An areal continuum model for mixed traffic

This study proposes a novel continuum first-order (LWR-type) macroscopic traffic flow model for mixed traffic conditions (heterogeneous and lane-free) based on vehicle-area conservation, offering a shift from traditional vehicle-count-based approaches. To address the limitations of existing models, particularly under heterogeneous, lane-free traffic, the model introduces two new macroscopic variables: areal density and areal flow, representing the space occupied by vehicles and the spatial flow of vehicle area, respectively. These variables provide a physically consistent and intuitive framework for analyzing traffic composed of diverse vehicle types and sizes. Using high-resolution trajectory data from three Indian cities, the model is empirically validated, and Smulders’ fundamental diagram is shown to best capture the observed relationships among areal variables. Notably, the study finds that the vehicle class with the largest area, not the longest length, exhibits the highest wave propagation speed, contrasting earlier findings. Multi-class extensions of the model enable class-specific analysis while maintaining compatibility with existing numerical and analytical methods for hyperbolic PDEs. The proposed model is particularly suited for lane-free, mixed traffic scenarios, and it integrates well with established numerical schemes like the method of characteristics and Godunov’s scheme. The Areal Continuum Model offers a more accurate and adaptable tool for traffic flow analysis and management in heterogeneous environments by replacing PCU-based and class-aggregated models with a spatially grounded framework.