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

2 Outline File Dissemination Systems Resource Allocation Problem Generic Multiclass Model Application : Service Differentiation Application : Bandwidth diversity Summary and Open Problems

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

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

5 File Dissemination Systems BitTorrent principle Tracker S B D C A E S, C B D A ,2,3, Downloader Seed

6 File Dissemination Systems BitTorrent principle Tracker S B D C A E B D A ,2,3, Downloader Seed

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

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 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)

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 ))  

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 = ∞)

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)

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 = 

14 Application: Service Differentiation Specialized multiclass model x (t)  1 1     min(cx 1, μηα(x 1 +x 2 ))min(cx 2, μη(1-α) ( x 1 +x 2 ))

15 Application: Service Differentiation Transitory regime Linear switched system:

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

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

18 Application: Service Differentiation Achieving a service differentiation ratio We can solve  2 = k  1 in  for a given k

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

20 Application: Bandwidth Diversity Maximum Download Cost

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

22 Conclusion Open issues Global stability Validate model through simulations Extend model to any number of classes Dynamic policies Implementation of allocation policies

23 Thank you!