Modeling and Performance Analysis of Bitorrent-LikePeer-to-Peer Networks

Dongyu Qiu and R. Srikant University of Illinois , 2004

Presented by : Ran Zivhon

Agenda P2P characteristics Bitorrent – characteristics , protocol Optimistic unchoking , free-riding Fluid model , steady state calculations and

Simulations Lemmas Peers strategy Nash Equilibrium Article evaluation

Previous Work Bram Cohen, 2003

“Incentives Build Robustness in Bitorrent”

G. de Veciana and X. Yang , 2003 “Fairness, incentives and performance in peer-

to-peer networks”

G. de Veciana and X. Yang , 2004

“Service Capacity of Peer to Peer Networks”

Z. Ge, D. R. Figueiredo and D. Towsley , 2003 “Modeling peer-peer file sharing systems.”

P2P - Characteristics A P2P computer network connects peers and relies

primarily on their computing resources Decentralized - Little or no infrastructure – no

central server Self-organizing All or most communication is symmetric The network connects Lots of nodes Dynamic nodes : join leave failure – high “churn” Communication between every pairs of nodes Nodes don’t have much resources

Bitorrent - Description Bitorrent is a P2P file-sharing application

The protocol was originally designed and created by programmer Bram Cohen

Files are divided into pieces of size 256 KB and sub-pieces of size 16KB

The client Software is “save as” like software

Bitorrent – the protocol A downloader first connects to a .torrent file (on

the web) ,finds the tracker of the file and get a list of all the peers which have the file (referred as peer list , torrent).

The .torrent file contains meta information - length, name, hash, URL of tracker etc.

After connection with the peers the downloader gets the piece list of the other peers.

Bitorrent – the protocol When downloading the peer uses the following

Piece selection schemes : Random First Piece

The piece to download is selected at random until the first complete piece is assembled

Rarest First The piece to download is the most rare

piece at the other peers in the peer list Endgame Mode

When all the remaining sub-pieces are requested , the peer ask for the sub-pieces from all the peers in the peer list .

Bitorrent – the protocol The peer advertises its complete pieces to the peer list

and get a new peer list from the tracker .

when a peer joins , leaves , complete it’s download it notifies the tracker.

The peer Periodically calculate data-receiving rates and continuesly look for the fastest partners

Each peer is allowed to upload to a fixed number of peers (default is 4) which provide it with the best downloading rate

Peers divided to downloaders (leechs) and seedersSeeders – peers that have the whole file and just upload it to others

Bitorrent– Description Cont.Web page with link to .torrent

A

B

C

Peer

[Seed]

Peer

[Leech]

TrackerWeb Server

.torr

ent

Peer]Leech[

New Downloader

Bitorrent – Description Cont.Web page with link to .torrent

A

B

C

Peer]Leech[

New Downloader

Peer

[Seed]

Peer

[Leech]

Tracker

Get-announce

join peer list

Web Server

Bitorrent – Description Cont.Web page with link to .torrent

A

B

C

Peer

[Leech]

New Downloader

Peer

[Seed]

Peer

[Leech]

Tracker

Response-peer list

Web Server

Bitorrent – Description Cont.Web page with link to .torrent

A

B

C

Peer

[Seed]

Peer

[Leech]

Tracker

Shake-hand get piece list

Web Server

Shake-hand

get piece list

Peer]Leech[

New Downloader

Bitorrent – Description Cont.Web page with link to .torrent

A

B

C

Peer

[Seed]

Peer

[Leech]

Tracker

pieces

pieces

Web Server

Peer]Leech[

New Downloader

Bitorrent – Description Cont.Web page with link to .torrent

A

B

C

Peer

[Seed]

Peer

[Leech]

Tracker

piecespieces

pieces

Web Server

Peer]Leech[

New Downloader

Bitorrent – Description Cont.

Web page with link to .torrent

A

B

C

Peer

[Seed]

Peer

[Leech]

Tracker

Get-announce

Response-peer list

piecespieces

pieces

Web Server

Peer]Leech[

New Downloader

Optimistic Unchocking A peer uploads to nu (default 4) other peers which

provide it with the best downloading rate.

Optimistic Unchoking happens once every 30 seconds

The peer selects randomly another (fifth ) peer to download to , for exploring other download rates.

Then the upload to the peer with the least downloading rate is dropped.

The optimistic-unchocking gives opportunity to the free-riders.

Free-Riding A peer which only downloads from others and not

upload called a free-rider.

Peer i which is a free-rider get selected 1/(N-nu) of the time by any other peer (optimistic unchocking).

