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  1. Ride-sourcing services play an increasingly important role in meeting mobility needs in many metropolitan areas. Yet, aside from delivering passengers from their origins to destinations, ride-sourcing vehicles generate a significant number of vacant trips from the end of one customer delivery trip to the start of the next. These vacant trips create additional traffic demand and may worsen traffic conditions in urban networks. Capturing the congestion effect of these vacant trips poses a great challenge to the modeling practice of transportation planning agencies. With ride-sourcing services, vehicular trips are the outcome of the interactions between service providers and passengers, a missing ingredient in the current traffic assignment methodology. In this paper, we enhance the methodology by explicitly modeling those vacant trips, which include cruising for customers and deadheading for picking up them. Because of the similarity between taxi and ride-sourcing services, we first extend previous taxi network models to construct a base model, which assumes intranode matching between customers and idle ride-sourcing vehicles and thus, only considers cruising vacant trips. Considering spatial matching among multiple zones commonly practiced by ride-sourcing platforms, we further enhance the base model by encapsulating internode matching and considering both the cruising and deadheading vacant trips.more »A large set of empirical data from Didi Chuxing is applied to validate the proposed enhancement for internode matching. The extended model describes the equilibrium state that results from the interactions between background regular traffic and occupied, idle, and deadheading ride-sourcing vehicles. A solution algorithm is further proposed to solve the enhanced model effectively. Numerical examples are presented to demonstrate the model and solution algorithm. Although this study focuses on ride-sourcing services, the proposed modeling framework can be adapted to model other types of shared use mobility services.« less