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
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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
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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
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