Cashing In On the Caching Game
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Transcript of Cashing In On the Caching Game
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
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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
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Selfishness can lead to Inefficiency
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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
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An Example with Payments
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An Example with Payments
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Finally, in NE
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Threshold: 2.0
Threshold: M
Pricing Helps!
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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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