HY-483 Presentation
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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
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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 - PowerPoint PPT Presentation
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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 U.C. Riverside Dept. of Comp. Science
[email protected] Petros Faloutsos
U. of Toronto Dept. of Comp. Science [email protected]
Christos Faloutsos Carnegie Mellon Univ. Dept. of Comp.
Science [email protected]
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.
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
First power law: the rank exponent R
Lemma1:
Lemma2:
The rank exponent in AS and router level
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
The outdegree exponent O
Approximation: the hop-plot exponent H
Lemma 3:
Definition deff:
Lemma 4: O (d·h^H)
Previous definition O(d^h)
The hop-plot exponent H
Average Neighborhood size
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
The eigenvalues exponent ε
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?
A First Principles Approach to Understanding the Internet’s
Router-level Topology
Lun Li California Institute of Technology [email protected]
David Alderson California Institute of Technology
[email protected] Walter Willinger
AT&T Labs Research [email protected]
John Doyle California Institute of Technology
Previous work
Random graphs Hierarchical structural models Degree-based topology generators.
Preferential attachment General model of random graphs
(GRG) Power Law Random Graph (PLRG)
A First Principles Approach
Technology constraints Feasible region
Economic considerations End user demands
Heuristically optimal networks Abilene and CENIC
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
Abilene-CENIC
Comparison of simulated topologies with power law degree distributions
and different features
Performane-Likelihood Comparison
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
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
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
Aspects of real-life networks Scale free property and high clustering
coefficient Biology Computer networks Sociology
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
Proposal: Gathering Mobility (2/2)
The model
Individuals Cycle behavior
Attractors Appear-dissapear
Probability an individual to choose an attractor
Attractiveness of an attractor
ExperimentScale-free spatial distribution
Scale-free Population growth
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
