Does e-hailing perform better than on-street searching? An investigation based on the temporal-spatial distributions of idle vehicles

This paper investigates whether e-hailing performs better than on-street searching for taxi services. By adopting the Poission point process to model the temporal-spatial distributions of idle vehicles, passengers’ waiting time distributions of on-street searching and e-hailing are explicitly modeled, and closed-form results of their expected waiting time are given. It is proved that whether e-hailing performs better than on-street searching mainly depends on the density of idle vehicles within the matching area and the matching period. It is proved that given the advantage of e-hailing in rapidly pairing passengers and idle vehicles, the expected waiting time for on-street searching is always longer than that of e-hailing as long as the number of idle vehicles within a passenger’s dominant temporal-spatial area is lower than 4/π. Moreover, we extend our analysis to explore the market equilibria for both e-hailing and on-street searching, and present the equilibrium conditions for a taxi market operating under e-hailing versus on-street searching. With a special reciprocal passenger demand function, it is shown that the performance difference between e-hailing and on-street searching is mainly determined by the ratio of fleet size to maximum potential passenger demand. It suggests that e-hailing can achieve a higher capacity utilization rate of vehicles than on-street searching when vehicle density is relatively low. Furthermore, it is shown that an extended average trip duration improves the chance that e-hailing performs better than on-street searching. The optimal vehicle fleet sizes to maximize the total social welfare/profit are then analyzed, and the corresponding maximization problems are formulated.