Download rate : N = number of peers , u = upload rate

The free-riders problem is not yet solved in Bitorrent.

Bitorrent - software

Fluid Model x(t) - number of downloaders in the system at time t.

y(t) - number of seeds in the system at time t.

λ - the arrival rate of new requests (Poisson process)

µ - the uploading bandwidth of a given peer (normalized by file size)

C - the downloading bandwidth of a given peer (normalized by file size).

θ - the rate at which downloaders abort the download (Poisson process)

γ- the rate at which seeds leave the system (Poisson process)

η - indicates the effectiveness of the file sharing , takes values in [0, 1].

Is this model realistic ?

Fluid Model

Total Upload rate - min{cx(t), µ(η x(t)+ y(t))} - c and µ dimensions are file/sec

The probability that some downloader becomes a seed in a small interval δ - min{cx, µ(η x+ y)}δ.

Is this proposition realistic ?

The rate of departures of downloaders - min{cx(t), µ(η x(t) + y(t))} + θx(t)

Steady-State Performance X¯ , Y ¯ are equilibrium values

β is determined by the bottleneckbetween download rate and upload rate

Average Download Time Little Law : (λ- θx) - average rate

downloads complete

The average downloading time T is not related to λ, even very popular files can be downloaded same time as less popular .

When η increases , T decreases. This is because the peers share the fille more efficiently.

When γ increases , T increases because a larger γ means that there are fewer seeds in the system.

η - Effectiveness of the File Sharing

A given downloader i, is connected to k = {x- 1, K} other downloaders

N – number of pieces in a file

ni – number of pieces at downloader i

Even if k=1 , η very close to 1

Local Stability and Markov model

eigenvalues of A1 and A2 have negative real parts – system is stable.

x^,y^ are the variance values around the fluid model values

Orenstein-Uhlenbeck process :

When λ is large – how large?

W are independent standard Wiener processes

With this model the system is simulated

X / λ – downloaders (3 days)

Y/ λ – seeds (3 days)

Histogram of Variation of x^,y^ around X,Y

Gaussian nature , the values look the same for all λλ

X,Y – real scenario (3 days)

95% confidence intervals , the fluid model resembles real life scenario results.

Peer Selection Algorithm Peer i selects the nu (default 4) peers that give it the best

upload to download to

Assumptions : Global information,No optimistic unchocking ,No download limit

sort the peers according to their uploading bandwidth (physical or determined)

first peer has the highest uploading bandwidth.

peer i choosing peers to upload at step i.

N total number of peers

µi the uploading bandwidth of peer i.

Peer Selection Algorithm - rules

Using these rules does the system converges ? Rule number 1 , is this rule realistic ? Does the arrangement of peers according to physical upload is necessary true ?

Lemmas Lemma 1. With the peer selection algorithm, when peer i

selects uploading peers, nii ≤ nu and for any k2 > k1 ≥ i,

nik2 ≤ ni

k1 ≤ nu

Lemma 2. Suppose that peers i, i+1, · · · , j have the same uploading bandwidth µ.If j –i+1 > nu ≥ 2, then for any k > j, we have

1. di ≥ di+1 ≥ · · · ≥ dj ≥ dk, 2. di > dk,

3. d(µ) > dk. This lemma gives the Optimal selfish behavior , and that

is what encourage peers to upload.

Peer Strategy peer i chooses µi such that :

Or more realistic

Where ε is the difference between two rates that a peer can differentiate.

Nash Equilibrium Point

Divide the network to sub-groups . In each group j, all peers have the same physical uploading bandwidth pj.

if the number of peers in a group ||gj|| > nu + 1 for all groups, a Nash equilibrium exists in the system, when µi = pj.

What if every group is Nu + 2 size - can the nu+2’th peer lower it’s uplink to the sub-group below ?

Strengths of Bitorrent Very high throughput of the network

tit-for-tat – encouraging cooperation

Ability to resume a download

Average download time doesn’t depends on popularity

Drawbacks of Bitorrent Small files – latency, overhead

Tracker : Millions of peers – Tracker behavior (uses

1/1000 of bandwidth) Single point of failure

Seeds have no benefit for cooperating

Fairness: those who do not contribute should not be able to receive good service (free – riding)

Article Evaluation Novelty ? – much of the ideas are from previous work Realistic ? – many of the assumptions aren’t real-life

(many constants are not constant , peer selection algorithm, BT unique piece selection)

Missing – how the upload bandwidth divided among downloaders Byzantine and selfish behavior how does the peer selection resembles real life scenarios.

Technically Sound Evaluated – simulations with real-life scenarios. Clear and self-contained