multiclass p2p networks: static resource allocation for service differentiation and bandwidth...
TRANSCRIPT
Multiclass P2P Networks: Static Resource Allocation for Service Differentiation and Bandwidth
Diversity
Florence Clévenot-Perronnin, Philippe Nain and Keith Ross
Performance 2005 Juan-les-Pins, October 5-7 2005
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Outline
• File Dissemination Systems
• Resource Allocation Problem
• Generic Multiclass Model
• Application : Service Differentiation
• Application : Bandwidth diversity
• Summary and Open Problems
3
File Dissemination SystemsIntroduction
• Example: BitTorrent• Peer-to-peer file diffusion
– Server points on a tracker– Published file is split into N chunks– Downloaders share (upload) the chunks
they already have
• Upload capacity scales with downloader population
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File Dissemination SystemsBitTorrent principle
Tracker?
S
B
D
C
A
E
1,2,3,4
3
4
2
1
1
3
2
1
2
4
43
21
Downloader
Seed
5
File Dissemination SystemsBitTorrent principle
Tracker
S
B
D
C
A
ES, C
B
D
A
1
2
1
2
4
43
21
3
1,2,3,42
4
13Downloader
Seed
6
File Dissemination SystemsBitTorrent principle
Tracker
S
B
D
C
A
E
B
D
A
1
2
1
2
4
43
21
3
1,2,3,42
4
13
2
3
Downloader
Seed
7
Resource Allocation ProblemProblem description
• Number of uploads capped (4)• Tit-for-tat mechanism• Optimistic unchoke• Possible secondary criteria:
– Missing chunks [Felber and Biersack 04]– Available bandwidth– Subscribed QoS
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Resource Allocation Problem Objective
• Goals:– Determine stability conditions
– Optimize individual resource allocation policy for various problems:
• Constraints:– Independently of seed connection time
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Resource Allocation ProblemMain Assumptions
• 2 classes of users
• In each class : Upload rate ≤ download rate (ex: ADSL)
• Users cooperate (i.e. send at full upload capacity)
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Generic Multiclass Fluid ModelOriginal model [Qiu & Srikant 04]
• Number of downloaders = x(t) (regardless how many chunks they have)
• Number of seeds = y(t)
• Download abort
x(t)
y(t)
min(cx, (x + y))
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Generic Multiclass Fluid Model Two-Class Simplified Model
• Based on [Qiu and Srikant 04]
– Number of downloaders = fluid xi , i =1,2
• Allocation Policy: – P (class i selects class i peer) = i
– P (class i selects class j ≠ i peer) = 1 – i
• Download abort i
• Simplification : No seeds ( i= ∞)
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Generic Multiclass Fluid Model Performance metric
• Sojourn time Ti ?
• Complete download probability Pi ?
Download cost: i = Ti / Pi
(Download time given that the download is complete)
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ApplicationsModel specialization
• Service differentiation:– Classes = QoS classes (1st and 2nd class)– Both classes have the same bandwidth
– Allocation policy: 1 = 1- 2 =
• Bandwidth diversity: – Classes = bandwidth classes– Both classes have same QoS subscription
– Allocation policy: 1 = 2 =
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Application: Service Differentiation Specialized
multiclass model
x (t) x (t)
1
1
2
2
1 2
min(cx1, μηα(x1+x2)) min(cx2, μη(1-α)(x1+x2))
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Application: Service Differentiation Transitory regime
)()1(,min
)(,min
2122222
2111111
xxcxxt
x
xxcxxt
x
• Linear switched system: BxAx x )(
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• Local stability proved
• Unique stable equilibrium
• Allocation policy determines: – Type of equilibrium
– Download Cost i for each class
• Closed-form expression for i
Application: Service Differentiation Results
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Application: Service Differentiation Type of equilibrium• Type 2 (resp.3) :
– Download bottleneck for class 1 (resp.2)– Upload bottleneck for class 2 (resp.1)
• Type 4 : – Upload bottleneck in both classes
D
c )(1 12
D
c )( 21
Type 3 Type 4 Type 2
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Application: Service Differentiation
Achieving a service differentiation ratio• We can solve 2 = k 1 in for a
given k
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Application: Bandwidth Diversity
Results• Results:
– Local stability proved– Several expressions for download cost
– Steady-state : (graphical) optimization of
• Problems :– Steady-state may depend on initial
conditions– Analysis depends on parameters
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Application: Bandwidth Diversity
Maximum Download Cost
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ConclusionSummary
• Proposed a multi-class model for resource allocation problem in P2P networks
• Obtained closed-form expression for service differentiation in a practical “worst case”
• Proposed numerical optimization in heterogeneous systems
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ConclusionOpen issues
• Global stability
• Validate model through simulations
• Extend model to any number of
classes
• Dynamic policies
• Implementation of allocation policies
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Thank you!