Urban low-altitude air transport management: Bridging dynamic traffic control and static network equilibrium

Urban air mobility is an innovative mode that lifts urban transport to the altitude dimension, giving rise to low-altitude air transport (LAAT) systems. Emerging LAAT systems involve large-scale point-to-point operations, which require new management schemes distinct from the centralized flight control used in conventional aviation. In this paper, we explore flow-based traffic modeling for LAAT systems, including the static model of network equilibrium, as well as dynamic models of demand management and air traffic control. The static model aggregates individual UAM trips into traffic flows on the LAAT network, aiming to optimize the network flow pattern in the planning phase. The dynamic models describe regional traffic dynamics based on demand queuing and airspace macroscopic fundamental diagrams (MFDs), aiming to regulate the dynamics to a desired equilibrium in the control phase. Static network planning yields a system-optimal (SO) equilibrium, which is consistent with the desired equilibrium concept in dynamic traffic control. Inspired by this, we establish the interaction between static network planning and dynamic traffic control by deriving the desired equilibrium from the SO network equilibrium. The derived equilibrium is ensured to exist as a stable equilibrium and can be adjusted in response to traffic demand and airspace capacity. We devise a control scheme to implement the planning-control interaction. The proposed scheme, by coupling dynamic traffic control and demand management, can adjust the desired equilibrium according to changes in demand patterns, thus guaranteeing the feasibility of the set-point control problem with respect to varying demand patterns. Numerical examples demonstrate the merits of the integrated dynamic traffic control and demand management scheme. Compared to a fixed equilibrium based on experience, a variable SO equilibrium given by the planning-control interaction can significantly improve network efficiency, especially when demand patterns admit abrupt changes and noise. To the best of our knowledge, this paper is one of the first to bridge dynamic traffic control and static network equilibrium.