On the Efficiency and Cost of Introducing QoS in BitTorrent.

Full text

Page 1

On the Efficiency and Cost of Introducing QoS in BitTorrent
Nazareno AndradeJaindson Santana
Walfredo Cirne
Francisco Brasileiro
Universidade Federal de Campina Grande
{nazareno,jaindson,fubica,walfredo}@ourgrid.org
Abstract
BitTorrent is currently a de facto standard for scalable
content-distribution. However, its peer-to-peer model for
resource allocation does not provide high availability and
its performance depends on best-effort contributions given
by peers. This has motivated several content-providers to
use a hybrid model in which they operate a superpeer in
order to attain a higher quality of service. In this paper,
we use BitTorrent traces and analytical modelling to inves-
tigate the cost incurred by such an entity in relation to the
benefits it can provide to the system.
1Introduction
BitTorrent is arguably the most popular scalable content
distribution mechanism presently. The efficiency of the pro-
tocol and some popular lightweight implementations of it
account for its success as a significant step in democratiz-
ing content publishing on the Internet. BitTorrent offloads
the content provider by leveraging the resources of content
consumers during download.
Nevertheless, although BitTorrent allows content to be
distributed cheaply, its typical use, which we call standard
BitTorrent, relies completely on content consumers to pro-
vide both availability and download performance. As the
contribution of peers varies, the quality of service may drop
below acceptable levels. Guo et al. [7] have found that an
average of 10% of all requests for a content object fail in a
popular content-sharing community.
Although this quality of service might be sufficient for
some settings, it is very low for the standards of traditional
content distribution. The need to provide a more reliable
service while taking advantage of the scalability and effi-
ciency of BitTorrent has motivated a growing use of an al-
ternative model which we dub a hybrid BitTorrent model.
In such model, a content provider tries to increase availabil-
ity and performance in its content distribution operating a
reliable component. We dub such component a superseeder
and its resemblance to a server in a peer-to-peer context ac-
counts for our nomenclature. The hybrid model is currently
used to distribute software updates [13], in user-generated
content-sharing communities [3, 2], is being experimented
by the TV and film industry [4, 1] and is sold as a product
by companies [6].
However, although appealing, the hybrid model is still
poorly understood. It is unclear how effective it is for a
content provider to introduce a superseeder with some ca-
pacity in the content distribution process. Furthermore, it is
also not clear what is the cost for this content provider to
use the hybrid model compared to providing an equivalent
quality of service through a centralized alternative. In this
study, we shed some light on these questions by modeling
and analyzing the efficiency and cost of the hybrid model.
Our methodology is to create an analytical fluid model of
the hybrid BitTorrent distribution and evaluate its behavior
on different scenarios which we obtain from traces of real
system usage. Our main contributions are the development
of a model which one can use to estimate the cost and effi-
ciency of operating a superseeder in a known setting and an
assessment of this cost and efficiency under real conditions
taken from a popular content-sharing community.
The rest of this paper is structured as follows. We first
review related work in Section 2 and explain briefly how
BitTorrent works in Section 3. We then present our model
for the hybrid BitTorrent in Section 4. In Section 5 we use
this model and data from a BitTorrent trace to analyze the
cost and impact of operating a superseeder in BitTorrent.
We discuss the implications of our analysis and make some
final remarks on Section 6.
2Related Work
A considerable amount of research has been conducted
recently on BitTorrent through analysis [11, 7], simula-
tion [12] and measurements [10, 8]. These studies collec-
tively assess the scalability and effectiveness of the standard
BitTorrent protocol.

