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

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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!