Cashing In On the Caching Game

1. Cashing In On the Caching Game Replica Management in P2P Networks with Payments By Kamalika Chaudhuri Hoeteck Wee CS252 Final Project

2. The Replica Management Problem • Consider: • Replicating a proteins or genomics database • Distributing video clips of the CS252 lectures • Given a network graph: • Choose a subset of nodes which replicate the file • Objective: Minimize Cost • Placement : Cost of replicating/caching • Access: Network latency in obtaining a copy

3. Overview • The Caching Game Model [C03] • Our approach : Introduce Payments • Results • Comparison with the Caching Game Model • Conclusion

4. 1 1 1 1 1 1 M - 2 1 1 1 1 Caching Game Model [C03] Fixed Replication Cost : M Access Cost : d(i, nn(i)) Social Cost: Σ d(i, nn(i)) + kM Find replica placement that minimizes the social cost

5. 1 1 1 1 1 1 M - 2 1 1 1 1 What if People are Selfish ? • All nodes are selfish • Each node decides whether to replicate the file • “Nash Equilibria” • When no one wants to switch, given what the others are doing

6. 1 1 1 1 1 1 1 1 1 1 1 1 M - 2 M - 2 1 1 1 1 1 1 1 1 Selfishness can lead to Inefficiency Optimum: Selfish: Placement Cost: 2M Access Cost: 10 x 1 = 10 Social Cost: 2M + 10 Placement Cost : M Access Cost : 5 + 5 x (M – 1) + M - 2 Social Cost : 7M - 2

7. Cost of Selfishness • Measure of the cost of selfishness: • Price of Anarchy (PoA) = Cost at N.E / Optimal Cost • PoA determines how efficient the Nash Equilibrium configuration is • Caching Game: worst-case PoA = O(N)

8. Introducing Payments • Each node makes a bid and chooses a threshold • A node replicates ifbid received > threshold • Access and Placement Costs as before • Each node pays access cost + placement + net payment • Social cost as before

9. An Example with Payments 1 1 1 1 1 1 M - 2 1 1 1 1

10. An Example with Payments 0.4 0.4 1 1 0.4 1 M - 2 0.4 1 0.4 1

11. An Example with Payments 0.4 0.4 1 1 0.4 1 M - 2 0.4 1 0.4 1

12. Finally, in NE 0.4 0.4 0.4 0.4 0.4 0.4 M - 2 0.4 0.4 0.4 0.4 Threshold: 2.0 Threshold: M

13. 1 1 1 1 1 1 1 1 1 1 1 1 M - 2 M - 2 1 1 1 1 1 1 1 1 Pricing Helps! Without Payments: With Payments: Placement Cost: M Access Cost: 6M - 2 Social Cost: 7M – 2 PoA : 3.5 Placement Cost : 2M Access Cost : 10 Social Cost : 2M + 10 PoA : 1

14. But not in the worst case! • Any N.E in Caching Game is also a N.E in the payment model • Threshold = 0, for people caching the file • Threshold = M, for people not caching the file • All bids are 0 • Worst Case PoA (Payment Model) ≥ Worst Case PoA (Caching Game) • Can do better in the best case

15. Pricing Helps ! Line Graph - No Payments Line Graph – with Payments

16. Pricing Helps! Transit Stub – No Payments Transit Stub – with Payments

17. Pricing Helps! Power Law Graph – with Payments Power Law Graph – no Payments

18. Variants of Our Model • Facility-client model • Bounded optimistic PoA (under certain conditions) • Other relevant parameters: • Nodes of limited capacity • Varying demands • Multiple files

19. Conclusion • Presented a payment model for replica management • Observations on the payment model: • Lower mean PoA for mid-range placement costs • Matches previous work for very high and very low placement costs • A step towards analyzing possible payment schemes in P2P network applications

20. Acknowledgements • Byung Gon Chun • John Kubiatowicz • Christos Papadimitriou • Kathryn Everett • All others who gave us comments, suggestions and encouragement

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