Modeling network equilibrium in integrated land-air mobility system with driver anxiety

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Abstract

Urban air mobility (UAM) is emerging as a promising solution to urban traffic congestion, yet its effective deployment hinges on seamless integration with ground transportation systems. With the increasing adoption of battery-powered electric vertical take-off and landing (eVTOL) vehicles in UAM systems, travel choices are no longer governed solely by conventional objective factors such as travel time, but are increasingly shaped by perception-driven range-related constraints. However, these constraints are rarely considered in existing UAM network equilibrium studies. To address these challenges, this paper develops an integrated land-air mobility network equilibrium model that incorporates travelers’ range anxiety and battery anxiety (ILAM-NE-RBA). These behavioral factors capture travelers’ subjective perceptions of path-level energy consumption and flight-stage risks, respectively, and are characterized by continuously distributed perceived weight limits of path weight and flight-stage weight. We further prove that the proposed ILAM-NE-RBA formulation constitutes a convex programming problem and that its Karush-Kuhn-Tucker (KKT) conditions characterize an anxiety-constrained generalized user equilibrium. To solve the model effectively, we develop a sub-demand decomposition-based improved gradient projection algorithm with three-dimensional Pareto (SD-IGP-TDP) guidance, which transforms conventional shortest-path search into a three-dimensional Pareto-optimal path search considering travel time, path weight, and flight-stage weight, thereby ensuring sufficient coverage of paths under dual-anxiety constraints. Meanwhile, sub-demand decomposition is introduced to address the inconsistency of feasible path sets across different anxiety intervals, enabling interval-based flow updates under heterogeneous perception constraints. Numerical results demonstrate that incorporating dual-anxiety mechanisms yields equilibrium flow patterns that differ significantly from those of conventional models; perception-driven constraints discourage travelers from selecting energy-intensive or high-risk paths, thereby inducing flow redistribution across the network. This study provides a unified behavioral perspective on the coupling between traveler route choice and network performance, and offers theoretical insights for the planning and operation of future integrated land-air mobility systems.

Graphical abstract

Keywords

urban air mobility / integrated land-air mobility / network equilibrium / range anxiety, battery

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