A Second-Order Lagrangian Macroscopic Traffic Flow Model for Freeways

摘要

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