In order to develop a suitable model, consider a P2P file sharing
system in which overlay management is implemented in a decentralised
fashion, e.g. using a distributed hash table and gossipping,
as in modern BitTorrent peers. The traffic related to overlay management
is very small compared to the amount of downloaded
data, usually in the order of a percent, and therefore we ignore it.
Let us consider that in the P2P system the average downlink and
uplink capacity of the (average) peer is CD and CU, respectively.
With a file size of B it takes on average at least B/CD time for a peer
to download the file. If CD > CU, as is usually the case, then on
average downloading the file takes less time than uploading it.
Assume now that an average peer leaves the P2P system upon
downloading. Then during the B/CD time that it spent in the P2P
system it only uploaded CUB/CD < B amount of data, which is
insufficient to maintain the file available for newly arriving peers.
Therefore, in order for the file to be available in the P2P file sharing
system in the long term, peers have to spend on average at least B/
CU time in the system. That is, an average peer would download and
upload the file during B/CD time and then would spend B/CU B/CD
more time uploading the file. The model can be interpreted in
another way too. In order for a peer to be able to download at rate
CD, there need to be CD/CU peers that upload data at rate CU each.
Note that the model is equivalent to the previous model if CD ¼ CU.
The model and the related reasoning are in accordance with the
most widely used fluid model of BitTorrent-like P2P systems (Qiu
and Srikant, 2004; Lehrieder et al., 2012).