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In wireless sensor networks (WSNs), one major challenge is how to prolong the network lifetime while maintaining a certain data collection rate for resource-limited static sensors. To achieve this goal, many mobility-assisted data collection (MADC) schemes have been proposed in the literature. However, there is a lack of systematic analysis on the behaviors of the MADC models in terms of both throughput capacity, which is defined as the maximal data collection rate, and lifetime, which will be associated with a specific data collection rate. In this paper, we address this issue in a large-scale WSN with mobile sinks from a theoretical perspective, which has not yet been studied. In particular, we first propose a general MADC model that includes many important parameters such as the number of mobile sinks, the velocity of a mobile sink, and the traveling path of a mobile node. We then develop a comprehensive theoretical approach to obtain the achievable throughput capacity and lifetime. By applying the proposed approach, we investigate the behaviors of WSNs with one or more mobile sinks. Our analysis not only shows how a WSN with mobile sinks can outperform a static WSN but also provides insights on how we can adjust the MADC parameters to improve the data collection rate and to maximize the lifetime. Finally, our analysis is validated through extensive simulations.