Performance Evaluation 64 (2007) 838–855 www.elsevier.com/locate/peva Random graphs as models of hierarchical peer-to-peer networks ✩ R. Gaeta, M. Sereno ∗ Dipartimento di Informatica, Universit` a di Torino, Torino, Italy Available online 29 June 2007 Abstract This paper proposes the development and application of random graphs-based performance evaluation techniques to understand design trade-offs for hierarchical unstructured peer-to-peer networks. In particular, the connections between lower and higher level peers (that are known as leaves and ultra-peers in the Gnutella jargon) are modeled as a bipartite random graph while the overlay network used by ultra-peers to forward queries is modeled as a generalized random graph. Both the random graph models consider peers of either level as partitioned into classes; this feature is included in the model description to consider the mismatch between the logical topology of the application and the physical deployment of peers throughout the Internet. To assign realistic values to the input model parameters and to validate the model predictions we obtained snapshots of the Gnutella application topology at both levels and conducted simulation experiments on these snapshots. The paper highlights a few exploitations of the modeling technique with a particular focus on the evaluation of the impact of locality awareness on user and network performance measures. c  2007 Elsevier B.V. All rights reserved. Keywords: Hierarchical peer-to-peer networks; Bipartite random graphs; Generalized random graphs; Topology mismatch 1. Introduction Peer-to-peer (P2P) paradigm has recently emerged as a new model for distributed networked services and applications. P2P applications have been deployed in many different areas, such as distributed grid computing, storage, web cache, Internet telephony, streaming, conferencing, content distribution, and so on. But file sharing applications are perhaps the most popular P2P applications: many different file sharing systems, such as Gnutella, Kazaa, Edonkey, Emule, BitTorrent, exist and collect millions of users. These kinds of applications are characterizing a great fraction of the Internet traffic nowadays and several statistics on IP traffic have recently provided evidence that P2P traffic is starting to dominate the bandwidth in certain segments of the Internet [1]. In a P2P-based application participants are termed as peers and play the dual role of both provider and requester of a service. Services are the location and transfer of (part of) a resource that can be owned by several peers thus defining the resource popularity. Peers organize in an overlay (logical) network on top of the physical network. Each peer ✩ This work has been partially supported by the Italian Ministry for University and Research (MIUR) within the frameworks of the FAMOUS (PRIN) and of the PROFILES (PRIN) projects. ∗ Corresponding author. Tel.: +39 011 6706718; fax: +39 011 751603. E-mail address: matteo.sereno@di.unito.it (M. Sereno). 0166-5316/$ - see front matter c  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.peva.2007.06.020