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Int. J. Communications, Network and System Sciences, 2010, 3, 916-924
doi:10.4236/ijcns.2010.312125 Published Online December 2010 (http://www.SciRP.org/journal/ijcns)
Copyright © 2010 SciRes. IJCNS
A Measurement Study on BitTorrent System
Lin Ye*, Hongli Zhang, Fei Li, Majing Su
School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China
Received September 27, 2010; revised October 29, 2010; accepted November 20, 2010
Measuring and characterizing peer-to-peer (P2P) file-sharing systems will benefit the optimization and
management of P2P systems. Though there are a lot of measurement studies on BitTorrent almost in every
important aspect, few of them focus on the measurement issues and the corresponding solutions, which can
strongly influence the accuracy of measurement results. This paper analyzes the key difficulties of measuring
BitTorrent and presents a measurement system with combination of active and passive ways, which can han-
dle with the problems well and balance the efficiency and integrity. Then compared to other work, a more
complete and representative measurement was performed for nearly two months and several characteristics
are concerned: 1) there are diverse content sharing in BitTorrent system, but multimedia files that are larger
than 100 MB are the most. 2) Distributed Hash Tables has indeed enhanced the ability of peer discovery
though there are some pitfalls to be addressed. 3) Pieces are distributed uniformly after the early stage and
there are few rare pieces. Furthermore, peer arrival rate shows a periodical pattern, which was not well mod-
eled before. Then an improved model is proposed and the experiment results indicate that new model is fitted
in with actual measurement results with high accuracy.
Keywords: P2P, BitTorrent, Measurement, Peer, Piece
With the enhancement of PC performance and bandwidth,
peer-to-peer (P2P) systems have become immensely
popular and attracted millions of users in the past few
years. Particularly, BitTorrent has become a ruling
heavyweight application that contributes about 53% of
P2P traffic. Though BitTorrent scales fairly well and is
now widely used in many fields, such as data distribution
 and media streaming , the performance still gets
much attention in the literature. With the introduction of
Distributed Hash Tables (DHT) , BitTorrent has gone
from single center to hybrid structure, which might bring
about the change of performance.
Nowadays more than ﬁfty kinds of BitTorrent clients
have been in use. Unlike other P2P systems such as
eMule  and Gnutella , BitTorrent is simple in de-
sign, which is made up of four parts: torrent, peer index,
seeds and leechers. A torrent, which is usually uploaded
onto a website, is an encoded ﬁle that digests the infor-
mation of sharing ﬁles and is necessary for peers to boot-
strap themselves into a swarm. Peer index is the set of
peers owning the same ﬁles. Peer index tracks the status
of the peers that are currently active, and acts as a ren-
dezvous point for all peers. So far BitTorrent system has
developed three mechanisms for index storage: tracker,
DHT and gossip . They are complementary with dif-
ferent working principles. The diversity meets the de-
mand for one peer to connect enough peers to achieve
better performance. Peers are divided into two classes
according to their states: peers that have already
downloaded all ﬁles and continue to serve others are
called seeds; peers that are still downloading are called
In BitTorrent, the ﬁles are divided into small pieces,
and one piece is further divided into smaller blocks.
Therefore, a peer can download multiple blocks of the
ﬁles in parallel, which capitalizes the resources from
peers to distribute large contents efficiently. Furthermore,
BitTorrent develops a “tit-for-tat” incentive mechanism,
which enables peers with high uploading bandwidth to
have priority of being served. In this way, peers will pay
the penalty for their selﬁshness, which effectively pre-
vents free-riding behaviors common in P2P systems.
The purpose of this paper is to aid in the understand-
ing of a real and developing P2P system, to provide
L. YE ET AL.
measurement data that may be useful in modeling and
improving BitTorrent, and to identify design issues in
such systems. Our contribution is to discuss the problems
and errors in the measurement in depth firstly and design
a complete solution to settle them, which is the essential
prerequisite to analysis work. We show for the first time
the consistency of peers from trackers and DHT, and
explore the inherent factors how the differences bring
about. Also, we demonstrate the contrast between dif-
ferent torrents in the piece view and propose an im-
proved model of peer arrival rate in the peer view.
The remainder of the paper is organized as follows.
Section 2 presents the related work. And then we intro-
duce the measurement system for BitTorrent through
analyzing several key difficulties with the corresponding
solutions in Section 3. We focus on some new findings in
our measurement results in Section 4. Finally an im-
proved model of peer arrival rate is proposed for better
fitting in with actual measurement results. We conclude
the paper with a discussion of the results in Section 6.
