1. Cashing In On the Caching Game
Replica Management in P2P Networks with Payments
TODO:
Check the font sizes
2. Plug in brite simulation graphs
3. Ask Gon about the parameters for the ts and brite graph
4. Ask Gon for examples of the type of files one might want to replicate
5. Ask Gon about line graph 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
-less text
-examples:

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

4. 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
M - 2 1

5. 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
M - 2 1

6. Selfishness can lead to Inefficiency
Optimum:
Selfish:
M - 2 1
M - 2 1
Placement Cost: 2M
Access Cost: 10 x 1 = 10
Social Cost: 2M + 10
Placement Cost : M
Access Cost : 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 if bid received > threshold
Access and Placement Costs as before
Each node pays access cost + placement + net payment
Social cost as before

9. An Example with Payments1 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
0.4 1 1

11. An Example with Payments
0.4
0.4 1 1
0.4 1
M - 2
0.4
0.4 1 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. Pricing Helps! Without Payments: With Payments: M - 2 1 M - 2 1
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
Line Graph: 10 nodes on a straight line (unit distance apart), 10 overlay nodes
Talk about: PoA is better with pricing
Undersupply is less (due to payments)
The jagged line is because this is the worst case among 100 random samples (more samples later….)
Payments do better in the mid-range of placement costs; they don’t do better when the costs are too large or too small. In the first case, there is only one replica in the whole network, so NE depends totally on the initial conditions. In the second case, everyone replicates the file.
Line Graph - No Payments
Line Graph – with Payments

16. Pricing Helps! Transit Stub – No Payments Transit Stub – with Payments
Poa is slightly better w/payments
Transit Stub – No Payments
Transit Stub – with Payments

17. Pricing Helps! Power Law Graph – with Payments
Brite Graph
Thing to note: Over supply in NE
Power Law Graph – with Payments
Power Law Graph – no Payments

18. Variants of Our Model Facility-client model Other relevant parameters:
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

21. not π [ This slide left for e ]