Optimal Scale Evaluation and Scheduling in Urban Air Mobility System

This paper focuses on urban air mobility systems and proposes an optimization method to simultaneously determine the minimum system scale required to meet passenger demand and the optimal system rebalancing strategy. A combined framework consisting of fluid model and multi-server M/M/s queueing model is developed to capture the migration of passengers, aircraft, and batteries among stations, as well as battery swapping and charging processes. Within this framework, the well-posedness of the numbers of aircraft and batteries is proven, and the necessary conditions for supply-demand equilibrium are derived. On this basis, linear programming is employed to compute the rebalancing allocation rates and the minimum fleet size under supply-demand equilibrium, and to determine the optimal locations of charging stations, the number of batteries, and the number of battery transport vehicles. Numerical simulations analyze the factors affecting system scale, and a case study verifies the effectiveness of the proposed rebalancing method.