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Florence Clévenot-Perronnin, Philippe Nain and Keith Ross Performance 2005

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. Outline. File Dissemination Systems Resource Allocation Problem

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Florence Clévenot-Perronnin, Philippe Nain and Keith Ross Performance 2005

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  1. 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

  2. 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

  4. Tracker File Dissemination SystemsBitTorrent principle 1 Downloader 3 3 A 2 1 1 B Seed 4 C 2 3 1,2,3,4 2 2 D 4 S E 1 4 ?

  5. Tracker File Dissemination SystemsBitTorrent principle 1 Downloader 3 3 A A 2 1 1 B B Seed 4 C 2 3 1,2,3,4 2 2 D D 4 S E 1 4 S, C

  6. Tracker File Dissemination SystemsBitTorrent principle 1 Downloader 3 3 A A 2 1 1 B B Seed 4 C 2 3 1,2,3,4 2 2 2 D D 4 S E 1 4 3

  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

  8. Resource Allocation Problem Objective • Goals: • Determine stability conditions • Optimize individual resource allocation policy for various problems: • Constraints: • Independently of seed connection time

  9. 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)

  10. Number of downloaders = x(t) (regardless how many chunks they have) Number of seeds = y(t) Download abort q Generic Multiclass Fluid ModelOriginal model [Qiu & Srikant 04] l x(t) q min(cx, m(hx + y)) y(t) g

  11. 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) = ai • P (class i selects class j≠ i peer) = 1 – ai • Download abort qi • Simplification : No seeds( gi= ∞)

  12. Generic Multiclass Fluid Model Performance metric • Sojourn time Ti ? • Complete download probability Pi?  Download cost: fi = Ti / Pi (Download time given that the download is complete)

  13. ApplicationsModel specialization • Service differentiation: • Classes = QoS classes (1st and 2nd class) • Both classes have the same bandwidth • Allocation policy: a1 = 1- a2 = a • Bandwidth diversity: • Classes = bandwidth classes • Both classes have same QoS subscription • Allocation policy: a1 = a2 = a

  14. Application: Service Differentiation Specialized multiclass model l l 1 2 a x (t) x (t) a 1- a 1 2 1- a q q 2 1 min(cx1, μηα(x1+x2)) min(cx2, μη(1-α)(x1+x2))

  15. Application: Service Differentiation Transitory regime • Linear switched system:

  16. Application: Service Differentiation Results • Local stability proved • Unique stable equilibrium • Allocation policy a determines: • Type of equilibrium • Download Cost fi for each class • Closed-form expression for fi

  17. 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 Type 2 Type 3 Type 4 a

  18. Application: Service DifferentiationAchieving a service differentiation ratio • We can solve f2 = kf1 in a for a given k

  19. Application: Bandwidth DiversityResults • Results: • Local stability proved • Several expressions for download cost • Steady-state : (graphical) optimization of a • Problems : • Steady-state may depend on initial conditions • Analysis depends on parameters

  20. Application: Bandwidth DiversityMaximum Download Cost

  21. 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

  22. ConclusionOpen issues • Global stability • Validate model through simulations • Extend model to any number of classes • Dynamic policies • Implementation of allocation policies

  23. Thank you!

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