Calibration and validation of matching functions for ride-sourcing markets

Ride-sourcing services have become increasingly important in meeting people's mobility needs since their emergence. Compared to traditional street-hailing taxi services, ride-sourcing services significantly reduce the matching frictions in the markets by matching drivers and passengers with relatively distant distances through an online platform. Motivated by this new feature as well as the need for designing operating and regulating strategies, researchers have attempted to describe these innovative ride-sourcing markets through mathematical models, the core of which is the matching functions for characterizing matching frictions. Previous studies have developed a variety of matching functions for ride-sourcing markets, including perfect matching function, Cobb-Douglas type matching function, queuing models, and some physical models. However, less is known about the applicability and performance of these matching functions, that is, under what situations each of these matching functions well characterizes the real market. To address this issue, this paper makes one of the first attempts to calibrate, validate, and compare the prevailing matching functions in the literature, and ascertain the conditions of their applicability. In particular, we establish a simulator to simulate a total of 420 scenarios of the ride-sourcing market under different combinations of supply and demand. The key performance metrics, including the matching rate in the market, passengers' average matching time, passengers' average pick-up time, and passengers' average total waiting time, are utilized to test and compare seven widely used matching functions under various market scenarios.