In this thesis, we study three models of passenger-taxi queueing systems. In this system, passengers arrive to a taxi station to take taxis, and taxis arrive to take passengers. The purposes of the thesis are to derive the performance measures of the systems, analyze the behavior of passengers, taxi drivers and the government, and optimize the social welfare, which are helpful for optimizing the allocation of taxi market resources. The first model we study is a double-sided system with instantaneous matching time. In this model, we assume that the waiting room for taxis is finite. We give the close forms of loss probabilities, expected waiting time. We derive the optimal buffer of taxis to maximize the social welfare. We then discuss the strategic behaviors of selfish and socially concerned passengers. Finally, we derive the strategies of the government. The second model we study is a double-ended system with instantaneous matching time. The double-ended system means the size of the waiting buffer for both passengers and taxis are limited. We investigate both centralized and decentralized cases. After obtaining the performance measures of this system, then we numerically investigate the system and conduct some sensitive analyses. The third model is a double-sided systems with nonzero matching time. We adopt a two-dimensional Markov process to model the system. By using the matrix-analytic method, we give a sufficient condition that ensures the existence of steady-state probabilities and present an algorithm to calculate the joint steady-state probabilities. We further derive the tail distributions of the sojourn times of passengers and taxi drivers. By running Matlab programs, we give the numerical results about the performance measures of the system. We find some very interesting managerial insights and derive some optimal strategies for government to utilize the facility. By studying these three passenger-taxi models and provide better service to passengers and taxi drivers.