Mapping the Internet Topology Via Multiple Agents

What does the internet look like?

Why do 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

Topics

• Power laws in the internet topology

• Sampling bias in existing topology measurements

• The DIMES project

• Potential applications

• Open issues

Mapping the Internet

• Required characteristics:– connectivity– delays

• Metrics– In/Outdegree– Distance (delay – problematic definition)

Problem definition

G – (un)directed graphN – number of nodesE – number of edgesdv – outdegree of a node v

fd – frequency of an outdegreeP(h) – number of pairs in the “h-hop

neighborhood”

On Power-law Relationships of the Internet Topology

Oct. 1999, Faloutsos Bros.

Mapped the internet at the AS and router level using BGP route views

Data sets: – Nov. ’97: 3015 nodes, 5156 edges– Apr. ’98: 3530 nodes, 6432 edges– Dec. ’98: 4389 nodes, 8256 edges

Outdegree Exponent Power Law

fd ~ d^σ

Other places that people look for power laws…

SCIENCE CITATION INDEX

( = 3)

Nodes: papers Links: citations

(S. Redner, 1998)

P(k) ~k-

2212

25

1736 PRL papers (1988)

Witten-SanderPRL 1981

Sex-web

Nodes: people (Females; Males)Links: sexual relationships

Liljeros et al. Nature 2001

4781 Swedes; 18-74; 59% response rate.

Recall – the Faloutsos graph

Is It Really Power Law?

• Sampling bias could exist

• Crovella article title

• Target – find out if bias exists in prevailing measurement methods, and identify the sources for this bias.

• Configuration – graph model, sampling method, distributions, why this is similar to currently used methods

Results

• Erdos – Renyi + graphs

Sources of sampling bias

• Disproportional sampling of nodes

• Disproportional sampling of edges

• Conclusion

• Identify problems in existing measurement methods (Faloutsos, Caida)

Analysis of Bias Cause

• Explanation– Better coverage with more measurement

sources

DIMES

• Targets

• How we try to solve the problem

DIMES Platform

• Description

• Screenshot

Internet according to DIMES

• maps

Application

• Research– Simulations

• Developing new algs, protocols• Evolution (how will the internet look like in 2020?)• Testing new tools, manufacturing scenarios

– “pure” research• Studying the internet “behavior”, growth• Developing models to describe it

More Application

• Potentially commercial– Improve existing algs’ using knowledge about

the characteristics of the internet.• Multicast alg’• Low – priority packet routing

– Identify (and work around?) network vulnerabilities

Open Issues

• Measuring delays– Asymmetry– round trip is problematic– triangle inequality doesn’t necessarily hold

• Mapping interfaces to server

• Identifying POPs

• Identifying motiffs