Approximation Models for Shared Mobility Rebalancing Under Structured Spatial Imbalance

Abstract

Shared mobility systems (e.g., shared cars and ride-hailing services) generate persistent spatial imbalances as vehicles concentrate at popular destinations, leaving trip origins depleted of supply. Operators incur substantial costs in repositioning empty vehicles, and quantifying the theoretical minimum rebalancing distance is practically important. Exact computation requires solving a transportation linear program that is challenging at the city scale. Closed-form approximation models are derived for the minimum rebalancing distance in rectangular service regions. Parallel derivations are presented for the Manhattan metric (grid road networks) and the Euclidean metric (unconstrained movement). A scalar spatial imbalance index condenses the full demand pattern into a single interpretable quantity. Both models share a unified structure: the per-vehicle rebalancing distance scales with the square root of service area, the imbalance index, and a shape factor that depends solely on the aspect ratio. Calibration and validation against 500 exact LP solutions per metric confirm the area-scaling exponent to within 2\% of the theoretical prediction, across three demand distribution families. An empirical case study using January 2026 New York City for-hire vehicle trip data across 263 traffic analysis zones confirms that the formula generalizes to real-world, network-constrained demand. The results equip operators and system designers with solver-free, theoretically grounded tools for benchmarking rebalancing performance and optimizing service, rebalancing frequency, and demand-management interventions.