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Peer-peer networking has recently emerged as a new paradigm for building distributed networked applications. We develop simple mathematical models to explore and illustrate fundamental performance issues of peer-peer file sharing systems. The modeling framework introduced and the corresponding solution methods are flexible enough to accommodate different characteristics of such systems. Through the specification of model parameters, we apply our framework to three different peer-peer architectures: centralized indexing, distributed indexing with flooded queries, and distributed indexing with hashing directed queries. Using our model, we investigate the effects of system scaling, freeloaders, file popularity and availability on system performance. In particular, we observe that a system with distributed indexing and flooded queries cannot exploit the full capacity of peer-peer systems. We further show that …