A Physical Model of Street Ride-Hail

Abstract

In this study, we show that the passenger-driver matching process in street ride-hail is dictated by the physical limitation of a passenger's average eyesight and the preference of cruising taxi drivers for certain locations. Together, these two spatiotemporal features, called effective hail distance (EHD) and local area attractiveness (LAA) respectively, define the number of vacant taxis that a passenger can reach, and accordingly the distribution of her waiting time. To calibrate the waiting time distribution, we extract maximum possible waiting times from taxis GPS trajectory data, by tracking the movements of vacant taxis cruising around a pickup location. Then we prove that, for a given EHD, the extracted maximum possible waiting time follows the same distribution as passenger waiting time. The proposed matching mechanism, along with the novel calibration method, leads to a general model of street ride-hail that can produce reliable estimates of passenger waiting time under a wide variety of market conditions. Moreover, the matching process in the phone-based ride-hail is shown to be a special case of the proposed model, when EHD approaches infinity. This result lays the foundation for understanding and comparing the performance of ride-hail services. It can also help address regulatory and operational questions facing key stake holders in this industry.