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HY-483 Presentation

HY-483 Presentation. On power law relationships of the internet topology A First Principles Approach to Understanding the Internet’s Router-level Topology On natural mobility models. On power law relationships of the internet topology. Michalis Faloutsos

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HY-483 Presentation

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  1. HY-483 Presentation • On power law relationships of the internet topology • A First Principles Approach to Understanding the Internet’s Router-level Topology • On natural mobility models

  2. On power law relationships of the internet topology • Michalis Faloutsos • U.C. Riverside Dept. of Comp. Science Michalis@cs.ucr.edu • Petros Faloutsos • U. of Toronto Dept. of Comp. Science pfal@cs.toronto.edu • Christos Faloutsos • Carnegie Mellon Univ. Dept. of Comp. Science christos@cs.cmu.edu

  3. Previous work • Heavy tailed distributions used to describe LAN and WAN traffic • Power laws describe WWW traffic • There hasn't been any work on power laws with respect to topology.

  4. Dataset & Methodology • Three inter-domain level instances of the internet (97-98), in which the topology grew by 45%. • Router-level instance of the internet in 1995 • Min,Max and Means fail to describe skewed distributions • Linear Regression & correlation coeficients, to fit a plot to a line

  5. First power law: the rank exponent R Lemma1: Lemma2:

  6. The rank exponent in AS and router level

  7. Second power law: the outdegree exponent O • Test of the realism of a graph • metric follows a power law • exponent is close to realistic numbers

  8. The outdegree exponent O

  9. Approximation: the hop-plot exponentH • Lemma 3: • Definition deff: • Lemma 4: O (d·h^H) • Previous definition O(d^h)

  10. The hop-plot exponent H

  11. Average Neighborhood size

  12. Third power law: the eigen exponent ε • The eigen value λ of a graph is related with • the graph's adjacency matrix A (Ax = λx) • diameter • the number of edges • the number of spanning trees • the number of CCs • the number of walks of a certain length between vertices

  13. The eigenvalues exponent ε

  14. Contributions-Speculations • Exponents describe different families of graphs • Deff improved calculation complexity from previous O(d^h) to O(d·h^H) • What about 9-20% error in the computation of E?

  15. A First Principles Approach to Understanding the Internet’s Router-level Topology • Lun Li California • Institute of Technology lun@cds.caltech.edu • David Alderson • California Institute of Technologyalderd@cds.caltech.edu • Walter Willinger • AT&T Labs Research walter@research.att.com • John Doyle • California Institute of Technology doyle@cds.caltech.edu

  16. Previous work • Random graphs • Hierarchical structural models • Degree-based topology generators. • Preferential attachment • General model of random graphs (GRG) • Power Law Random Graph (PLRG)

  17. A First Principles Approach • Technology constraints • Feasible region • Economic considerations • End user demands • Heuristically optimal networks • Abilene and CENIC

  18. Evaluation of a topology • Current metrics are inadequate and lack a direct networking interpretation • Node degree distribution • Expansion • Resilience • Distortion • Hierarchy • Proposals • Performance related • Likelihood-related metrics

  19. Abilene-CENIC

  20. Comparison of simulated topologies with power law degree distributions and different features

  21. Performane-Likelihood Comparison

  22. Contributions-Speculations • Different graphs generated by degree-based models, with average likelihood, are • Difficult to be distinguished with macroscopic statistic metrics • Yield low performance • Simple heuristically design topologies • High performance • Efficiency • Robustness not incorporated in the analysis • Validation with real data

  23. On natural mobility models • Vincent Borrel • Marcelo Dias de Amorim • Serge Fdida • LIP6/CNRS – Université Pierre et Marie Curie 8, rue du Capitaine Scott – 75015 – Paris – France {borrel,amorim,sf}@rp.lip6.fr

  24. Previous work • Individual mobility models • Random Walk • Random Waypoint • Random Direction model • Boundless Simulation • Gauss-Markov model, • City Section model, • Group mobility models • Reference Point model, • Exponential Correlated • Pursue model

  25. Aspects of real-life networks • Scale free property and high clustering coefficient • Biology • Computer networks • Sociology

  26. Proposal: Gathering Mobility (1/2)Why? • Current group mobility models • Rigid • Unrealistic • Match reality using scale free distributions • Human behavior • Research on Ad-hoc inter-contacts

  27. Proposal: Gathering Mobility (2/2)The model • Individuals • Cycle behavior • Attractors • Appear-dissapear • Probability an individual to choose an attractor • Attractiveness of an attractor

  28. Experiment Scale-free spatial distribution Scale-free Population growth

  29. Contributions-Speculations • A succesive merge of individual and group behavior: • Individual movement • No explicit grouping • Vs • Strong collective behaviour • Influence by other individuals • Gathering around centers of interest of varying popularity levels • Determination of maintenance of this distribution in case of population decrease and renewal

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