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.

运输网络公司（TNC）提供的新兴按需骑行采购计划正在重塑运输行业。该领域的研究工作涵盖了供需均衡，定价，匹配，调度等主题，但尚未完全传播到拼车对多式联运系统中公共交通的潜在影响。一方面，乘车采购服务可作为便捷的接驳车，为公共交通乘车者解决首英里/最后一英里的问题。另一方面，从原点到目的地的直接乘车服务也可能从公共交通中吸收乘客。在本文中，我们提出了一个基于用户平衡的数学模型，以分析乘车来源对公共交通的补充和替代。通过分析和数值讨论，我们发现，乘车出行车辆的车队规模会严重影响乘车出行与公共交通之间的互补和替代关系，而乘车出行服务的票价会影响头一英里/后一英里（即始发地）之间的市场份额到运输枢纽或从枢纽到目的地）和直接（即从始发地到目的地）的骑行采购服务。我们还研究了使TNC的利润和/或社会福利最大化的最佳策略，并发现TNC可以实施帕累托高效策略，使这两个目标都变得更好。从始发地到交通枢纽或从枢纽到目的地）和直接（即从始发地到目的地）的骑行采购服务。我们还研究了使TNC的利润和/或社会福利最大化的最佳策略，并发现TNC可以实施帕累托高效策略，使这两个目标都变得更好。从始发地到交通枢纽或从枢纽到目的地）和直接（即从始发地到目的地）的骑行采购服务。我们还研究了使TNC的利润和/或社会福利最大化的最佳策略，并发现TNC可以实施帕累托高效策略，使这两个目标都变得更好。