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Understanding Internet Topology: Router Connection, Efficiency, and Optimization

Learn about the structure of the Internet, router connections, communication protocols, network topologies, and graph models such as Erdös-Rényi, Waxman, and scale-free networks. Explore the dynamics of Internet topology and its impact on efficiency and protocol optimization.

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Understanding Internet Topology: Router Connection, Efficiency, and Optimization

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  1. The structure of the Internet

  2. How are routers connected? • Why should we care? • While communication protocols will work correctly on ANY topology • ….they may not be efficient for some topologies • Knowledge of the topology can aid in optimizing protocols

  3. The Internet as a graph • Remember: the Internet is a collection of networks called autonomous systems (ASs) • The Internet graph: • The AS graph • Nodes: ASs, links: AS peering • The router level graph • Nodes: routers, links: fibers, cables, MW channels, etc. • How does it looks like?

  4. Poisson distribution Random graphs in Mathematics The Erdös-Rényi model • Generation: • create n nodes. • each possible link is added with probability p. • Number of links: np • If we want to keep the number of links linear, what happen to p as n?

  5. The Waxman model • Integrating distance with the E-R model • Generation • Spread n nodes on a large enough grid. • Pick a link uar and add it with prob. that exponentially decrease with its length • Stop if enough links • Heavily used in the 90s

  6. 100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100

  7. The Faloutsos brothers Measured the Internet AS and router graphs. Mine, she looks different! Notre Dame Looked at complex system graphs: social relationship, actors, neurons, WWW Suggested a dynamic generation model 1999

  8. The Faloutsos Graph1995 Internet router topology3888 nodes, 5012 edges, <k>=2.57

  9. 25 2212 SCIENCE CITATION INDEX Nodes: papers Links: citations Witten-Sander PRL 1981 1736 PRL papers (1988) P(k) ~k- ( = 3) (S. Redner, 1998)

  10. Sex-web Nodes: people (Females; Males) Links: sexual relationships 4781 Swedes; 18-74; 59% response rate. Liljeros et al. Nature 2001

  11. Web power-laws

  12. (2) The attachment is NOT uniform. A node is linked with higher probability to a node that already has a large number of links. Examples : WWW : new documents link to well known sites (CNN, YAHOO, NewYork Times, etc) Citation : well cited papers are more likely to be cited again SCALE-FREE NETWORKS (1) The number of nodes (N) is NOT fixed. Networks continuously expand by the addition of new nodes Examples: WWW : addition of new documents Citation : publication of new papers

  13. Scale-free model P(k) ~k-3 (1)GROWTH: At every timestep we add a new node with m edges (connected to the nodes already present in the system). (2)PREFERENTIAL ATTACHMENT :The probability Π that a new node will be connected to node i depends on the connectivity ki of that node A.-L.Barabási, R. Albert, Science 286, 509 (1999)

  14. The Faloutsos Graph

  15. The Internet Topology as a Jellyfish Shells: Core 1 • Core: High-degree clique • Shell: adjacent nodes of previous shell, except 1-degree nodes • 1-degree nodes: shown hanging • The denser the 1-degree node population the longer the stem 2 3

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