A General Matching Model for On-Demand Mobility Services

This paper presents a general matching model to delineate the matching process in on-demand mobility service markets under different matching mechanisms with different matching time intervals and matching radii. The matching model characterizes a stationary matching process for the on-demand mobility service market in which passengers can be matched with idle drivers in consecutive batches. With passenger demand, vehicle fleet size and matching strategies as inputs, the general matching model can well approximate drivers’ idle time, passengers’ matching time and the pick-up time. Properties of the general matching model are then analyzed, including the relationship between passengers’ matching time and drivers’ idle time, and their changes with respect to the scaling factor of passenger demand and vehicle fleet size. The general matching model can also unify several prevailing inductive and deductive matching models developed in the literature and spell out their specific application scope. In particular, when the matching radius is sufficiently small, the general matching model reduces to a Cobb-Douglas type matching model proposed by Yang and Yang (2011) for street-hailing taxi markets, in which the matching rate depends on the pool size of waiting passengers and idle vehicles. Under an instant matching mechanism with a large matching radius, the general matching model reduces to Castillo et al.’s model (Castillo et al. 2017) based on an instant matching mechanism, or a bottleneck type queuing model, in which passengers’ matching time is derived from a deterministic queue at the bottleneck with the arrival rate of idle vehicles as its capacity and waiting passengers as its customers. When both the matching time interval and matching radius are relatively large, the general matching model also reduces to the bottleneck type queuing model. A set of simulation studies verifies that the proposed general matching model well approximates the reality