performance evaluation of peer-to-peer video streaming systems

Performance Evaluation of Peer-to-Peer Video Streaming Systems

Wilson, W.F. PoonThe Chinese University of Hong Kong

Content

Introduction Related Works System Model Experimental Results Conclusion

Introduction (1)

Providing video streaming services have long been a research topic

– parallel server designs such as RAID– multicast/broadcast transmission schemes – distributed VoD systems

Tremendous growth in computer power of personal computers

– peer-to-peer (p2p) systems– Peers contribute storage, content and bandwidth

Introduction (2)

Most of these p2p systems have been developed for file sharing/web caching services

– Search mechanism– Storage management

Maximize file availability or system reliability The work on p2p video streaming has not been thoroughly

studied Investigate whether such a p2p system is applicable to

supporting video streaming applications– Distributed data storage and its impact on streaming performance– Analytical framework incorporated the effect of data replication and

placement policies

P2P Streaming Systems (1)

One of major challenges of a p2p system– Peer machines may be turned on and off in an unpredictable manner – The system experiences very worse availability

video replica

replica

replica

Full Replication

serving peer

free rider

Replication

P2P Streaming Systems (2)

A network has G peers in which I peers (serving peers) stores a set of J different videos

The other peers (free riders) just make requests but not contribute their resources

Assume is the “up” probability of the peers– Tup is the mean up time duration– Tdown is the mean down time duration

downup

up

TT

T

Assume– Ni is the amount of shared storage in peer i

– bj is the size of video j

– qj is the request probability for video j

– Cj is the bit rate for video j

P2P Streaming Systems (3)

nj is the number of replicas for video j, vj

Requests to a serving peer for vj is given by

j

jj

n

qw

In

nb

j

J

jjj

1

1

System storage constraints

INNN 21

System Availability

With full replication scheme– The video j is not available when all the peers storing vj are

off-line simultaneously

System Availability

J

j

nj

jq1

])1(1[

System Arrival (1)

peer

peer

peer

new:Rate Arrival New

redirect:Rate ArrivalRedirect

redirecti:arrivalRedirect

peer i

newi:arrivals New

partiali:system theinto Redirected

requested video available

Playback is unsuccessful if the request is blocked

rejected

Availability

System Arrival (2)

New requests to peer i

iVj j

jnewnewi

n

q

Requests partially served by peer i

)1)(( blockredirecti

newi

partiali P

Probability of requests redirectedProbability of

requests blocked

Vi: Set of videos stored in peer i

System Arrival (3)

Assume– Service time (video length) follows an exponential distribution– “up” duration is exponentially distributed

Probability of requests redirected by the “up” peer

LT

L

up

L: mean video length

Tup: mean “up” time duration

System Arrival (4)

Total partially served traffic

I

i

redirecti

newi

blockI

i

partiali

partialtotal P

11

)()1(

Redirect requests to peer k

k

k

Vj j

jI

i

redirecti

newi

block

Vj j

jpartialtotal

redirectk

n

qP

n

q

1

)()1(

System Arrival (5)

where

,

kVj j

jk

n

qA

,)1(

1

I

iik

newblockk AAPB

,))1(1(

2

kblock

kk

AP

BC

))1(1(

)1(

kblock

kblock

kAP

APD

I

kii

redirectikk

redirectk DC

,1

System Arrival (6)

The equations can be represented

IredirectI

redirect

redirect

I

I

C

C

C

DD

DD

DD

2

1

2

1

21

1

2

1

1

1

Redirect arrivals can be solved

System Blocking (1)

Unsuccessful playback– Proportion of requests that cannot completely playback the

whole video

Assume– Poisson Arrival Process– Video length, “up” and “down” durations follow exponential

distribution

States of peer i can be represented by a Markov Model

System Blocking (2)

OFF

ON/0 ON/1 ON/2 ON/K

downT

1

upT

1

redirecti

newii

i

L

1 2 3 K

i i

Peer’s state diagram

System Blocking (3)

Since a peer will not receive any requests (new/redirect) in “off” state, the probability of requests blocked by a peer is equal to

K

i

iONP

KONPP

0

)/(

)/(k)Peer by Blocked(

I

itotaliblock iPP

1

)Peer by Blocked(

I

ii

total

1

System Blocking (4)

A new video request may be redirected by peers several times to finish the video playback

If either the new request or the redirected request is blocked, the playback is considered to be unsuccessful