Page 2

Qiu and Srikant defined a fluid model to study BitTor-
rent [11] in which they assumed a Poisson arrival model for
the arrival time of requests. Later, Powelse et al. [10] as
well as Guo et al. [7] identified, based on traces of BitTor-
rent usage, that this assumption is not realistic. Guo et al.
modeled the request arrival as an exponential function and
adapted Qiu and Srikant’s fluid model to reflect that.
Guo et al. also found shortcomings on the BitTorrent
distribution model: low content availability, high fluctua-
tion of client performance and unfairness of contributions.
The first two shortcomings are of interest to us. Guo et al.
have proposed an extension of the BitTorrent protocol to
tackle these limitations based on inter-torrent cooperation.
In this work, however, we focus on another method to tackle
this limitations which is currently in production: operating
a superseeder in a hybrid BitTorrent model.
Also related to our work, Stutzbach, Zappala and Re-
jaie have modelled a swarming system and analyzed its
effectiveness when compared to the plain client/server
model [12]. Their study uses a conservative model and
shows that swarming scales much better than a centralized
server. We are interested in evaluating how this scalability
is affected by introducing the superseeder.
3 BitTorrent
To download a file using BitTorrent, a user must join a
torrent, which is the network formed by all peers taking
part in the distribution of a content object at a given in-
stant. Peers which have an incomplete copy of the object
are called leechers, while peers which have finished down-
loading and are still in the torrent are called seeders.
To distribute a file using BitTorrent, a content producer
creates a .torrent metadata file which describes the division
of the original file in chunks and specifies a tracker which
must be used to join the torrent of the file. This .torrent file
is usually distributed through web servers and serves as an
entrance point for the torrent.
When a client downloads this file and contacts the
tracker, it receives a list of other peers it should connect to.
It then starts to exchange chunks of the file with them. Bit-
Torrent has a built-in incentive mechanism through which
leechers reward each other for serving file chunks with
higher rates. Seeders, however, only upload chunks, and
there are no incentives for seeding.
4Model
In this section we present the model for a hybrid BitTor-
rent system in which an entity operates a superseeder. Our
model is an extension of that devised by Guo et al. [7] upon
a previous one proposed by Qiu and Srikant [11].
We make one main simplifying assumption in this
model: that all peers in a torrent have identical upload band-
widths and identical download bandwidths.
Legout et al. [9] studied experimentally the service peers
with homogeneous and heterogeneous upload links get
from a torrent and found that the download speed each peer
gets is generally related to its upload speed. This suggests it
is reasonable to assume that heterogeneous peers would get
the average benefit predicted by our model with individual
peers obtaining download rates weighted by their contribu-
tion to the torrent.
We now present the model for a standard BitTorrent and
then we discuss the extension of this model to encompass
the hybrid BitTorrent.
4.1 Standard BitTorrent
Guo et al. [7] found that the peer arrival rate at a torrent
is given by an exponential decreasing function of the time.
Given an initial arrival rate of peers λ0and a popularity
attenuation parameter τ, the arrival rate λ(t) at time t is
given by λ(t) = λ0e−t
to find the total number of requests for the torrent Nall =
?∞
We consider that after joining a torrent, a peer has some
probability of giving up the download and leaving forever.
If it does not give up, it stays online until it finishes down-
loading, seeds for some time and leaves the torrent forever.
At any given time t there are x(t) leechers and y(t) seeders
in a torrent. Leechers give up downloading with rate θ and
seeders leave the system with rate γ. Each peer has an up-
load bandwidth µ and a download bandwidth c, with c ≥ µ.
For the sake of simplicity, the model considers a file of size
1, what implies that both µ and c must be normalized by the
file size when considering a real system.
τ. From this function it is possible
0λ0e−t
τdt = λ0τ.
A seeder is always able to upload to a leecher. A leecher
is able to upload to another leecher with some probability
which is defined as the file sharing efficiency η. Qiu and
Srikant have shown that for a file which is divided in P
parts, if peers maintain connections to k other peers, η ≈
1 − (log(P)
P
)k[11].
At each instant t, a number of peers finish download-
ing and become seeders. As the file size is 1, this number
is given by the amount of bandwidth provided by peers at
time t. We denote this amount Φ(t), which is the minimum
between all upload bandwidth made available by all peers
and the total download bandwidth of leechers, defined as
Φ(t) = min{µ(ηx(t) + y(t)),cx(t)}.
We can express the rate of change in x(t) and y(t) using
λ(t), θ, γ and Φ(t) through the following set of ordinary
differential equations:
2

