Peer-to-peer (P2P) systems have proved the most effective and popular file sharing applications in recent years. Previous studies mainly focused on equal service and differentiated service strategies when peers have no initial data before their downloads. For an upload-constrained P2P file sharing system, we model both the equal service process and the differentiated service process when the initial data distribution of peers satisfies some special conditions. Moreover, we show how to minimize the time required to distribute the file to any number of peers. The proposed fluid-based models can reveal the intrinsic relations among the initial data amount, the peer set size, and the minimum last finish time. The closed-form expressions derived from the extended models can closely approximate chunk-based models and systems, especially for relatively large files. As an application of the extended models, we show how to provide differentiated service efficiently to multiple peer sets. Since no limits are imposed on the upload bandwidth of peers or the size of each peer set, we believe that our analytic process and the results achieved can provide not only fundamental insights into bandwidth allocation and data scheduling but also a helpful reference for both improving system performance and building an effective incentive mechanism for P2P file sharing systems.