Recently, there has been a rapid rise of on-demand ride-hailing platforms, such as Uber and Didi, which allow passengers with smartphones to submit trip requests and match them to drivers based on their locations and drivers' availability. This increased demand has raised questions about how such a new matching mechanism will affect the efficiency of the transportation system, in particular, whether it will help reduce passengers' average waiting time compared to traditional street-hailing systems. In this talk, we address this question by building a stylized model of a circular road and comparing the average waiting times of passengers under various matching mechanisms. After identifying key trade-offs between different mechanisms, we find that surprisingly, the on-demand matching mechanism could result in higher or lower efficiency than the traditional street-hailing mechanism, depending on the parameters of the system. To overcome the disadvantage of both systems, we further propose adding response caps to the on-demand hailing mechanism and develop a heuristic method to calculate a near-optimal cap. We also test our model using more complex road networks to show that our key observations still exist.