Peer-To-Peer (P2P) networks have using commonly used for tasks such as file sharing or file distribution, and for building distributed applications in large scale network. Their performance measures are generally based on simulation methods software such as NS-2, P2PSim, OpenNet, etc. Hence, the absence of a validation of the simulation model is a critical issue. In this paper, the authors propose a new analytical model derived from to evaluate the performance of HPM protocol (Hierarchical Peer-to-peer Model). Performance is done principally in terms of total download time of requested resources in the P2P network, and then they analyze the impact of various parameters associated with the heterogeneity of nodes.