A first-order link-based flow model with variable speed limits and capacity drops for freeway networks

First-order link-based traffic flow models are computationally efficient in simulating freeway networks. However, the standard link transmission models fall short of reproducing traffic phenomena such as capacity drop (CD). Moreover, traffic control measures such as variable speed limits (VSLs) control may change the fundamental diagram and should be captured by traffic flow models. This study proposes a first-order link-based flow model incorporating VSL and CD for freeway simulation. In the proposed model, the vehicle flow through each link is characterized by cumulative inflow and outflow, which are influenced by the time-varying free flow speed caused by the VSL at the link's upstream boundary. CD is modeled by incorporating the traffic state-dependent capacity at the freeway lane-drop positions. A node model is then developed to determine and regulate the flow propagation between adjacent links. Simulation experiments were conducted on freeways to evaluate the model's effectiveness. The results demonstrate its ability to accurately predict traffic operations under VSL and CD while maintaining a computationally tractable representation of flow propagation.