Page 3




dx(t)
dt
dy(t)
dt
x(0) = 0,y(0) = 1.
= λ0e−t
= Φ(t) − γy(t),
τ − θx(t) − Φ(t),
(1)
This setof equations isslightlydifferent fromthatpresented
by Guo et al. because we assume c ≥ µ, instead of c ? µ.
To assess the capacity of the model of predicting reality,
we get the parameters for the model through linear regres-
sion from the Umass BitTorrent trace [5] similarly to [7]
and compare the torrent population and lifespan got in the
traces with those predicted by the model. Figure 1 shows
thiscomparisonforthetorrentswhichstartandfinishwithin
the trace time frame. Further analysis of the accuracy of the
model has been performed by Guo et al. [7].
1
10
100
1000
10000
1 10 100 1000
total population of torrent
torrents
model
trace
(a) Total torrent population (log-log scale).
1
10
100
1000
10000
0 100 200 300 400 500 600 700
torrent lifespan (hour)
torrents
model
trace
(b) Torrent lifespan (vertical axis in log-scale)
Figure 1. Comparison of model prediction
and trace for the population and lifespan of
torrents.
4.2Hybrid Model
We now consider that an entity is able to provide an
amount of bandwidth ζ(t) at time t to the leechers in a tor-
rent. This can be done through one or more superseeders
which act as seeders and are always available. For the sake
of simplicity, in the remainder of the paper we refer to a sin-
gle superpeer, which is analogous to a group of superpeers
with the same total capacity. The superseeder acts a seeders
and is always online. The bandwidth provided by this peer
is used as a complement to that already available.
As we consider a file of size 1, the amount of leechers
which turn into seeders at time t is Φ(t)+ζ(t) and the set of
ordinary differential equations which describes the hybrid
model is:



dx(t)
dt
dy(t)
dt
x(0) = 0,y(0) = 0.
= λ0e−t
= Φ(t) − γy(t) + ζ(t),
τ − θx(t) − Φ(t) − ζ(t),
(2)
Note that y(t) is the amount of seeders besides the super-
seeder at time t. We assume the superseeder has the content
being distributed in the start of the torrent and there is no
other seeder at this time, so y(0) = 0.
We consider that the superseeder is able to provide a
maximum total bandwidth b at a given instant. As ζ(t) is
provided by the superseeder only if there is spare download
bandwidth among leechers, it is defined as:
ζ(t) = min{b,cx(t) − Φ(t)}
(3)
The total data transfer performed by the superseeder is
D =
?∞
peers at time t in the hybrid model is u(t) =Φ(t)+ζ(t)
The download time δ(t) for a peer which joins the torrent
at time t and does not relinquish downloading is δ = t?− t
such that?t?
load time of all peers which can be found through the fol-
lowing integration:
0ζ(t)dt and the average downloading speed of
x(t)
.
tu(t)dt = 1. We note δ for the average down-
δ =
?∞
0[λ(t) − θx(t)]δ(t)dt
?∞
0[λ(t) − θx(t)]dt
.
(4)
5Analysis
We now turn to evaluate the cost and efficiency of op-
erating a superseeder to increase the quality of service in a
torrent. As our set of equations has eight independent vari-
ables, it does not yield an elegant solution and we opted to
analyze its results at points numerically instead of symboli-
cally.
In the rest of this section, we first explain the metrics
and the values for the parameters we use to then evaluate
the model under different scenarios.
5.1Metrics
We use the average download time δ in a torrent as our
metric to evaluate the efficiency of the hybrid model.
3