2. Related Work
The amount of P2P traffic and the population of P2P
users on the Internet keep increasing. Previous work on
BitTorrent has focused on modeling [7,8], incentive
mechanisms and improvements [9-11]. In order to get
more understanding of BitTorrent, a lot of measurement
studies [12-20] have been performed, which can be
summarized in four aspects:
1) Torrents: Study  collects the information from
two popular trackers that continuously update the statis-
tics on their torrents and connected users, revealing that
torrents have a wide range in size and the average size
exceeds 600MB. Work  gathers and parses the web
pages of the Supernova, and downloads all torrents. They
gives the number of downloads among three types
(games, movies and music) and finds that movies are the
most popular. Work  focuses on the difference be-
tween video and non-video swarms. Their results show
the torrents shared by video swarms are mostly large
while the size of non-video swarms is relatively smaller.
But existing measurement on torrents are insufficient due
to their limited range with only two trackers or single site,
which is sensitive to specific user community.
2) Core components: Work  monitors the status of
all trackers for a long time and points out the overall per-
formance and stability are strongly influenced by the
availability of core components. Study  analyzes the
prevalence and impact of new mechanisms, including
multiple trackers and DHT. There are some findings: a)
the introduction of multiple tracker and DHT both can
improve availability; b) Trackers might not be inde-
pendent because many of them are hosted in the same
machine and multiple trackers may cause swarm splitting;
c) Tracker and DHT show complementary characteristic
features that trackers provide more information and
faster, but DHT can significantly increase the availability
of the whole system.
3) Peers: Work  depicts the evolution of peers by
analyzing five-month tracker log, such as the characteris-
tics of session and geographical analysis. The results
demonstrate that BitTorrent is highly effective and can
sustain flash-crowd. However, the measurement on sin-
gle torrent (Linux Redhat 9 distribution) cannot stand for
torrents with different popularity. Study  finds that the
number of peer arrivals decreases exponentially with
time in general after its birth. But the work lacks in
fine-grained modeling, especially in the peer arrival rate
at the early stage. Study  reveals that the session
length in BitTorrent follows a Weibull distribution more
accurately. Work  also points out only 17% of peers
have an uptime longer than one hour after downloading.
4) Pieces: Studies [18,19] both prove that rarest-first
piece selection strategy is better than random strategy.
But the simulation results  present that the perform-
ance benefits provided by network coding in terms of
throughput can be more than 2-3 times better in com-
parison with transmitting unencoded blocks. Different
from simulation methodology, study  explores the
efficiency of rarest-first mechanism by means of instru-
mented clients that are able to record messages sent or
received with the detailed content of the messages, state
change in the choke algorithm and other important
events. The measurement results show that rarest-first
algorithm guarantees close to ideal diversity of the pieces
among peers. But limited measurement scope (at most 80
peers) and time (8 hours) cannot give a direct impression
on piece distribution in a long term. Work  performs
a detailed measurement study on the distribution and
evolution of piece population. They analyze snapshot
data of the near-instantaneous population of pieces, and
long-term data of evolution of the piece population over
several days. The results validate that the downloading
policy of BitTorrent is quite effective in the view of
piece distribution and evolution.
Compared with previous work, this paper differs from
the following aspects:
The data are more representative. Our measure-
ment collected about 382,624 torrents from 72 hot
websites, which are comprehensive as well as par-
ticular only serving cartoon, TV, games and so on.
Compared to studies [13,14], the data are more
The measurement methods and content are more
complete. Several methods including active and
Copyright © 2010 SciRes. IJCNS
918 L. YE ET AL.
passive ones are integrated to measure BitTorrent
system in multilevel view. The combined design
can complement each other and solve the limitation
of using any single method.
The difference between torrents is concerned. Two
torrents with different popularity are measured
continuously for a long time. The details of them
are shown in Table 1. We can get a deep under-
standing of different torrents by comparing them.
3. Measurement Methodology
P2P file-sharing systems usually adopt two-level index to
maintain the announcement and search of the files, which
means descriptive meta data and peer information are
separately stored in overlay network. Therefore, a stan-
dard process is that users search meta information,
choose interested items and then start downloading. If
piece information is also viewed as a kind of index, a
complete measurement system for P2P should contain
Meta measurement: meta data such as filename,
file ID, size and type are collected through search-
ing keywords in this level.
