On-Demand Ride-Matching in a Spatial Model with Abandonment and Cancellation

Ride-hailing platforms such as Uber, Lyft, and DiDi coordinate supply and demand by matching passengers and drivers. The platform has to promptly dispatch drivers when receiving requests, since otherwise passengers may lose patience and abandon the service by switching to alternative transportation methods. However, having less idle drivers results in a possible lengthy pick-up time, which is a waste of system capacity and may cause passengers to cancel the service after they are matched. Due to complex spatial and queueing dynamics, the analysis of the matching decision is challenging. In this paper, we propose a spatial model to approximate the pick-up time based on the number of waiting passengers and idle drivers. We analyze the dynamics of passengers and drivers in a queueing model where the platform can control the matching process by setting a threshold on the expected pick-up time. Applying fluid approximations, we obtain accurate performance evaluations and an elegant optimality condition, based on which we propose a policy that adapts to time-varying demand.