Modeling multilane traffic flow in Lagrangian coordinates

Abstract

This paper proposes a multilane traffic flow model based on the notions of conservation laws in Lagrangian coordinates. Both continuous formulation and discretization of the model are derived explicitly considering lane-changing characteristics. For model discretization, a lane-changing number estimation model is developed to calculate the net lane-changing number for each vehicle group considering the relative position between vehicle groups in the current and adjacent lanes. With model discretization, the spacing of vehicle groups for each lane can be dynamically calculated. In addition, the boundary conditions for both the continuous Lagrangian model and its discretization are also derived. A numerical implementation of the model in the case of a three-lane highway section with a lane-drop is discussed, and results indicate that the proposed Lagrangian model can well simulate traffic dynamics, including the generation and propagation of congestion, and the perturbation caused by lane-changing behaviors. The lane-changing characteristics in terms of a cumulative net number of lane-changing vehicles for each lane, and the spacing dynamics of vehicle groups can be estimated as well. We further validate the proposed model using real-world data observed from a two-lane freeway section in Japan. The results show that the proposed multilane Lagrangian model can well capture traffic dynamic properties and could provide a relatively accurate estimation in terms of lane volume dynamics, vehicle spacing dynamics, and the cumulative net number of lane-changing vehicles. Comparisons with the Eulerian multilane model indicate that the Lagrangian model offers superior performance in predicting vehicle counts and spacing, especially under congested conditions. This improved performance can be attributed to the Lagrangian model's capability to track individual vehicle groups, resulting in a more precise representation of traffic dynamics.