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Cashing In On the Caching Game. Replica Management in P2P Networks with Payments. 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 - PowerPoint PPT Presentation
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Cashing In On the Caching Game
ByKamalika ChaudhuriHoeteck WeeCS252 Final Project
Replica Management in P2P Networks with Payments
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
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 1
1
1
11
1
111
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 1
1
1
11
1
111
Selfishness can lead to Inefficiency
M - 2
1 1
1
1
11
1
111M - 2
1 1
1
1
11
1
111
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
Optimum: Selfish:
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
M - 2
1 1
1
1
11
1
111
An Example with Payments
M - 2
1 1
1
1
0.4
0.4
0.4
10.40.4
An Example with Payments
M - 2
1 1
1
1
0.4
0.4
0.4
10.40.4
Finally, in NE
M - 2
0.4 0.4
0.4
0.4
0.4
0.4
0.4
0.40.40.4
Threshold: 2.0
Threshold: M
Pricing Helps!
M - 2
1 1
1
1
11
1
111M - 2
1 1
1
1
11
1
111
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
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
Pricing Helps!
Transit Stub – No Payments Transit Stub – with Payments
Pricing Helps!
Power Law Graph – no Payments
Power Law Graph – with Payments
Variants of Our Model
Facility-client model 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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