Page 4

As a measurement of cost, we compare cost of the distri-
bution of a content object using a superseeder with that of
using a centralized server to provide the same average qual-
ity of service for a population with the same dynamics as
that in the torrent. In this case, we compare the maximum
bandwidth Bcneeded by a centralized server with the max-
imum bandwidth B used of the superseeder and the total
data transfer Dcdone by the centralized server with the to-
tal data transfer D performed by the superseeder. Note that
the maximum bandwidth used of the superseeder might be
lower than the total bandwidth it has available b.
We obtain B and D numerically from our model and Bc
and Dcanalytically as follows. Considering requests arrive
with rate λ(t) = λ0e−t/τand the centralized server is able
to provide a download speed q ≤ c for each requester, we
model the variation in the number of downloaders w(t) at
time t as:
?
dw(t)
dt
w(0) = 0.
= λ0e−t
τ − θw(t) − qw(t),
(5)
From which we find that w(t) =λ0τ(e−t
The function w(t) assumes its maximum when t = t?=
τ · log((θ + q)τ)/((θ + q)τ − 1). Thus, the maximum
instantaneous bandwidth needed by a server to provide a
download speed q for each of its users under this circum-
stances is Bc= qw(t?).
The total data transfer from the centralized server, on the
other hand is
τ −e−(θ+q)t)
τ(θ+q)−1
.
Dc= q
?∞
0
w(t)dt = λ0τ(
q
θ + q).
(6)
Both Bcand Dcare normalized by the file size in these
expressions.
Note that the performance of the standard BitTorrent
with 100% availability is equivalent to the hybrid model
with b = µ and the cost of the standard model is always
zero to the content provider.
5.2Parameters
To analyze a scenario with the hybrid model, we need to
instantiate eight variables. Naturally, a parameter sweep of
all factors is not sensible. There are ranges of values for the
variables which are unrealistic and there might be relation-
ships among the variables which make certain combinations
of them unlikely to be seen in practice.
We therefore use the trace of a real system to obtain rep-
resentative combinations of the parameters which happen
in standard BitTorrent to use in our analysis. We use the
Umass trace [5], which consists of over 500 fully traced
torrents over four months.
We get λ0and τ for each torrent through linear regres-
sion similarly to the process described in [7]. The parame-
ters γ and θ are given by the reciprocal of the average seeder
service and time between quits of downloaders for each tor-
rent, respectively. The file sizes are obtained directly from
the description of torrents in the trace.
A limitation of the trace we used is that it only reports
the download and upload rates of a peer accumulated over
all torrents it is taking part in. It is not possible to derive
the amount of bandwidth a peer devotes to each of these
torrents. We opted to capture the ratio between download
and upload rate and estimate values for one of them. For
that, we computed the average ratio between download and
upload bandwidth for peers in the trace1and found it to be
2.7. We then assumed an upload bandwidth of 10 KB/s for
all peers, from which we got a download bandwidth of 27
KB/s.
We used hierarchical clustering to group our observa-
tions of λ0, τ, γ, θ and f accordingly to their similarity,
from which we got 7 significant clusters. For each cluster,
we select as a representative observation the torrent which
has the smallest Euclidean distance to the point represented
by the mean values of all observations in the cluster. We de-
scribe the clusters in terms of the 95% confidence intervals
for the means of their parameters and of the representative
values chosen for these parameters in Table 1. For presenta-
tion purposes, we also name each cluster accordingly to its
most distinguishing characteristic.
The file sharing efficiency η is obtained from the file size
as defined in Section 4. In BitTorrent, a file is typically
divided in 256 KB pieces, and we consider peers maintain
connection only to one other peer as a pessimistic boundary
for our analysis.
Finally, we instantiate different values of b to investigate
the effect of varying it in our metrics.
5.3Evaluation
We look at the effect of varying the quality of service
provided by the superseeder in our metrics for all torrents
which we defined as representative in Table 1. We vary the
bandwidth available to the superseeder so that b · f varies
between 10 KB/s – that available to the other peers – and
600 KB/s.
Figure 2 shows the ratio of δ over the optimal download
time of peers (1/c) when b·f varies. Each line on the graph
shows the behavior of a torrent, and is named accordingly
to the cluster this torrent represents.
We can see that for most torrents δ decreases exponen-
tially as b grows.This is because increasing b implies
1Among which we filtered only peers which were both uploading and
downloading at least 3 KB/s, so as to avoid including peers whose down-
load or upload rate were strongly limited by the state of the torrent they
were participating into.
4

