A Simple Model for Analyzing
P2P Streaming Protocols
Zhou Yipeng
Chiu DahMing
John, C.S. Lui
The Chinese University of Hong Kong
Outline
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Introduction
Model & Chunk Selection Strategies
Simulation
Conclusion
Introduction

Unicast
Client server is the bottleneck and waste
bandwidth
Bottleneck
Router
Waste
Bandwidth
Introduction

Application Layer Multicast (or CDN)

Rely on a single distribution tree
Leaf peers
server
Untapped
bandwidth
resource
Weak point
Introduction
P2P Streaming System
-P2P resolves this scalability problem by using all resources of all clients. It is like
using multiple trees simultaneously to deliver content.
Server
Peer
Peer
Peer
Fully connected
Peer
Peer
Peer
Peers maintain:
* buffer
* neighbor list
Introduction
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P2P application:
-file distribution, p2p streaming

Summary work on p2p streaming:
-PPlive, PPstream, CoolStreaming, BiTos
-Much work on system study, architecture design and measurement but little
theoretic work

Our Contributions:
-Analytical Models on p2p streaming system to better understand
-Chunk selection strategy study and a new strategy is proposed.
-Trade off between continuity and scalability
Outline
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
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Introduction
Model & Chunk Selection Strategies
Simulation
Conclusion
Model & Chunk Selection
Strategies
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How buffer works?
server
t=1
t=2
t=3
playback
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

Server sends out chunks
sequentially.
Peer downloads one chunk
every time slot
Buffer shits ahead one
position one time slot
1
2
3
1
2
1
Buffer
……….
Model & Chunk Selection
Strategies
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M peers with the same
playback requirement
Each has a playback buffer
In each time slot, the server
randomly selects one peer and
uploads one chunk
Users’ metric is the continuity,
defined as p(n) , the probability
chunk n available
To compute p(n), recursively
compute p(i). p(i) is defined as:
p(i)=prob(position i filled)
server
playback
1/M
1
2
…………… n
2
…………… n
1/M
1
… M peers
1/M
1
2
…………… n
Model & Chunk Selection
Strategies
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Each peer’s buffer is a sliding
window
In each time slot, each peer
downloads a chunk from
server or its neighbor
q(i) = the probability Buf[i] gets
filled at this time slot, for i>1
p(1)=1/M
time=t
p(i  1)  p(i)  q(i)
P2p technology effect
1
2
p(n)=?
…………… n
sliding window
t+1
1
2
p(1)=1/M
…………… n
Model & Chunk Selection
Strategies
q(i)  w(i)  h(i)  s(i)
sliding window


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w(i) = probability peer
wants to fill Buf[i]
w(i)=1-p(i)
h(i) = probability the
selected peer has the
content for Buf[i]
h(i)=p(i)
s(i) = Buf[i] determined by
chunk selection strategy
p(1)=1/M
q(i )  w(i )  h(i )  s(i )
p(n)
peer
1
2 …… i
… n
neighbor
1
2 .….. i
…
p(1)=1/M
n
Model & Chunk Selection
Strategies

Greedy Strategy
-try to fill the empty buffer closest to playback

Rarest First Strategy
-try to fill the empty buffer for the newest chunk since p(i) is an
increasing function, this means “Rarest First”
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An example
playback
1
Buffer map
2
3
X
RF Selection
4
5
X
X
6 7
8
X
Greedy Selection
Model & Chunk Selection
Strategies
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Greedy
p(i+1)=p(i)+ (1-p(i)) * p(i) * (1-p(1)-p(n)+p(i+1))
w(i)

h(i)
s(i)
Rarest first
p(i+1)=p(i)+ (1-p(i)) * p(i) * (1-p(i))
w(i)
h(i)
s(i)
Also studied
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continuous forms for these difference equations to study
sensitivity
Simulation to validate models
Model & Chunk Selection
Strategies
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From our models we can get the following
conclusions:

Rarest First Strategy is more scalable than the Greedy
Strategy as the peer population increases.

The Greedy Strategy can achieve better continuity than
Rarest First Strategy for small number of peers.
A New Chunk Selection
Strategy
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Partition the buffer into [1,m] and [m+1,n]
Use RF for [1,m] first
If no chunks available for download by RF, use Greedy for [m+1,n]
Buffer map
1 …….. ..
m
m+1 ....……… n
First do RF

Second do Greedy
Difference equations become
1
M
p (i  1)  p (i )  p (i )(1  p (i )) 2
p (1) 
p (i  1)  p (i )  p (i )(1  p (i ))(1  p (m)  p (n)  p (i  1))
for i = 1,…,m-1
for i = m, … n-1
Outline
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Introduction
Model & Chunk Selection Strategies
Simulation
Conclusion
Comparing Different Chunk
Selection Strategies
What do you mean by “better”?
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Playback continuity: p(n) as large as possible
n
Start-up Latency: E[Chunks] / DR   p(i) / 1
i 1
Given buffer size (n) and relatively large peer population (M)
1) “Rarest first” is better in continuity!
2) “Greedy” is the best in start-up latency
3) “Mixed” is the best one of them
Simulation
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M=1000
N=40
In simulation,
 # neighbors=60
 Uploads at most 2
in each time slot
for one peer
Validate our model
Simulation
Rarest First
Mixed
Greedy
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1000 peers, 40 buffer
Compare three strategies, especially the curve for
Mixed.
Simulation
Mixed
RF
Mixed
RF
Greedy
1000 peers, buffer length varies from 20 to 40.
For different buffer sizes
 Mixed achieves best continuity than both RF and Greedy
 Mixed has better start-up latency than RF
Greedy
Simulation
RF
Greedy
RF
Greedy
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For (a), there are 40 peers. Greedy is better.
For (b), the continuity requirement is fixed at 0.93. RF is
better
Simulation
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Simulate 1000 peers,
2000 time slots
Continuity is the average
continuity of all peers
Continuity for Mixed is
more consistent, as well
highest
Mixed
Simulation
How to adapt m for the mixed strategy
Mixed
RF
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Adjust m so that p(m) achieves a target probability (e.g. 0.3)
In simulation study, 100 new peers arrive every 100 slots
m adapts to a larger value as population increases
Outline




Introduction
Model & Chunk Selection Strategies
Simulation
Conclusion
Conclusion

Related work
-Coolstreaming, BiTos

Summary work on p2p streaming:
-There are many designed p2p streaming systems, such as PPLive, PPstream
-Many measurement papers on these system
-Little work on model analysis
-Little study on chunk selection strategies

Our Contribution:
-Analytical Models on p2p streaming system to better understand
-Chunk selection strategy study
-Mixed strategy is proposed, which is better than RF or Greedy
-Trade off between continuity and scalability