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

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 Statics Dynamics • The Internet – A collection of interconnected ASs (40,000-50,000) Data Analysis • 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 Modeling the inter-AS topology Network formation games Model • Most models are stochastic Statics Dynamics Data Analysis • 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 Overview Network formation games Model • Network Formation Games: Statics Dynamics • A game theoretic approach for modeling the inter AS-topology Data Analysis • 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

Model Inter-AS topology Overview Network formation games • A network formation game Model Statics Dynamics • Each AS is a player Data Analysis • Heterogeneous players – Major players and minor players. • Cost:      ( ) ( ) ( , ) ( , ) C i deg i c A d i j d i j A A   j T j T A B      ( ) ( ) ( , ) ( , ) C i deg i c A d i j d i j B B   j T j T A B Distance between Number of edges AS i and AS j Relative importance

Model (cont.) Inter-AS topology Overview Network formation games • Solution concept: pairwise equilibrium ( pairwise – interactions ) Model Statics Dynamics • Allow monetary transfers. Data Analysis           ( ) ( ) ( , ) ( , ) C i deg i c A d i j d i j P P A A ij ji    , j T j T j ij E A B • Focus on: • Dynamics • Generated topologies • Comparison with data.

Statics Inter-AS topology Overview • The major players form a clique (tier 1) Network formation games Model Statics Dynamics Data Analysis • Price of Stability = 1 (or asymptotically 1)

Inter-AS topology Overview Statics (Cont.) Network formation games Model • Monetary transfers: An edge will be established iff Statics Dynamics Data Analysis       ( , ) ( , ) 0 C i E ij C j E ij • Non-empty core • Distance to the clique • Without monetary transfers:       Bounded by 2 (2 1) 4 2 1 A c A • With monetary transfers:   2 Bounded by   | | 4 | | | | A T cA T A T A A A

Dynamics - Settings Inter-AS topology Overview Network formation games • Pairwise interactions Model Statics Dynamics • Turns, acts Data Analysis • Random vs. orderly • Strategic Planning • Timescales between cost evaluation and dynamics • Preference order (under monetary transfers) • “Free market” • Strategic pricing

Dynamics - Results Inter-AS topology Overview Network formation games • Convergence is restricted to a limited subset of equilibria Model Statics Dynamics • Fast Convergence – O(n) Data Analysis • Emergence of a new “major player” • By topological centrality, rather than type

Dynamics – Results (cont.) Inter-AS topology Overview Network formation games • Often, convergence is to the optimal state or to an asymptotically Model Statics optimal state. Dynamics Data Analysis • Monetary transfers does not always improve the social cost.

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

Data Analysis (cont.) Inter-AS topology Overview Network formation games Model Statics Dynamics Data Analysis

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

Inter-AS topology Overview Conclusions Network formation games Model • Established a heterogeneous AS network formation game Statics Dynamics Data Analysis • 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

Thank you! QUESTIONS?