Peer measurement: peer information (IP/Port pairs)
is gathered by file ID.
Piece measurement: in order to get piece informa-
tion, the system needs to connect as many peers as
possible and exchange piece information with each
other based on peer measurement.
3.1. Meta Measurement
Most of P2P systems provide an interface to search meta
information for users, but BitTorrent has only limited
support. The reason lies in the fact that torrents exist on
the websites. Users have to browse many pages and
choose proper torrents. To gather meta data rapidly and
automatically, a crawler based on Nutch is developed
and focuses on the following problems:
1) Unrelated Pages Filtering. There are many pages
unrelated to torrents on the websites, such as descriptions
or advertisements, which will waste a lot of bandwidth to
fetch. By analyzing the hierarchical structure of most
BitTorrent websites, it is found that URLs on the same
site are similar and can be represented in one or more
regular expressions. So URLs are clustered to extract the
regular expressions and the useful pattern of torrents’
links in our work. When crawling the site, we decide
whether pages should be fetched according to regular
expressions. Furthermore, these filtering rules have the
generalization ability and can be adjusted dynamically by
the previous result to guide the next fetching.
Table 1. Information of two torrents.
Torrents Hot Ordinary
Type video (movie) video (cartoon)
Size 457.06 MB 176.15 MB
Website bbs.wofei.net bt.ktxp.com
Publishing Time 2009-4-20 16:39 2009-4-20 15:56
Start Time 2009-4-20 16:41 2009-4-20 15:58
End Time 2009-5-19 22:03 2009-5-19 22:05
The Number of Peers 28856 6315
2) Complex Pages Parsing. Complex pages are the
tions to trigger some events for real content, which poses
an obstacle to traditional crawlers. Many sites have al-
ready used complex pages which make the torrents dif-
ficult to obtain. To solve the problem, an ajax parsing
corresponding events and abstracting real content. The
architecture is shown as Figure 1.
3.2. Peer Measurement
There are three ways to collect peers: log analysis, pas-
sive and active. Although tracker log can record the
status of peers more accurately, there are a few draw-
backs to be addressed. First, tracker log is not available
for anyone, which puts a hard restriction on this method.
Second, tracker log does not cover the whole information
because more than one tracker may be appointed to a
torrent, and it is not practical to obtain their logs all.
Third, tracker log cannot represent DHT. Passive method
usually deploys several controlled clients in target swarm
and waits for incoming connections from others. Passive
Figure 1. Ajax Parsing Engine.
Copyright © 2010 SciRes. IJCNS
L. YE ET AL.
method is able to handle with the peers behind NAT or
firewall, which cannot be connected by external hosts.
But passive method needs a long measurement period
with low efficiency, especially for a large swarm. Active
method acts as a normal user to make requests for other
peers to tracker and DHT. However, some mechanisms
reduce the efficiency of active method. For example,
peer index randomly returns a few peers and does not
guarantee the dissimilarity between successive requests.
The churn  also changes the index at all times, which
makes active method hard to converge.
Compared to log analysis and passive method, active
method can obtain peers freely and diversely. So this
paper mainly implements active measurement on tracker
and DHT. To address the limitations, the following set-
tles for bounding or estimating the errors and makes a
tradeoff between the efficiency and integrity. To bound
the errors, we assume peer index contains N peers for
one torrent and responses n peers every request. We de-
note T(m) as total number of distinct peers that we dis-
covered after m requests and P(m) representing the cover-
age as the fraction of all peers. Obviously, if n > N, T(1) =
N and P(1) = 1 in one request. If n < N, T(1) = n at the
ﬁrst request. Since the index randomly returns peers, we
need to avoid the redundancy and T(m) does not increase
with linear growth. We suppose T(m−1) is the total
number of distinct peers after m−1 requests. When the
mth request is sent, the probability that undiscovered
peers will be returned is:
The recursion formula of T(m) after m requests is:
The coverage P(m) is:
According to (2) and (3), for example, more than 230
requests have to be made for measuring a torrent about
5000 peers with 50 peers returned every time, which can
obtain 90% of all peers. The process may last 8 minutes
or more, and will introduce additional errors into the
measurement results. Because every swarm has its own
size, there is different measurement time for all of them
in real experiments. It is about 10 minutes on average in
our measurements for nearly 1,000 torrents. So we dis-
guise ourselves as many legal peers to probe in parallel,
which succeeds in speeding up the measurement. To
overcome the churn and make the measurement easy to
converge, we deﬁne F(m) as the number of new discov-
ered peers between successive measurements, which is
equal with T(m) − T(m−1). We use a threshold of F(m)
to ﬁnish the measurement. When F(m) is less than the
threshold in successive measurement, we will end up the
measurement. From (2), we can conclude that as long as
the threshold is less than n/10, 90% of peers should be
discovered. In order to avoid the inﬂuence of randomness,
we ﬁnish the measurement when the times that the num-
ber of new discovered peers is less than the threshold is
more than 5, which always empirically discovers 95% of
In addition, when active method is running, many dis-
guised clients that we control are also operating in pas-
sive mode, which are able to accept incoming connec-
tions and collect the peers that might be behind NAT or
firewall. As long as we can own enough peers, the high
probability that peers are discovered is guaranteed.
