Macroscopic Modeling for Urban Low-Altitude Airspace Using Projected-Speed: Theory and Estimation

Abstract

The growth of Low-Altitude Air Transport (LAAT) systems calls for effective macroscopic modeling and control tools to manage dense drone traffic. Although the Macroscopic Fundamental Diagram (MFD) provides a useful framework for large-scale ground traffic analysis, its conventional formulations do not directly account for the three-dimensional interactions and path deviations that characterize drone operations. To address this issue, we introduce the concept of projected speed, which maps drone motion onto the shortest origin–destination path while preserving time-invariant trip lengths. Under this setting, we establish, with suitable assumptions, the theoretical validity of both accumulation-based and trip-based models for LAAT systems. In particular, we show that the accumulation-based model is exact at steady state, and that its mismatch under congestion is mainly caused by its inability to correctly capture transient dynamics rather than by trip-length heterogeneity itself. We then evaluate these models through extensive numerical experiments in a decentralized conflict-avoidance environment. The results verify that the proposed macroscopic models formulated in the projected space can be successfully applied to LAAT traffic and reproduce behaviors similar to those observed in ground transportation under a range of operating conditions, including hysteresis. These findings clarify the theoretical basis of macroscopic LAAT models and support their use for real-time estimation and airspace operations.