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The structure of the Internet 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 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? 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? Poisson distribution 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 100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 1999 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 The Faloutsos Graph 1995 Internet router topology 3888 nodes, 5012 edges, <k>=2.57 SCIENCE CITATION INDEX Nodes: papers Links: citations 25 Witten-Sander PRL 1981 1736 PRL papers (1988) 2212 P(k) ~k- ( = 3) (S. Redner, 1998) Sex-web Nodes: people (Females; Males) Links: sexual relationships 4781 Swedes; 18-74; 59% response rate. Liljeros et al. Nature 2001 Web power-laws GROWING 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 (2) The attachment is NOT uniform. (Rich get Richer) 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 Barabasi Scale-free model (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 ki ( ki ) jk j P(k) ~k-3 A.-L.Barabási, R. Albert, Science 286, 509 (1999) The Faloutsos Graph node degree for AS20000102.m 4 10 3 10 2 10 1 10 0 10 0 10 1 10 2 10 3 10 4 10 The Internet Topology as a Jellyfish Shells: 1 3 2 Core Core: High-degree clique Shell: adjacent nodes of previous shell, except 1degree nodes 1-degree nodes: shown hanging The denser the 1-degree node population the longer the stem But is it? Not necessarily ER in disguise? • Our sampling practices are far from being perfect: – Few traceroute hosts measure multitude of addresses – The problem of the blind mice… – However, the Internet is probably much more broad scale than ER (the Jellyfish still stands) Past Attempts • Measurements were done from a few (up to 10s) points ►too many links are missed – especially in the periphery - Hidden peer connections ►measurements traffic was too dense • Some maps were created based on central databases ►data was not up to date Past Measurements DIMES@Home Distributed Internet MEasurement & Simulation • Creating a distributed platform that will enable: – Global scale measurement of Internet graph structure, packet traffic statistics, demography – Simulation of Internet behavior under different conditions (let the net simulate itself) – Simulation of the Internet future: • Active networks • Novel routing algorithms • Distributed resource allocation – grid computing • P2P DIMES@Home Challenges • Get A growing community of users to download and install our DIMES agent • Optimize the architecture: – Minimize the number of measurements – Expedite the discovery rate • • • • Flying under the NOC radar screens Study self-emerging agent collaboration Data analysis and more …. When will DIMES solve the puzzle? • Connectivity statistics (links power law) including hidden links – 12 months • Delay map – 12 months • Topology (K-Core, small worldness) including hidden links – 18 months • Corresponding I/O traffic statistics – 24 months – Usage mode statistics (e.g. HTTP vs. P2P) – Traffic flow mapping you’ll just have to wait and see…