Page 5

Table 1. Clusters of Torrents. For each variable, the representative value chosen and the 95% confi-
dence interval for its mean.
clustertorrents
λ0· 102(s−1)
0.07 / [0.07;0.08]
0.12 / [0.13;0.17]
0.04 / [0.07;0.34]
1.27 / [1.29;1.54]
0.11 / [0.11;0.16]
0.02 / [0.01;0.04]
0.29 / [0.07;0.29]
τ (days)
γ · 105(s−1)θ · 105(s−1)
f (MB)
1-AverageCase
2-AverageCase+Smaller-f
3-Small-f+High-θ,γ
4-Large-λ0+Small-τ
5-Small-f+High-θ+Small-τ
6-Largest-f
7-Small-f+High-γ+Small-τ
344
261
11
6
34
3
2
4.71 / [3.72;5.23]
2.12 / [2.94;3.97]
0.83 / [0.33;0.86]
0.94 / [0.7;1.37]
1.59 / [0.77;1.52]
10.62 / [2.28;10.62]
0.22 / [0.09;0.22]
2.16 / [1.84;2.04]
2.29 / [2.6;2.9]
6.29 / [5.99;6.95]
1.74 / [1.7;3.27]
3.51 / [3.02;3.74]
0.62 / [0.62;1.34]
9.17 / [9.17;15.87]
1.6 / [1.51;1.72]
3.01 / [3.61;4.32]
19.04 / [17.11;22.23]
3.43 / [1.95;6.35]
18.21 / [17.42;20.46]
0.51 / [0.51;0.7]
2.16 / [0.72;2.16]
698.0 / [746.27;796.95]
212.18 / [173.1;211.66]
34.69 / [11.41;35.94]
636.13 / [104.13;650.96]
52.91 / [33.6;85.48]
4096.0 / [3072.0;4096.0]
49.88 / [5.46;49.88]
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0 50 100 150 200 250 300 350 400 450 500
Average / optimal download time
Reliable peer’s bandwidth (KB/s)
cluster 1
cluster 2
cluster 3
cluster 4
cluster 5
cluster 6
cluster 7
Figure 2. Performance evaluation of the hy-
brid model varying b.
in seeders being created earlier, which changes the rate at
which the coming leechers are turned into seeders.
On the other hand, when the initial rate of arrival of peers
λ0is very high, b becomes less effective in reducing the
average download time. We can see that for the torrent of
cluster 4, δ decreases approximately linearly as b increases.
For the torrents which represent cluster 3 and 5 and have
small f values, δ is very close or equal to the optimal even
for small values of b. Although the torrent of cluster 7 is
similar to those of clusters 3 and 5, it performs 10% worse
for small values of b. This is due to the lower service its
seeders provide (represented by a much higher γ value).
For torrents with higher values of f, δ needs higher val-
ues of b to reach the optimal value. This is explained by
the fact that, for a given b, leechers take a time which is
proportional to the file size to become seeders. The longer
this takes to happen, the longer the system takes to reach
its maximum throughput, and the more peers will be down-
loading with less than their full download speed.
Next, we look at how the cost of operating the super-
seeder behaves when b varies. For each value of b in each
torrent we calculate B, Bc, D and Dcand observe B/Bc
and D/Dc. These represent the comparison of the cost of
operating the hybrid and a fully centralized model which
provide a same δ to an identical population of requesters.
Figure 3 plots D/Dcfor different values of b and for
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 50 100 150 200 250 300 350 400 450 500
D / Dc
Reliable peer’s bandwidth (KB/s)
cluster 1
cluster 2
cluster 3
cluster 4
cluster 5
cluster 6
cluster 7
Figure 3. Comparison of total data transfer in
the hybrid and centralized models varying b.
each of the 7 representative torrents. We can see that this
valuegrowssub-linearlyformosttorrentsandarelimitedby
the point where there is a larger offer of upload bandwidth
than demand for it. Again, an exception to these behaviors
are the torrent of cluster 4 – with an approximately linear
growth of D/Dc– and of clusters 3 and 5, where D/Dcis
constant. The reasons are similar to those which explain the
behavior of δ: the initial arrival rate of peers in cluster 4 is
much higher than in the other torrents and there is always
more bandwidth available than demanded for it in clusters
3 and 5.
The maximum value of D/Dcfor the torrents we have
examined is ordered similarly to the file size of the torrents.
The exception is the torrent of cluster 7, which shows a high
value of D/Dccompared to the other torrents. This denotes
a smaller saving in data transfer and is due to its low seeder
service, evidenced by a large value of γ.
Furthermore, it is worth mentioning that all values for
D/Dcin the scenarios we analyzed were smaller than 0.14,
and most were smaller than 0.05, assessing a great saving
in the volume which needs to be transfered by a content
provider which opts for the hybrid model in place of a cen-
tralized one.
Finally, we look at B/Bcfor the scenarios we evaluate.
Figure 4 shows this value for our different torrents when b
varies. Recall that B is limited to the maximum amount
5

