Control of dynamic ride-hailing networks with a mixed fleet of autonomous vehicles and for-hire human drivers

This study examines a ride-hailing platform that employs a mixed fleet of autonomous vehicles (AVs) and human drivers to offer on-demand ride-hailing services across a network over a finite planning horizon. In the mixed fleet, AVs have a fixed fleet size and are centrally managed by the platform, while human drivers can dynamically enter and exit from the ride-hailing market based on the prospective earning opportunities at various time periods. We introduce a game- theoretic model that encapsulates the strategic behavior of human drivers, passengers, and the ride-hailing platform. In this model, passengers choose between ride-hailing and alternative transportation options by considering fares and waiting times. Human drivers schedule their working hours in response to potential earnings and strategically relocate to maximize passenger pickups, while the platform adjusts pricing and AV repositioning strategies to maximize its profit. The solution is characterized as a Nash equilibrium within a two-player game, with one player representing the ride-hailing platform, and the other as a virtual representative of the collective human drivers. To address the non-convex nature of the game, we employ a convex relaxation technique to ascertain a near-optimal solution framed as an epsilon-Nash equilibrium, with epsilon accurately characterized. The proposed model and solution algorithm are validated in a case study for Manhattan, New York City. The simulation results underscore that the distribution of human drivers is closely aligned with the immediate, minute-to-minute fluctuations in passenger demand, enabling them to effectively meet the surge during peak demand windows. Conversely, the deployment patterns of AVs are more attuned to the extended, daily cycles of passenger movements throughout different city zones, from daytime to nighttime. We further compare the mixed fleet model with scenarios where the platform exclusively utilizes human drivers or AVs, respectively. The comparison show that the mixed fleet model excels in balancing the supply and demand over space and time, thereby leading to shorter wait times and reduced travel cost for ride-hailing passengers, as well as improved profit for the ride-hailing platform.