3.3. Piece Measurement
Every peer sharing the same files owns its local piece
information, which means a global view of pieces needs
the piece information from all peers. In this paper two
methods are used as follows:
1) Active: we instrument several clients to connect the
peers actively to exchange piece information with each
2) Passive: in order to overcome the shortcoming that
some peers cannot be connected from the outside. We
register many forged users or entities into trackers and
DHT, and then wait for incoming connections from oth-
ers. As long as there are enough controlled forged enti-
ties, others will connect them with high probability so as
to collect the piece information in a passive way.
Moreover, a traffic monitor system is deployed for
passive data collection, which uses deep packet inspec-
tion (DPI) to capture the communication between peers
and trackers. The parameters of requests from peers to
trackers can help us analyze the users and resources,
such as what files are sharing and when the peers
download and finish. In a word, the proposed system in
this paper can carry off all related measurement contain-
ing torrents, peers, pieces and user behaviors, whose ar-
chitecture is shown in Figure 2. On the basis of it, a
measurement had been performed from 4/2/2009 to
5/27/2009 for about two months.
4. Measurement Results
Size and type are the main static characteristics of the
torrents, which can tell what ind of torrents are the most k
Copyright © 2010 SciRes. IJCNS
L. YE ET AL.
Copyright © 2010 SciRes. IJCNS
Figure 2. The architecture of BitTorrent measurement system.
times more than trackers. The diversity of peer index
indeed reinforces the availability of BitTorrent. Second,
peers from DHT are more than trackers, which implies
peers from them may not follow the same pattern. To
show the consistency between trackers and DHT, the
percentage of the same peers in trackers and DHT is
given in Figure 5. The high consistency implies DHT
makes a good complement to trackers.
popular in BitTorrent. It is helpful to design better mecha-
nisms for resources management and replicas control.
Figure 3 gives the distribution of torrent size with sev-
eral common bins. About 21% of torrents are more than
1024 MB, which are usually games, HD movies and
video collection. 34% of torrents that might be video lie
in between 250 MB and 1024 MB. Both of them take up
55% of all torrents, which means large torrents occupy a
dominant position in BitTorrent system.
In order to have a close view on real sharing file type,
we abstracted the packed filenames from each torrent
and counted the corresponding percentage according to
file extension. Text files are omitted because they are
small and should not be considered as the main content.
RAR, MP3, RMVB, JPG and AVI are the top 5 file types
with percentage 31.23%, 20.42%, 10.42%, 9.03% and
6.19% respectively. Furthermore, we classified file ex-
tension into six types: video, audio, image, executable,
archive and other and the corresponding percentage are
shown in Table 2.
4.2. Core Components
As a rendezvous point, trackers and DHT both play an
important role in BitTorrent, which maintain the peers’
status and provide other peers for new ones. Study 
has given a detailed description of tracker type and activ-
ity, and drawn a comparison between trackers and DHT
in the efficiency of finding peers.
Figure 3. The distribution of torrent size.
Table 2. File type, file extension and corresponding per-
In this paper, we focus on the number of peers and
their consistency in trackers and DHT, and explore the
inherent factors how the differences bring about. The
number of peers is a direct metric presenting the per-
formance of different index. Figure 4 gives the result of
our measurement on ordinary torrent during its first ten
days. The total number is the sum of tracker and DHT
peers without duplicate ones. Although there are three
gaps missing data due to network failure, it has nothing
to do with the conclusion we make. First, Figure 4 shows
that with the help of DHT, the total number is almost two
File type File extension Percentage
video rmvb, avi, mkv, mp4, rm, wmv, mpg,… 22.8%
audio mp3, flac, cbr, wma, ogg, cue, m4a,… 23.5%
image jpg, png, gif, bmp,… 9.5%
archive rar, zip,… 32.1%
other … 11.2 %
L. YE ET AL.
Figure 4. The number of peers in total, trackers and DHT.
