Service Capacity of Peer to Peer Networks

1
Service Capacity of Peer to Peer Networks

• Xianying Yang
• Gustavo de Veciana
• IEEE INFOCOM 2004

2
Outline

• Introduction
• Transient Analysis of Service Capacity
• Steady State Analysis of Average Delays
• Trace Measurements and Traffic Charaterization
• Conclusion

3
Introduction

• Service Capacity
• The number of peers available to serve a document
• Throughput of P2P system
• Average delay
• Rate of dissemination

4
Introduction
5
Introduction

• The service capacity in these two regimes depends
  on a number of factors
• data management
• Partitioned
• concurrent downloading from multiple peers
• peer selection
• admission and scheduling policy
• limiting the number of concurrent downloaders
• traffic
• the dynamics of how peers stay online and/or
  delete documents.

6
Introduction

• Related Work
• Previous research P2P design , traffic
  measurement , workload analysis
• Peer selection schemes using measurements
• Recently analytical models to performance

7
Introduction

• This papers contributions
• Model the transient service capacity
• By deterministic and branching process
• Consider how to optimize service policies to
  maximize the service capacity growth rate
• Simple steady state model
• Captures the impact of peer departures or
  document deletions

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Transient Analysis of Service Capacity
Deterministic
0
Time

• N-1 users want a doc
• N2k
• S bits per request
• S(n-1) bits total
• Time interval ? at s/b seconds
• Exponential growth
• Ability to serve large bursts
• Average delays scales by lg(n)

Rate
1
0
Count
1
9
Transient Analysis of Service Capacity
Deterministic
1
Time

• N-1 users want a doc
• N2k
• S bits per request
• S(n-1) bits total
• Time interval ? at s/b seconds
• Exponential growth
• Ability to serve large bursts
• Average delays scales by lg(n)

Rate
1
0
Count
2
1
10
Transient Analysis of Service Capacity
Deterministic
2
Time

• N-1 users want a doc
• N2k
• S bits per request
• S(n-1) bits total
• Time interval ? at s/b seconds
• Exponential growth
• Ability to serve large bursts
• Average delays scales by lg(n)

Rate
2
0
Count
4
1
2
2
11
Transient Analysis of Service Capacity
Deterministic
3
Time

• N-1 users want a doc
• N2k
• S bits per request
• S(n-1) bits total
• Time interval ? at s/b seconds
• Exponential growth
• Ability to serve large bursts
• Average delays scales by lg(n)

Rate
4
0
Count
8
1
2
3
3
2
3
3
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Transient Analysis of Service Capacity Multipart

• M identical size chunks
• Service completions at s/mb??m seconds
• Optimization, peers favor others with no chunks
• At time k, system is partitioned into k sets
  Ai,i1k.
• Ai2k-i
• Ai corresponds to peers who have only received
  the ith chunk

A4
A2
A3
A1
Time slot k
13
Transient Analysis of Service Capacity Multipart

• M identical size chunks
• Service completions at s/mb??m seconds
• Optimization, peers favor others with no chunks
• At time k, system is partitioned into k sets
  Ai,i1k.
• Ai2k-i
• Ai corresponds to peers who have only received
  the ith chunk

A4
A2
A3
Time slot k1
14
Peer groups
A1
A2
A3
A4
S
t0
t1
t2

tk
15
Transient Analysis of Service Capacity Multipart

• Delay is in effect reduced by a factor of m
• Large values of m better, but require more
  network overhead
• Congestion, bandwidth bottleneck ignored in this
  model

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Branching Process Model

• Let Nd(t)peers serving document d at time t.
• Ti is a random variable, transfer time
• ET?1/?
• Age dependent branching process model, v2

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Branching Process Model
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Branching Process Model

• ????are growth characteristics
• Depend on the distribution of the transfer times
  T
• If T is exponentially distributed, ??????????
• If T is deterministic, ?????ln2???????
• Exponential distribution increases growth
  exponent
• In the exponential case ??? and in deterministic
  case ?????ln2lt ?

