Urban taxi offers great flexibility and mobility via its door-to-door service and 7/24 availability, and plays an important role in urban transportation system. By the end of 2014, there were over 50,000 taxi drivers serving 600,000 passengers daily in New York City (NYCTLC, 2014). Moreover, in other large cities such as Tokyo and Paris, there is one taxicab per hundred population (Consultant, 2014). In light of the size and significance of urban taxi industry, framing regulation policies is of key concern for stakeholders in order to correct market imperfection (Schaller, 2007) and maintain level of service. To help frame regulations, economists have developed aggregate demand and supply models to examine the effectiveness and consequences of policies mainly associated with entry and fare controls (Douglas, 1972; De Vany, 1975; Beesley and Glaister, 1983; Häckner and Nyberg, 1995; Cairns and Liston-Heyes, 1996; Shreiber, 1981; Dempsey, 1996; Çetin and Yasin Eryigit, 2011). Nevertheless, as suggested by Yang and Wong (1998), since taxi service takes place over space, aggregate models are oversimplified, and are incapable of capturing the influence of road network structure and the equilibrium nature of taxi service. This motivates to model taxi service at the network level.  The first work which models urban taxi service at the network level was exemplified by Yang and Wong in 1998 (Yang and Wong, 1998), where a network model was developed to characterize the movement of vacant and occupied taxis on the network. It was assumed that passengers will always receive the service and any driver will eventually find a passenger, and taxi waiting time and utilization rate were analyzed with the change of taxi fleet size. Based on the network model, Wong and Yang developed an efficient algorithm to solve the taxi network movement problem as an optimization problem Wong and Yang (1998), Wong et al. (2001) improved the model by incorporating network congestion and demand elasticity, Wong et al. further proposed a sensitivity-based solution algorithm to solve their congestion model more efficiently (Wong et al., 2002), and the basic taxi network model was implemented to study how different regulations may affect the demandsupply equilibrium (Yang et al., 2002). While drivers’ behavior is the main focus of the aforementioned studies, Yang et al. (2010) proposed to model the behavior of drivers and passengers jointly, where the Cobb-Douglas function (Varian, 1992) was implemented to characterize trip waiting time as a function of the choices made by passengers and drivers. While the taxi service model (Yang and Wong, 1998) serves as the base for all these studies, they are observed to share two fundamental assumptions: (1) the taxi service is well-regulated and the market is monopolistic, and (2) all passengers will be serviced and all drivers will eventually find a trip during the modeling period. However, as Uber launched their transportation service in 2009, it breaks the convention of traditional taxi service (TTS), where street hailing is the main way of getting a taxi ride. Instead, it offers app-based third-party taxi service (ATTS), which allows passengers to request taxi service using smartphones. In a few years, we have witnessed the revolution of taxi industry globally with the entrance of other ATTS providers such as Lyft and Didi, and the market property has been complicated as it transforms from oligopoly to shared economy. Consequently, to understand the nature of the new market, there is an emerging need of a network model which accounts for the coexistence of TTS and ATTS. And modeling the market with TTS and ATTS is the objective of the study