The Cult AGP

BitTorrent or BitTrickle !

Mike Godwin notes a serious error in the recent NYT future-of-TV article:

Created by Bram Cohen, a 29-year-old programmer in Bellevue, Wash., BitTorrent breaks files hundreds or thousands of times bigger than a song file into small pieces to speed its path to the Internet and then to your computer. On the kind of peer-to-peer site that gave the music industry night sweats, an episode of “Desperate Housewives” that some fan copied and posted on the Internet can take hours to download; on BitTorrent, it arrives in minutes.

That hasn’t been my experience of BitTorrent, and I doubt many other ordinary users routinely experience the downloading of TV programs in “minutes.” On the off chance that BitTorrent speeds had suddenly improved since I had last used the application, I conducted an experiment — I downloaded the latest episode of Showtime’s program “Huff,” which stars Hank Azaria, within 24 hours of its having aired. (Downloading a program shortly after it has aired, when interest in the episode is at its peak, is the way to maximize download speed on BitTorrent.) The result? Even with the premium broadband service I have at my office, downloading Episode 13 of “Huff” — the final episode of the season — took six hours, with download speeds rarely exceeding 30KB/sec.

The NYT article seems to make a common error in thinking about BitTorrent. BitTorrent’s main effect is not to make downloads faster as the number of users increases, but to keep downloads from getting much slower. A simple model can explain why this is so. (As with all good models, this one gets the important things right but ignores some details.)

Let’s assume that a file is being offered by a server, and the server’s net connection is fast enough to transmit the entire file in S seconds. We’ll assume that N users want to download the file simultaneously, and that each user has a net connection that would take U seconds to transmit the entire file . (Generally, the user is willing to pay less for Net service than the server, so S < U.)

In an old-fashioned (pre-BitTorrent) system, all N copies of the file must go through the server’s connection. That takes SN seconds. One copy goes through each user’s connection, which takes U seconds. The two steps, taking times SN and U, can happen simultaneously, so the time to do both is equal to the larger of SN and U.

T_old(N) = max(SN, U)

If the file is popular (i.e., N is large), the SN term will dominate and the download time will be proportional to N. For popular files, adding users makes downloads slower.

In BitTorrent, the file only needs to go through the server’s connection once, which takes N seconds. On average, each block of the file must traverse a typical user’s link twice, since each block must be downloaded once, and BitTorrent expects each user to upload as many blocks as it downloads. So with BitTorrent, the total time to serve the N users is max(S, 2U). Recalling that S < U, we can see that

T_bt(N) = 2U

Now we can see the big win offered by BitTorrent: the download time is independent of the number of users (N), and of the speed of the server’s connection (S). Adding more users doesn’t make the download faster, but it doesn’t make it slower either. (It’s also worth noting that if N, the number of users, is small, BitTorrent is worse than old-fashioned systems, by a factor of two.)

With BitTorrent, the bottleneck is the end user’s net connection, only half of which can be used for BitTorrent downloads. (The other half must be used for uploads.) Most users’ connections, even the broadband ones, will take an awfully long time to download high-quality video content, BitTorrent or not.

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