A General Matching Function for Ride-Sourcing Services

Abstract

This paper presents a general matching function to delineate the on-demand matching process in ride-sourcing markets under different matching mechanisms with different matching time intervals and matching radius. The matching function characterizes a stationary matching equilibrium for the ride-sourcing market in which passengers can be matched in consecutive batches, and drivers are in either an idle, pick-up, or delivery state. The function well approximates the expected driver idle time and the expected passenger matching time and pick-up time under different supply-demand conditions and platform matching strategies. The general function also unifies several prevailing inductive and deductive matching functions developed in the literature and demonstrates their specific application scope. In particular, when the matching radius is sufficiently small, the function reduces to the Cobb-Douglas-type matching function 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 drivers. Under an instant matching mechanism with a large matching radius, the function reduces to the model of Castillo et al. (Castillo et al. 2017) or a variant of the Cobb-Douglas-type matching function, in which the matching rate depends on the pool size of waiting passengers and drivers in the pick-up phase. In addition, when both the matching time interval and matching radius are relatively large, the function reduces to a variant of the Cobb-Douglas-type matching function.