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

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:

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

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

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

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 : 5 + 5 x (M – 1) + M - 2 Social Cost : 7M - 2

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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