When examining the file transfer performance in a peer-to-peer file sharing system, a fundamental problem is how to describe the service rate for a file transfer. In this paper, the problem is examined by analyzing the distribution of server-like nodes' upstream-bandwidth among their concurrent transfers. A sufficient condition for the service rate, what a receiver obtains for downloading a file, to asymptotically be uniform is presented. On the aggregate service rate for transferring a file in a system, a sufficient condition for it to asymptotically follow a Zipf distribution is presented. These asymptotic equalities are both in the mean square sense. These analyses and the sufficient conditions provide a mathematic base for modeling file transfer processes in peer-to-peer file sharing systems.
