings indicate that the queue discharge rate increases with the speed in congestion, that is the capacity drop is strongly correlated with the congestion state. Incorporating this varying capacity drop into a kinematic wave model is essential for assessing consequences of control strategies. However, to the best of authors' knowledge, no such a model exists. This paper fills the research gap by presenting a Lagrangian kinematic wave model. "Lagrangian" denotes that the new model is solved in Lagrangian coordinates. The new model can give capacity drops accompanying both of stop-and-go waves (on homogeneous freeway section) and standing queues (at nodes) in a network. The new model can be applied in a network operation. In this Lagrangian kinematic wave model, the queue discharge rate (or the capacity drop) is a function of vehicular speed in traffic jams. Four case studies on links as well as at lane-drop and on-ramp nodes show that the Lagrangian kinematic wave model can give capacity drops well, consistent with empirical observations.

A hybrid model predictive control for traffic flow stabilization and pollution reduction of freeways

“…For the thresholds, values around the critical density are chosen. Furthermore, they are tuned considering the hysteresis effect in the traffic dynamics (see Yuan et al (2017)): the choice of unequal threshold values leads to the exclusion of the oscillation and ensures the stability of the switching control. The threshold values are chosen based on manual tuning following a set of test runs.…”

Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops

“…Finally, our capacity drop theory can be seen as a simplified version of the recent proposal by Yuan et al (2017) who vary the queue discharge rate not only depending on whether the queue is a standing or a moving one, but also on the congestion density, thereby deviating from a fixed inverted-lambda FD. Our simplification is necessary for the link-level solution method that will be developed in the next section.…”

Lagrangian formulation for mixed traffic flow including two-wheelers

“…However, recent studies show that Lagrangian representation, which tracks the evolution of flow properties of vehicle/platoon of vehicles, offers several advantages over the Eulerian representation, with the main benefits being numerical accuracy [2] and flexibility to easily incorporate traffic phenomena (e.g. capacity drop [14]) and vehicle characteristics.…”