The rapid expansion of ride-sourcing services such as Uber, Lyft, and Didi Chuxing has fundamentally reshaped urban transportation by offering flexible, on-demand mobility via mobile applications. Despite their convenience, these platforms confront significant operational challenges, particularly vehicle rebalancing - the strategic repositioning of thousands of vehicles to address spatiotemporal mismatches in supply and demand. Inadequate rebalancing results in prolonged rider waiting times, inefficient vehicle utilization, and inequitable distribution of services, leading to disparities in driver availability and income. To tackle these complexities, we introduce scalable continuous-state mean-field control (MFC) and reinforcement learning (MFRL) models that explicitly represent each vehicle's precise location and employ continuous repositioning actions guided by the distribution of other vehicles. To ensure equitable service distribution, an accessibility constraint is integrated within our optimal control formulation, balancing operational efficiency with equitable access to the service across geographic regions. Our approach acknowledges realistic conditions, including inherent stochasticity in transitions, the simultaneous occurrence of vehicle-rider matching, vehicles' rebalancing and cruising, and variability in rider behaviors. Crucially, we relax the traditional mean-field assumption of equal supply-demand volume, better reflecting practical scenarios. Extensive empirical evaluation using real-world data-driven simulation of Shenzhen demonstrates the real-time efficiency and robustness of our approach at the scale of tens of thousands of vehicles. The code is available at https://github.com/mjusup1501/mf-vehicle-rebalancing.

翻译：以Uber、Lyft和滴滴出行为代表的网约车服务通过移动应用程序提供灵活按需的出行方式，从根本上重塑了城市交通格局。尽管这类服务带来了便利，但其运营平台仍面临重大挑战，尤其是车辆再平衡问题——即通过策略性地重新调配数千辆车辆以应对供需的时空错配。不充分的再平衡会导致乘客候车时间延长、车辆利用效率低下以及服务分布不均，进而造成驾驶员可用性与收入水平的差异。为应对这些复杂问题，我们提出了可扩展的连续状态均值场控制（MFC）与强化学习（MFRL）模型，该模型能精确表征每辆车的实时位置，并依据车辆分布信息执行连续的重新调度决策。为确保服务分布的公平性，我们在最优控制框架中引入了可及性约束，以平衡运营效率与跨地理区域的服务公平获取。我们的方法充分考虑了现实条件，包括状态转移的固有随机性、车辆-乘客匹配与车辆再平衡/巡航的同步发生、以及乘客行为的可变性。尤为重要的是，我们放宽了传统均值场理论中供需总量相等的假设，从而更好地反映实际场景。基于深圳真实数据的实证模拟表明，我们的方法在数万辆车的规模上具有实时高效性与鲁棒性。相关代码已开源：https://github.com/mjusup1501/mf-vehicle-rebalancing。