Looking at BitTorrents with Fluids
I read “Modeling and Performance Analysis of BitTorrent-Like Peer-to-Peer Networks” by Dongyu Qiu and R. Srikant (2004). The paper discussed analysing the performance of the BitTorrent protocol using flow mechanics.
For those who don’t know, BitTorrent is a popular file distribution protocol used to distribute content between computers such as caches, backups, updates. Microsoft and many game companies have begun using BitTorrent or similar protocols to relieve load on their servers. Now, your Windows computer will silently send data to other Windows computers when it has newer updates that they do not. Games (such a League of Legends) will spend out new updates to computers on the internet while playing the game.
As someone interested in computer infrastructure and networking, I find these protocols very interesting. They represent a new standard of distributed protocols promising near infinite scalability and fault tolerance. Their relation to networks is obvious.
What’s interesting about this paper is that it did not model a foreign problem as a network (as is incredibly common and useful) but instead modeled a complicated network problem as a fluid problem.
In this paper the researcher considered a variety of parameters describing BitTorrent networks, such as the number of downloaders, unloaders, their bandwidth, and the rate of entering and leaving nodes. Using reductions to fluid models, the researchers were able to solve for several interesting steady states to possible relationships between parameters. The first, and most interesting result was that the average download time was independent of the number of incoming nodes, meaning that (assuming quality nodes) the BitTorrent protocol has the potential for infinite scalability.
Other results include that increasing the effectiveness of the system (which prioritizes files that have not yet been copied to many nodes) has the trade off of decreasing the speed of the system. Additionally, in some cases a slow download speed could still result in a very high download speed because of the ability of the network to produce many seeders (nodes with all of the files download, especially the case in game updates).
Interestingly enough the paper also considered Nash Equilibrium points and the incentivization of independent nodes of the system. The BitTorrent network has a simple procedure built in to reward fast uploading nodes with many download connections. While this works well in the large scale, there actually instances where no Nash Equilibrium exists.