Equilibrium analyses and operational designs of a coupled market with substitutive and complementary ride-sourcing services to public transits

The emerging on-demand ride-sourcing programs provided by transportation network companies (TNCs) have been reshaping the transportation industry. Research efforts in this area have covered topics such as supply-demand equilibrium, pricing, matching, dispatching, but have not fully spread to the potential impacts of ride-sourcing on public transit in multi-modal transportation systems. On the one hand, ride-sourcing services act as convenient feeders to solve first-mile/last-mile problems for public transit riders. On the other hand, direct origin-to-destination ride-sourcing services may also absorb passengers from public transit. In this paper, we propose a user equilibrium based mathematical model to analyze complement and substitution of ride-sourcing to public transit. Through both analytical and numerical discussions, we find that the fleet size of ride-sourcing vehicles can critically affect the complementary and substitutive relationship between ride-sourcing and public transit, and ride-sourcing service fares affect the market share between first-mile/last-mile (i.e., from origin to the transportation hub or from the hub to destination) and direct (i.e., from origin to destination) ride-sourcing services. We also examine the optimal strategies to maximize the TNC's profit and/or social welfare and find that the TNC can implement a Pareto-efficient strategy that makes both the two objectives better off.