© 2018 Instituto Politecnico Nacional. All rights reserved. In Peer-to-Peer (P2P) networks it is not uncommon to find users that have initiated a file transfer and decide to leave the system before the end of the download. This is a particularly harmful behavior due to the resources (bandwidth or energy) wasted in such an aborted process. This negative effect is amplified when the system's conditions are such that the peers are not downloading at the maximum capacity. This is because in these conditions, there are not enough peers uploading the file, and a part of the bandwidth is wasted on peers that do not share their resources to the network once they leave the system. In this paper, the case of managed P2P networks is of special interest. As such, the variability in the transfer rates, such as the download and upload rates, is expected to be much less than in the case of the unmanaged P2P network. The limit case, where these transfer rates are constant is considered as an alternative to the exponential distribution. Additionally, two priority schemes are presented for a BitTorrent-based P2P network where the peers that are more likely to remain longer in the system are served first.