A Second-Order Lagrangian Macroscopic Traffic Flow Model for Freeways

A macroscopic traffic flow model describes the evolution of aggregated traffic characteristics over time and space, which is a basic and critical component for various modern intelligent transportation systems, e.g., a real-time freeway control system. Traditional macroscopic traffic flow models are built in the Eulerian coordinates using Eulerian traffic characteristics, such as density, speed and flow. Recently, the Lagrangian traffic flow modeling using Lagrangian traffic characteristics, such as spacing and speed, began to attract research attentions. It is favored over the Eulerian model mostly for its more accurate and simplified discrete simulation results (1, 2), and its convenience in incorporating vehicle-based information. However, up to now only a firstorder model is presented (1, 2). Our paper proposes a new second-order Lagrangian macroscopic traffic flow model for freeways. The idea originates from Payne’s second-order Eulerian model which was derived on the basis of car-following considerations (3). It reflects the fact that a driver usually adjusts the speed based on the traffic condition ahead, and that a time delay exists as a driver reacts to the changed traffic condition. A dynamic speed equation is formulated to represent these behavioral facts. A lane-drop scenario is simulated to examine the model performance. Comparison with the first-order Lagrangian model confirms the effectiveness and advantages of the proposed second-order model.