PRESENTATION OUTLINE
1. INTRODUCTION.
2. MODULARITY.

Traffic Dynamic in Modularity Structure ofComplex Networks.

3. SIMULATION RESULTS.
1) Coarse grained traffic fluctuation.

Dr. Suyong Eum2) Fine grained traffic fluctuation.
4. CONCLUSIONS.

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 1INTRODUCTION

Slide 2Modularity: Discover & Quantification
 Split a network into many sub-networks.

 People have tried to understand robustness of a systemfrom its topological properties such as degree distribution.

 M.E.J. Newman and M. Girvan, PRE 2003.

 However, this information mainly focuses on theconnectivity of network components.

Strength ofModularity

Module 1

 This phenomenon is similar to a saying that people
cannot see the forest for the trees.
 Forest? -> Topological structure such as modularity orhierarchy.

Iteration

 We are going to talk about how modularized structure
impacts on network robustness from a traffic fluctuation
point of view.

Q_ M = ∑(eii − ai )2Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong EumiModule 3

Module 2

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 3

Scale free models: BA & FKP models

Two different types of topologies for simulation.

BA Degree of a node (k):Number of links that a node has Scale-free property:

k=2node (vertex)

follows the POWER LAW

P ( k ) ∝ k −γ

4Large
k =Degree
2link (edge)

1

3
6

1

k=2

FKP02

SmallDegreek = 4

Probability distribution of degree

Slide 4075

k=2N BA model: Preferential attachment mechanism.

∑ FKP model: Optimization mechanism.
Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

kii=N

Slide 5Degree of node i

ki Total degree

1

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 61

Coarse grained traffic fluctuation – (1)Coarse grained traffic fluctuation – (2)

B

E

F

C

DGH

IJM

NK

LOPTOTINTEXT=INT

TOTSTD[N]A

α : Gradient
STD[N]

 Menezes & Barabashi “Fluctuations in network dynamics”
 Traffic fluctuation is divided into the internal and externalfluctuations.
 INTERNAL : Topology,
 EXTERNAL: Traffic burstiness

EXT+Traffic burstiness

E[N]

STD[V ]i = E[V ]i

M(t) = <M> + ∆M sin(kt)Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

STD

Slide 8

Coarse grained traffic fluctuation – (5) We increases traffic burstinessbut keeps the topology.

BA

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 7Coarse grained traffic fluctuation – (3)αE[N]Random routing

FKPBA

 That is why we see multiple reddata sets but only one blue dataset.

E

αFKP
Shortest path routing

FKPBABAFKP

Traffic burstness
Traffic burstiness
Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 9Fine grained traffic fluctuation – (1)Slide 10

Fine grained traffic fluctuation – (3)η ( p) Saturation pointη ( p)

FKPBAP (Offered Traffic)

Saturation pointη ( p ) = limt→ ∞1 < ∆N >∆tSlowρS

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 11γ

High packet process
Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 122

CONCLUSIONS.

QUESTIONS?

 We investigated traffic fluctuation in modularized andnon-modularized topologies with two different
simulation scenarios, viz coarse and fine.

Thanks foryour attention

 In the coarse traffic scenario, we found that atopology with strong modularity structure tends toexperience high traffic fluctuation. However, thisfluctuation is observed only when traffic is routedrandomly. (Robust against intruder)

Presenter : Dr. Suyong Eum
E-mail: suyong@ist.osaka-u.ac.jp

 With fine traffic, we found that a topology with highmodularity structure becomes saturated earlier as
traffic load increases than one with non-modularized
structure. (Bottleneck)
Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Advanced Network Architecture Research Group inGraduated School of Information and Technology,
OSAKA University.

Slide 13

Copyright ⓒ 2008 OSAKA UNIVERSITY. All rights reserved.
Prepared by Dr. Suyong Eum

Slide 143