A Density-Based and Lane-Free Microscopic Traffic Flow Model Applied to Unmanned Aerial Vehicles

Gharibi, Mirmojtaba; Gharibi, Zahra; Boutaba, Raouf; Waslander, Steven L. · 2021 · DOAJ

DOI: 10.3390/drones5040116

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Summary

This paper introduces the Scalar Capacity Model (SCM), a microscopic traffic flow model designed for Unmanned Aerial Vehicles (UAVs) that eliminates the traditional concept of lanes. The research is motivated by the impending integration of UAVs into airspace for tasks such as delivery and surveillance, which requires robust traffic management tools. Existing models rely on a One/Multi-Lane View (OMV) adapted from ground vehicle traffic, which is ill-suited for UAVs due to their 3D movement capabilities and the ambiguity of lane definitions in airspace. The authors argue that OMV models artificially restrict passing maneuvers, reducing traffic efficiency. To address this, the paper proposes a Density/Capacity View (DCV) that models individual vehicle motion based on perceived congestion and channel capacity rather than discrete lanes. The SCM is formulated as a nonlinear differential equation where each vehicle’s velocity is determined by its maximum free-flow speed and a congestion factor. This factor is calculated using an exponentially weighted sum of distances to all preceding vehicles within a defined horizon, normalized by a scalar capacity parameter. The model assumes fully autonomous drones with awareness of other vehicles' locations. The authors transform the nonlinear equations into linear forms to derive analytical solutions. Specifically, the model is analytically solvable in a "blocking regime" (analogous to single-lane flow) and piece-wise analytically solvable in a "passing regime" (analogous to multi-lane flow), depending on the set capacity parameter. The study includes stability analysis, demonstrating linear local and asymptotic stability, alongside numerical simulations providing evidence for nonlinear stability. Key findings indicate that the SCM successfully captures both passing and blocking behaviors without requiring explicit lane-changing logic. By removing the artificial restriction that vehicles can only pass via adjacent lanes, the model allows for more realistic and efficient traffic flow in 3D space. The analytical solvability of the model facilitates rigorous stability analysis, a standard requirement in traffic engineering often missing in prior UAV-specific models. The results suggest that the SCM serves as a stable speed assignment scheme, preventing collisions by adjusting velocities based on local density. The significance of this work lies in providing a foundational tool for Unmanned Aircraft System Traffic Management (UTM) and the Internet of Drones (IoD). Unlike macroscopic models or complex mixed-integer programming approaches, the SCM offers a computationally efficient, microscopic view that can analyze congestion formation and inform airway capacity adjustments. The model’s ability to handle 3D trajectories without lane constraints makes it a superior alternative to ground-vehicle-derived models for UAV traffic control, supporting the development of scalable air traffic architectures for autonomous drone operations.

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• traffic density