Figure 5. The percentage of the same peers in trackers and
The number of peers has given a preliminary impres-
sion on different index. As above mentioned, we seem to
draw a specious conclusion that DHT is better than
tracker by the number of peers. Actually, the number of
available peers is more convincing than the number of
peers. We define a peer is available when the peer can be
connected by others. The peers behind NAT or firewall
are treated as unavailable ones because they cannot ac-
cept incoming requests though they can offer pieces to
others in reverse way. The ratio of available peers in
tracker on average is 25.3% as the same as the statistics
work on peers behind NAT , and DHT is 19.1% in
Figure 6, which shows the ratio of available peers in
tracker is higher than DHT.
It is interesting that though there are more peers from
DHT than trackers, the peers from DHT are less avail-
able. It is the architecture that makes the difference.
Tracker is a global component in BitTorrent and can be
visible by all peers, but DHT is a completely distributed
network. As a result, when some events happen, for ex-
ample, arrival or departure, tracker can update the peers’
status without delay, which keeps the index fresh and
Figure 6. The percentage of available peers in trackers and
correct. On the other hand, DHT has a complex process
to route various messages among peers. A successful
event notiﬁcation needs more than 3-5 messages. More-
over there is no corresponding message for departing,
and stale peers are not removed until the pre-set timer is
timeout. Many useless peers are left because of delay or
forgetting, which wastes a lot of resources and introduces
Pieces are the smallest appreciable unit of data in Bit-
Torrent since smaller blocks do not directly affect
whether torrent contents finish transferring. The distribu-
tion of the pieces across the swarm is important for
availability in two aspects. First, if there are not enough
replicas for each piece, the whole process will be held
due to some missing pieces. Second, if the distribution is
not uniform with many rare pieces, the efficiency will be
low because the peers owning rare pieces have to afford
the pressure from others who want them. Though study
 was able to obtain 90% of peers by using instru-
mented clients, it failed to cope with peers behind NAT
or firewall. Our combined method can give a more com-
plete view on the distribution. Moreover, we pay close
attention to the difference in replicas and rarity of pieces
We suppose one file F is divided into n pieces P1,
P2,, Pn and there are ri replicas of piece Pi at time t in
the swarm. Therefore, the rate of replicas R(t) is defined
at time t:
Rtr trtrt (4)
The meaning of R(t) is to give the number of equiva-
lent replicas for the whole file F at time t and reflect the
availability of the file in BitTorrent system. The value of
R(t) is no less than the number of seeds in existence at
Copyright © 2010 SciRes. IJCNS
922 L. YE ET AL.
To explore whether the distribution of pieces is uni-
form, the rate of rarity Cr(t) is defined at time t:
ravg(t) is the average replicas of all pieces as calculated
The rates of replicas between hot and ordinary torrents
are contrasted in Figure 7. First, it is shown that at the
early stage the rates of replicas are low though the files
can be downloaded slowly. Once the seeds leave, the
downloading cannot be finished at all. And then the rates
go into a steady stage when there are enough equivalent
replicas with the best system service ability. The offline
of any peer (seed or leecher) has no significant effect on
the downloading. With the departure of seeds and the
decreasing peer arrival rate, the rates reduce dramatically
at the last stage. Second, there is a big difference be-
tween two torrents mentioned above. The rate of hot tor-
rent is higher than ordinary one, especially at the last
stage, and the steady stage of hot torrent is also longer
than ordinary one, which means BitTorrent is more suit-
able for popular content because it will be difficult for
ordinary ones to obtain if users do not find them as soon
Figure 8 demonstrates the rates of rarity between hot
and ordinary torrents, which are similar as a whole. The
fluctuation is very drastical at the early stage because the
downloading has just begun and only a few pieces have
the opportunity to be propagated, and after that the rate
gradually approach at 0, which indicates the distribution
of pieces is nearly uniform.
