In this paper we describe a novel scheme that efficiently distributes the resources provided by seeders in a P2P network for Video on Demand (VoD) services. In the proposed scheme, that we have called Prioritized-Windows Distribution (PWD), the amount of seeders' resources assigned to a peer depends on its current progress in the process of downloading a video which is divided into ordered fragments (windows). We demonstrate through a fluid model analysis and Markov chain numerical evaluations that PWD improves the P2P network performance in terms of the level of cooperation that is required from seeders to keep the system under abundance conditions. Additionally, we analyze the performance of the system as a function of two parameters that highly influence the Quality of Service (QoS) perceived by the users, namely, the initial playback delay and the time required to download the video. Our results show that PWD outperforms previous proposals. Keywords Video on demand (VoD) · Peer to peer (P2P) network · Resource allocation · Markovian model · Fluid model · Video quality of service (QoS)