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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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2 Outline File Dissemination Systems Resource Allocation Problem Generic Multiclass Model Application : Service Differentiation Application : Bandwidth diversity Summary and Open Problems
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3 File Dissemination Systems Introduction 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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4 File Dissemination Systems BitTorrent principle Tracker ? S B D C A E 1,2,3,4 3 4 2 1 1 3 2 1 2 4 4 3 2 1 Downloader Seed
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5 File Dissemination Systems BitTorrent principle Tracker S B D C A E S, C B D A 1 2 1 2 4 4 3 2 1 3 1,2,3,4 2 4 1 3 Downloader Seed
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6 File Dissemination Systems BitTorrent principle Tracker S B D C A E B D A 1 2 1 2 4 4 3 2 1 3 1,2,3,4 2 4 1 3 2 3 Downloader Seed
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7 Resource Allocation Problem Problem 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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8 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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9 Resource Allocation Problem Main 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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10 Generic Multiclass Fluid Model Original 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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11 Generic Multiclass Fluid Model Two-Class Simplified Model Based on [Qiu and Srikant 04] –Number of downloaders = fluid x i, 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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12 Generic Multiclass Fluid Model Performance metric Sojourn time T i ? Complete download probability P i ? Download cost: i = T i / P i (Download time given that the download is complete)
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13 Applications Model specialization Service differentiation: –Classes = QoS classes (1 st and 2 nd 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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14 Application: Service Differentiation Specialized multiclass model x (t) 1 1 2 2 12 min(cx 1, μηα(x 1 +x 2 ))min(cx 2, μη(1-α) ( x 1 +x 2 ))
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15 Application: Service Differentiation Transitory regime Linear switched system:
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16 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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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 3 Type 4 Type 2
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18 Application: Service Differentiation Achieving a service differentiation ratio We can solve 2 = k 1 in for a given k
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19 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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20 Application: Bandwidth Diversity Maximum Download Cost
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21 Conclusion Summary 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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22 Conclusion Open issues Global stability Validate model through simulations Extend model to any number of classes Dynamic policies Implementation of allocation policies
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23 Thank you!
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