Page 6

of bandwidth peers can simultaneously consume, which is
smaller than that available for a high enough value of b.
Also, note that as b grows linearly and δ decreases expo-
nentially in the scenarios we have observed, Bcincreases
logarithmically. Therefore, B/Bcincreases approximately
linearly up to a point where δ = 1 and B stops growing.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 50 100 150 200 250 300 350 400 450 500
B / Bc
Reliable peer’s bandwidth (KB/s)
cluster 1
cluster 2
cluster 3
cluster 4
cluster 5
cluster 6
cluster 7
Figure 4. Comparison of maximum band-
width used in the hybrid and centralized mod-
els varying b.
Interestingly, the largest saving in the maximum band-
width needed to provide a certain quality of service hap-
pens for the torrent which represents cluster 4. Its most dis-
tinguishing characteristic is having a very large number of
requests. In this case, although the performance of peers is
not highly affected by b, the use of peers’ resources makes
the demand for bandwidth much lower for the superseeder
than for the centralized alternative even for an optimal δ.
Again, the savings in the torrent which represents cluster
7 are smaller than those in the other torrents when compar-
ing B and BC. This happens because the high value of γ
in this torrent implies in less resources from the peers and a
higher load on the superseeder.
Another interesting observation is that most sets of pa-
rameters which happen in practice yield similar savings in
themaximumbandwidththeydemandtoprovideanoptimal
δ. For all representative torrents except those of clusters 4
and 7, B/Bcis between 0.22 and 0.75 when δ = 1.
It is also possible to compare D/Dcand B/Bcand see
that for providing a certain quality of service, the savings in
the hybrid model are smaller for the maximum bandwidth
than for the total amount of data which the content provider
will provide.
6Conclusion
BitTorrent has proven to be a highly-scalable and effi-
cient content distribution mechanism. However, when rely-
ing completely on the resources provided by content con-
sumers, it fails to provide quality-of-service guarantees.
In this study we have investigated a method to circum-
vent this limitations which is gaining growing popularity:
operating a superseeder to assist content distribution. We
have presented a model which can be used by a content
provider to analyze its costs and efficiency when operating
such a model.
We have also analyzed the cost and efficiency of oper-
ating a superseeder with varying capacity in the scenarios
derived from real BitTorrent usage. From this analysis it is
possible to conclude that the hybrid model is still consid-
erably cheaper than its centralized equivalent while able to
provide near optimal performance with limited resources.
The efficiency and savings were affected significantly by
the seeding behavior of a class of torrents which we identi-
fied, however very low seeding was uncommon in the trace
as a whole.
Acknowledgements
This work was partially developed in collaboration with HP
Brazil R&D.
References
[1] BitTorrentCompanywebsite: http://www.bittorrent.com/2006-
05-09-warner-bros.myt. Warner Bros. Home Entertainment
Group Announces Revolutionary Deal to Publish Legal Film
and TV Content using the BitTorrent Platform, May 2006.
[2] OurMedia: http://www.ourmedia.org, Dec. 2006.
[3] Overmundo: http://www.overmundo.com.br, Dec. 2006.
[4] BBC. Bbc imp homepage, 2006.
[5] A. Bellissimo, P. Shenoy, and B. N. Levine. Exploring the use
of bittorrent as the basis for a large trace repository. Technical
Report 04-41, University of Massachusetts, June 2004.
[6] M. Digital. Company website, 2006.
[7] L. Guo, S. Chen, Z. Xiao, E. Tan, X. Ding, and X. Zhang.
Measurements, analysis, and modeling of bittorrent-like sys-
tems. In Internet Measurement Conference 2005 (ACM SIG-
COMM/USENIX IMC 2005), pages 19–21, Oct. 2005.
[8] M. Izal, G. Urvoy-Keller, E. W. Biersack, P. Felber, A. A.
Hamra, and L. Garc´ es-Erice.
Months in a Torrent’s Lifetime. In PAM2004, April 2004.
[9] A. Legout, N. Liogkas, E. Kohler, and L. Zhang. Clustering
and sharing incentives in bittorrent systems. Technical Report
inria-00112066, version 1 - 21, INRIA, Nov. 2006.
[10] J. A. Powelse, P. Garbacki, D. H. J. Epema, and H. J. Sips.
Measurement study of the bittorrent peer-to-peer file-sharing
system. Technical Report PDS-2004-003, Delft U. Technol-
ogy, Apr. 2004.
[11] D. Qiu and R. Srikant. Modeling and performance analysis
of bittorrent-like peer-to-peer networks. In SIGCOMM, pages
367–378, Aug. 2004.
[12] D. Stutzbach, D. Zappala, and R. Rejaie. The scalability of
swarming peer-to-peer content delivery. In NETWORKING,
pages 15–26, 2005.
[13] Wikipedia. Blizzard downloader, 2006.
Dissecting BitTorrent: Five
6