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

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, =2.57

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

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

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 : A t 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 k i of that node A.-L.Barabási, R. Albert, Science 286, 509 (1999) P(k) ~k -3

The Faloutsos Graph

The Internet Topology as a Jellyfish  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 Core Shells: 1 2 3

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

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

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…