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This paper presents a generalised framework to model the interactions between human-driven vehicles (HVs) and connected autonomous vehicles (CAVs) in multi-lane settings using Lagrangian coordinates. The framework integrates lane-specific fundamental diagrams and conservation laws considering lane-changing behaviour, available in both continuous and discrete formulations. A novel method estimates net lane-changing rates by balancing demand and capacity across lanes, enabling dynamic calculation of vehicle group spacing and simulating both longitudinal and lateral dynamics. Validation includes numerical experiments involving accidents and lane drops, and one real-world trajectory dataset. Results show the model effectively captures the emergence, propagation, and dissipation of congestion, reproduces capacity drop, and provides both macroscopic flow characteristics and microscopic vehicle group dynamics. Compared to Lagrangian single-lane and Eulerian multi-lane models, the proposed framework better captures multi-lane mixed traffic complexities and reduces numerical diffusion. Real-world validation confirms its accuracy in estimating vehicle counts, spacing, and lane-changing behavior.
Lu et al. (Thu,) studied this question.