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Modeling parallel uploads when vgt2

• With the proposed re-scaling of the transfer
  times density
• According to the theorem the growth rate b must
  satisfy
• The growth rate b might decrease if v is large
• ??is inversely proportional to v
• Intuition limit number of downloads at each peer

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Uncooperative peers under a parallel uploading
scenario

• Peers exit system with probability 1-??upon
  completion
• Family size is a random variable with mean v?
• If v??lt1, system becomes extinct
• So maximize the growth rate
• Avoid extinction select a family size
  satisfying v?gt1
• System increases slowly with increasing v
• When peers exit, allowing multiple upload ensures
  document availability and system growth

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Role of multi-part downloads on transient capacity

• The growth in service capacity for a given chunk
• Growth rate increases from b to bm
• Given a burst of demands q , the time to complete
  q jobs is roughly
• Delay factor is reduced by 1/m
• Allowing multipart downloads increases
  performance by factor m
• Above multi-part model is quite optimistic
• Assumes peers are not simultaneously sharing
  multiple parts of files
• Such concurrency would slow down file sharing

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Discussion Optimizing P2P systems to deal with
flash crowds

• Service capacity grows as quickly as possible
• i.e. b is high
• Multi-part downloads
• Parallel upload
• Not clear unless peers tend to be uncooperative
• Media grid , file sharing application
• Credit system

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Summary
Multipart
Branching
Deterministic

• Time interval ???m
• Delays bounded by (??m)?log n
• Space partitioned into sets
• More chunks is faster
• Network overhead is high

• Time interval ? is a random variable
• Delays bounded by log ?
• Parameters ??? determine operation
• Accounts for congestion, churn

• Time interval ??for transfer
• N2k
• Delays bounded by ??log n
• Exponential growth

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Markov Chain

• Distant past irrelevant with knowledge of recent
  past
• Sequence of random variables, X1Xn
• Transition matrix
• Eigenvectors determine stable state conditions

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Markov Chain
Sunny
Rainy
P(RainySunny)
Sunny
Rainy
P(RainyRainy)
P(SunnyRainy)
P(SunnySunny)
Weather, day 0
Weather, day 1
Weather, day 2
Weather, day n
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Markov Model

• Request Poisson process with rate
• State
• xof peers requesting
• y peers hosting
• Multipart files
• Partial peers contribute at rate
• Total rate
• Exponentially distributed
• Full service rate
• Exit rate

i
Q
S0
Si
(1)
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Markov Model
Offered load Exit rate
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Markov Model
Offered load Exit rate
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Estimating effective throughput realized by peers

• Seeds/downloaders
• The total aggregate throughput
• is upload ratio of downloader to seed
• System with high ? leverages capacity
• Marginal change of system performance low when
  offered load is high
• Likely to depend on the file size s

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Trace Measurements and Traffic Charaterization

• BitTorrent (BT)
• a document is introduced by a single peer which
  is encouraged to stay in system for a long period
  of time
• Chunk size 220 bytes
• Credit system

• BT tracker
• updated approximately every 5 minutes
• simultaneously tracks about 150200 files

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• seeds
• refers to the number of peers with complete
  replicas of a document that are currently on
  line
• downloaders
• is the number of peers currently downloading the
  document
• finished
• is the number of completed downloads so far
• TX vol
• is the cumulative data volume transferred
  associated with the given document
• throughput
• is the sum of the throughputs seen by peers
  currently downloading a document
• life
• is the time that has elapsed since the document
  was first introduced in the system.

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Trace Measurements and Traffic Charaterization

• B.Methodology
• System capacity
• Throughput and delay
• The KByte transmission delay

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Is there an exponential growth in the transient
service capacity and average throughput per peer?
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Is there an exponential growth in the transient
service capacity and average throughput per peer?
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How does the offered load impact average
throughput performance per peer?
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Impact of file size on the per seed and
downloaders effective throughput?
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Impact of file size on the per seed and
downloaders effective throughput?
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Discussion

• Transient
• Initial flash crowd
• the overall service capacity quickly catches up
  with the demands
• Steady state
• Performance improves in the popularity of the
  file
• Subsequenct burst of demands does not lead to a
  dramatic exponential growth
• Maybe lack scalability
• Signaling overheads
• Or the result of a credit system

40
Conclusion

• Model the service capacity of a P2P system in two
  regimes
• Suggest at higher offered loads and with
  cooperative users improve the system performance
• Various techniques might help improve P2P
  performance
• Multi-part combined with parallel uploading when
  properly optimized
• Particularly peer exit at high rate
• Credit system
• A simple credit system based on short term
  history of peers may limit the system