An areal continuum model for mixed traffic

Maiti, Nandan; Chilukuri, Bhargava Rama · 2026 · Crossref

DOI: 10.1016/j.physa.2026.131465

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Summary

This paper addresses the limitations of traditional traffic flow models in handling mixed traffic conditions, where vehicles of varying sizes (e.g., cars, motorcycles, trucks) coexist. Existing approaches often rely on Passenger Car Units (PCUs) to convert heterogeneous traffic into homogeneous equivalents, but this method suffers from dynamic variability, calibration difficulties, and a failure to conserve vehicle number effectively in continuum models. To resolve these issues, the authors propose a novel areal continuum model based on the principle of vehicle area conservation rather than vehicle count conservation. This approach aims to more accurately capture the spatial occupancy and physical interactions of diverse vehicle types in lane-free environments. The methodology introduces two new traffic flow variables: areal flow ($q_a$) and areal density ($k_a$), defined by the total projected vehicle area crossing a road section or occupying a space-time volume, respectively. The authors derive a hyperbolic conservation law analogous to the Lighthill-Whitham-Richards (LWR) model, but conserving area instead of vehicle count. They establish theoretical relationships between these new variables and traditional metrics like density, occupancy, and area occupancy. To validate the model, the authors utilize empirical data collected from three Indian cities (Chennai, Surat, and Guwahati) on six-lane divided highways. The data, extracted via image processing, categorizes vehicles into cars, two-wheelers, and heavy vehicles, allowing for the construction of stream-based fundamental diagrams using the new areal variables. The study finds that areal density and flow are scaled versions of traditional density and flow, with the scaling factor dependent on average vehicle area and road width. Empirical analysis reveals linear relationships between areal density and traditional metrics, confirming that areal density better accounts for the physical space occupied by larger vehicles. The authors demonstrate that conventional solution methods for hyperbolic conservation laws remain applicable to the proposed model. Furthermore, they develop a multi-class cell transmission model numerical scheme to simulate mixed traffic dynamics. This simulation successfully replicates specific mixed traffic phenomena, such as vehicle seepage (overtaking) and platoon dispersion, which are difficult to capture using standard PCU-based models. The significance of this work lies in providing a robust theoretical framework for modeling mixed traffic that overcomes the inconsistencies of PCU-based approaches. By conserving vehicle area, the model offers a more physically consistent representation of traffic flow in heterogeneous environments. The introduction of areal flow and density provides new tools for analyzing traffic states, particularly in lane-free conditions where spatial arrangement is critical. This approach improves the accuracy of capacity estimation and congestion modeling, offering a viable alternative for macroscopic traffic simulation and control in regions with high vehicle heterogeneity.

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• traffic density