Internet Structure ELI MEIROM ARIEL ORDA SHIE MANNOR Introduction - - PowerPoint PPT Presentation

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Internet Structure ELI MEIROM ARIEL ORDA SHIE MANNOR Introduction - - PowerPoint PPT Presentation

Jan 26, 2024 266 likes •454 views

Network Formation Games with Heterogeneous Players and the Internet Structure ELI MEIROM ARIEL ORDA SHIE MANNOR Introduction inter-AS topology Inter-AS topology Overview Network formation games AS Autonomous System Model

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SLIDE 1

Network Formation Games with Heterogeneous Players and the Internet Structure

ELI MEIROM ARIEL ORDA SHIE MANNOR

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SLIDE 2

Introduction – inter-AS topology

  • AS – Autonomous System
  • The Internet – A collection of interconnected ASs (40,000-50,000)
  • An important example of a large, dynamic, complex network
  • Known statistical properties: Node degree distribution, diameter,

clustering coefficient etc.

  • Reconstructed by BGP updates

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 3
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SLIDE 4

Modeling the inter-AS topology

  • Most models are stochastic
  • ASs are “rational”, utilitarian enterprises – Game theory / Economic

approach.

  • Previous works:
  • Homogenous players
  • Common solution concept – Nash Eq.
  • Static properties (Price of Anarchy, Price of Stability)
  • No comparison with the real AS-topology
  • Finding Nash-equilibria is NP-Hard

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 5

Overview

  • Network Formation Games:
  • A game theoretic approach for modeling the inter AS-topology
  • The cost is composed from maintaining links and distances to other players
  • Heterogeneous players
  • Static properties:
  • quality of stable solutions
  • topological constraints
  • Dynamic analysis:
  • Time evolution of topological quantities
  • Convergence rate
  • Resulting equilibria, basin of attraction
  • Data Analysis

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 6

Model

  • A network formation game
  • Each AS is a player
  • Heterogeneous players – Major players and minor players.
  • Cost:

( ) ( ) ( , ) ( , ) ( ) ( ) ( , ) ( , )

A B A B

A A j T j T B B j T j T

C i deg i c A d i j d i j C i deg i c A d i j d i j

   

     

   

Number of edges Distance between AS i and AS j Relative importance

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 7

Model (cont.)

  • Solution concept: pairwise equilibrium (pairwise – interactions)
  • Allow monetary transfers.
  • Focus on:
  • Dynamics
  • Generated topologies
  • Comparison with data.

 

,

( ) ( ) ( , ) ( , )

A B

A A j T j T ij ji j ij E

C i deg i c A d i j d i j P P

  

    

  

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 8

Statics

  • The major players form a clique (tier 1)
  • Price of Stability = 1 (or asymptotically 1)

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 9

Statics (Cont.)

  • Monetary transfers: An edge will be established iff
  • Non-empty core
  • Distance to the clique
  • Without monetary transfers:

Bounded by

  • With monetary transfers:

Bounded by

( , ) ( , ) C i E ij C j E ij      

 

2

(2 1) 4 2 1 A c A    

 

2

| | 4 | | | |

A A A

A T cA T A T  

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 10

Dynamics - Settings

  • Pairwise interactions
  • Turns, acts
  • Random vs. orderly
  • Strategic Planning
  • Timescales between cost evaluation and dynamics
  • Preference order (under monetary transfers)
  • “Free market”
  • Strategic pricing

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 11

Dynamics - Results

  • Convergence is restricted to a limited subset of equilibria
  • Fast Convergence – O(n)
  • Emergence of a new “major player”
  • By topological centrality, rather than type

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 12

Dynamics – Results (cont.)

  • Often, convergence is to the optimal state or to an asymptotically
  • ptimal state.
  • Monetary transfers does not always improve the social cost.

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 13

Data Analysis

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 14

Data Analysis (cont.)

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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Data Analysis (cont.)

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis Reliability Model Statics Peering vs. transit Detecting Epidemics Diffusive processes Previous work Rare events Local ball algorithm Simulations References

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Conclusions

  • Established a heterogeneous AS network formation game
  • Monetary transfers, different dynamical settings
  • Statics
  • Core-shell partition
  • maximal distance, price of anarchy, price of stability
  • Dynamics
  • Fast convergence to a limited subset of equilibiria
  • Explicit topologies
  • Predictions confirmed by data

Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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SLIDE 17

Thank you!

QUESTIONS?