  In this paper, we address the problem of content placement in peer-to-peer
systems, with the objective of maximizing the utilization of peers' uplink
bandwidth resources. We consider system performance under a many-user
asymptotic. We distinguish two scenarios, namely "Distributed Server Networks"
(DSN) for which requests are exogenous to the system, and "Pure P2P Networks"
(PP2PN) for which requests emanate from the peers themselves. For both
scenarios, we consider a loss network model of performance, and determine
asymptotically optimal content placement strategies in the case of a limited
content catalogue. We then turn to an alternative "large catalogue" scaling
where the catalogue size scales with the peer population. Under this scaling,
we establish that storage space per peer must necessarily grow unboundedly if
bandwidth utilization is to be maximized. Relating the system performance to
properties of a specific random graph model, we then identify a content
placement strategy and a request acceptance policy which jointly maximize
bandwidth utilization, provided storage space per peer grows unboundedly,
although arbitrarily slowly, with system size.
