Peer-to-Peer (P2P) systems have proved to be the most effective and popular
file sharing applications in recent years. Previous studies mainly focus on the
equal service and the differentiated service strategies when peers have no
initial data before their download. In an upload-constrained P2P file sharing
system, we model both the equal service process and the differentiated service
process when peers' initial data distribution satisfies some special
conditions, and also show how to minimize the time to get the file to any
number of peers. The proposed models can reveal the intrinsic relations among
the initial data amount, the size of peer set and the minimum last finish time.
By using the models, we can also provide arbitrary degree of differentiated
service to a certain number of peers. We believe that our analysis process and
achieved theoretical results could provide fundamental insights into studies on
bandwidth allocation and data scheduling, and can give helpful reference both
for improving system performance and building effective incentive mechanism in
P2P file sharing systems