Real-time Approximate Routing for Smart Transit Systems

The advent of ride-hailing platforms such as Lyft and Uber has revolutionized urban mobility in the past decade. Given their increasingly important role in today's society, recent years have seen growing interest in integrating these services with mass transit options, in order to leverage the on-demand and flexible nature of the former, with the sustainability and cost-effectiveness of the latter. Our work explores a set of operational questions that are critical to the success of any such integrated marketplace: Given a set of trip requests, and the ability to utilize ride-hailing services, which mass-transit routes should the transit agency operate? How frequently should it operate each route? And how can ride-hailing trips be used to both help connect passengers to these routes, and also cover trips which are not efficiently served by mass transit?

We study these under a model in which a Mobility-on-Demand provider (the platform ) has control of a vehicle fleet comprising both single-occupancy and high-capacity vehicles (e.g., cars and buses, respectively). The platform is faced with a number of trip requests to fill during a short time window, and can service these trip requests via different trip options : it can dispatch a car to transport the passenger from source to destination; it can use a car for the first and last legs of the trip, and have the passenger travel by bus in between; or it can use more complicated trips comprising of multiple car and bus legs. Given a set of rewards for matching passengers to trip options, and costs for operating each line (i.e., a bus route and associated frequency), the goal of the platform is to determine the optimal set of lines to operate (given a fixed budget for opening lines), as well as the assignment of passengers to trip options utilizing these lines, in order to maximize the total reward. We refer to this as the Real-Time Line Planning Problem (RLpp).

We first demonstrate the computational limits of RLpp by showing that no constant-factor approximation is possible if we relax either one of two assumptions: (i) access to a pre-specified set of feasible lines, and (ii) no bus-to-bus transfers. These assumptions are practically motivated and common in the literature, but our work is the first to formally demonstrate their necessity.