Lagrangian formulation for mixed traffic flow including two-wheelers

The Lagrangian formulation of kinematic waves provides a more accurate representation than the most commonly used Eulerian formulation, and is better suited to study cooperative traffic phenomena requiring individualized rather than aggregated flow parameters (e.g. trajectory planning, traffic monitoring). The growing penetration of Powered Two Wheelers (PTW) in regular traffic is typically expected to require smart cooperative trajectory planning to maximize flow and avoid accidents. This paper therefore presents a multi-class Lagrangian representation for a traffic flow consisting of cars and PTW. The capability of PTW to have higher speeds than cars makes the existing Lagrangian discretization approaches inadequate. We accordingly introduce a novel discretization method for mixed cars and PTW traffic mitigating such limitation, and also capable of reproducing a follow-the-leader type mobility. We finally evaluate our Lagrangian discretization against the Eulerian formulation and show its high accuracy.