)1( I

1i

I

1iulunsuccessf

block

newi

redirecti

newi

PP

Experimental Results

Simulation is built to verify the model– Randomly determine the number of replicas for each video

(random replication)– Randomly store the replicas among peer (random

placement)– Video popularity follows a Zipf distribution with parameters

0.271– Mean video length is 2 hours– Tup + Tdown = 10 hours

Measure the unsuccessful playback rate– Peers cannot complete the video playback

Results – Arrival Rate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Arrival Rate /sU

nsuc

cess

ful P

layb

ack

Rat

e

Sim: Exp, Tup=60, S=10 Sim: Fix, Tup=60, S=10 Math: Tup=60, S=10Sim: Exp, Tup=240, S=10 Sim: Fix, Tup=240, S=10 Math: Tup=240, S=10Sim: Exp, Tup=420, S=10 Sim: Fix, Tup=420, S=10 Math: Tup=420, S=10

Number of peers=1200 Number of videos=200 Video length=7200s

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Arrival Rate /s

Uns

ucce

ssfu

l Pla

ybac

k R

ate

Sim: Exp, Tup=60, S=2 Sim: Fix, Tup=60, S=2 Math: Tup=60, S=2Sim: Exp, Tup=240, S=2 Sim: Fix, Tup=240, S=2 Math: Tup=240, S=2Sim: Exp, Tup=420, S=2 Sim: Fix, Tup=420, S=2 Math: Tup=420, S=2

Results – Serving Peers

Arrival rate=0.04/s Number of videos=200 Video length=7200s

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

No of Servering Peers

Uns

ucce

ssfu

l Pla

ybac

k R

ate

Sim: Exp, Tup=60, S=10 Sim: Fix, Tup=60, S=10 Math: Tup=60, S=10Sim: Exp, Tup=240, S=10 Sim: Fix, Tup=240, S=10 Math: Tup=240, S=10Sim: Exp, Tup=420, S=10 Sim: Fix, Tup=420, S=10 Math: Tup=420, S=10

Results – Peer Availability

Arrival rate=0.02/s Number of peers=1200 Number of videos=200 Video length=7200s

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

60 120 180 240 300 360 420 480 540Up Time Duration (minutes)

Uns

ucce

ssfu

l Pla

ybac

k R

ate

Sim: Exp, Arr=0.02, S=2 Sim: Fix, Arr=0.02, S=2 Math: Arr=0.02, S=2Sim: Exp, Arr=0.02, S=10 Sim: Fix, Arr=0.02, S=10 Math: Arr=0.02, S=10Sim: Exp, Arr=0.02, S=40 Sim: Fix, Arr=0.02, S=40 Math: Arr=0.02, S=40

Replication Strategy - MinReq

For video streaming, a request that can be served requires:

– The requested video is available in the system– The serving peers have the available bandwidth

Determine the number of video replicas by minimizing the load of the serving peers

J

j j

jnew

reqn

qP

1

In

nb

j

J

jjj

1

1Subject toMinimize:

Optimal replication profile: **2

*1

* ,,, Jreq nnnn

Results – Serving Peers (MinReq)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

No of Serving Peers

Uns

ucce

ssfu

l Pla

ybac

k R

ate

Math(Random): Tup=60 Math(MinReq): Tup=60Math(Random): Tup=240 Math(MinReq): Tup=240Math(Random): Tup=420 Math(MinReq): Tup=420

Arrival rate=0.04/s Number of videos=200 Video length=7200s Peer Storage=10

0

50

100

150

200

250

300

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

113

120

127

134

141

148

155

162

169

176

183

190

197

Video ID

No

of R

eplic

as

Random

MinReq

Error on Video Popularity

Considering an estimation error

jjj eqq ˆˆ

J

jj

jj

q

qq

1

ˆ

ˆ~

Estimated popularity is used to generate the replication profile

Results – Estimation Error

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500No of Serving Peers

Uns

ucce

ssfu

l Pla

ybac

k R

ate

Tup=60, Err=0% Tup=60, Err=20% Tup=60, Err=50%Tup=240, Err=0% Tup=240, Err=20% Tup=240, Err=50%Tup=420, Err=0% Tup=420, Err=20% Tup=420, Err=50%

Arrival rate=0.04/s Number of videos=200 Video length=7200s

Conclusion

Consider the performance of a p2p system for video streaming services

Evaluate data storage and its impact on video streaming

Develop analytical framework to capture the properties of the system

– Data replication– placement policy

Optimal replication scheme may not significantly improve the successful playback rate