A Hybrid Kinematic Wave Model Incorporating Capacity Drops

Literature indicates that on a freeway the capacity is higher than the queue discharge rate. This is called the capacity drop. Recent studies show that the queue discharge rate increases as the speed in congestion increases. For many applications, such as dynamic speed limit control design and evaluation, macroscopic models are needed. A kinematic wave model aiming to assess consequences of control strategies should firstly reproduce different queue discharge rates depending on congestion states, and secondly capture the capacity drop for both standing queues and stop-and-go waves. However, no such kinematic wave model exists until now. Therefore, this paper fills in the gap, incorporating the capacity drop into a kinematic wave model. The new model can reproduce different queue discharge rates corresponding to the vehicular speed in congestion, which means the new model can reproduce speed limit effects accurately. By formulating the model in Lagrangian coordinates and applying an upwind discretization method, this paper presents a hybrid model which captures the capacity drop with stop-and-go waves and can be applied to reproduce the capacity drop with standing queues. A case study shows the working of the model with two different queues.