5. Model of Peer Arrival Rate
Many studies have already proved the close relationship
between the performance and the peer arrival rate in
BitTorrent. However, they usually suppose the peer arri-
val rate follows Poisson distribution, which does not fit
in with the results . In fact, in our measurement some
new pattern is found in the peer arrival rate, which is also
not well modeled before. Before the measurement begins,
there are always some peers existing that cannot be con-
sidered as new ones in target network. So we use the last
result as a point of reference. If some peers are not found
in last result but discovered in this experiment, they will
be viewed as new ones. Figure 9 and Figure 10 show
the number of new arrival peers from both torrents.
From Figure 9 and Figure 10, the number of new arrival
Figure 7. The rate of replicas.
Figure 8. The rate of rarity.
Figure 9. The number of new peers from hot torrent with
Copyright © 2010 SciRes. IJCNS
L. YE ET AL.
Figure 10. The number of new peers from ordinary torrent
with fitted curve.
peers shows a typical fluctuation pattern in both torrents,
which seems to follow a daily cycle. Therefore, we count
the appearance time of the crest and trough with their
corresponding value in detail as shown in Tab le 3. First,
Table 3 can tell that the interval between two adjacent
crests or troughs on average is about 24 hours as long as
one nature day. This pattern implies the fluctuation
seems to follow the behaviors of normal users in the
whole day. Second, the value of crests shows an overall
decreasing trend with time, although the 3rd crest of hot
torrent is an exception.
However, this obvious fluctuation pattern of new arri-
val peers is not well modeled in the literature as far as we
know, so the goal of this paper here is to improve the
model of the peer arrival rate in the thought of periodic-
ity. The new model is based on the study  as below:
In the above formula, is the number of new ar-
rival peers at time t. A0 is the initial oscillation amplitude
when the measurement starts, which is related to the
popularity of torrents and the state (transient or steady).
To be specific, the more popular torrent owns a bigger A0.
is the attenuation parameter of the rate. The more
popular torrent has a bigger
, which means slower
attenuation. T is the period and B is the phase shift.
In order to quantify the parameters in (7), we define
objective function as below:
Mod(k) is the kth computation value of the model
while Obs(k) is the kth measurement value. This paper
uses the BFGS quasi-Newton method to search the para-
Table 3. The Crest and Trough of new arrival peers in both
time (hour) value appearance
time (hour) value
Crest 1 6.09 85 4.2 35
Trough 1 12.64 0 14.05 0
Crest 2 22.78 58 24.06 26
Trough 2 36.05 0 40.32 0
Crest 3 49.01 110 50.76 10
Trough 3 60.21 0 62.16 0
Crest 4 75.03 57 73.11 4
Trough 4 84.03 0 86.97 0
meters and make objective function minimum.
Figure 9 and Figure 10 also give the fitted curves of
the periodical model for both torrents. The new proposed
model is close to the same with actual measurement re-
sults. Furthermore, compared to ordinary one, hot torrent
has a higher A0, which implies hot torrent has a larger
network. And hot torrent also has a higher
means the corresponding resource can stay active for a
longer time. Considering the value of T in both torrents
with separately 0.26 and 0.29, the period is about
6. Discussion and Conclusions
The existing measurement works on BitTorrent pay little
attention to the measurement issues and the correspond-
ing solutions, which may lead to the inaccuracy of the
results. In this paper we design a complete solution to
settle them and have presented a detailed measurement
study and an analysis of BitTorrent. We believe that this
study is a contribution to the ongoing effort to gain in-
sight into a real and developing P2P system.
Though all kinds of torrents are sharing in BitTorrent,
the measurement results show that it is more suitable for
popular content that are very “heavy”. And the high con-
sistency of peers between trackers and DHT implies
DHT makes a good complement to trackers. However,
DHT still needs considerate improvements for better
performance. Also, the fluctuation of peer arrival rate
modeled in this paper will cause the difference of system
performance, which needs further research, such as in-
centive mechanisms beyond “tit-for-tat” mechanism and
Copyright © 2010 SciRes. IJCNS
L. YE ET AL.
Copyright © 2010 SciRes. IJCNS
This work is partially supported by National High-Tech
Development 863 Program of China (2009AA01Z437);
National Grand Fundamental Research 973 Program of
China (G2007CB311101); National Natural Science
Foundation of China (60703014);Program for New Cen-
tury Excellent Talents in University (NCET-07-0245);
The authors also gratefully acknowledge the helpful
comments and suggestions of the reviewers, which have
improved the presentation.
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