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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