Using Complex Networks for Mobility Modeling and Opportunistic Networking: Part II

Eurecom, Sophia-AntipolisThrasyvoulos Spyropoulos / [email protected]

Using Complex Networks for Mobility Modeling and Opportunistic Networking: Part II

Thrasyvoulos (Akis) SpyropoulosEURECOM

Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis

Outline Motivation

Introduction to Mobility Modeling

Complex Network Analysis for Opportunistic Routing

Complex Network Properties of Human Mobility

Mobility Modeling using Complex Networks

Performance Analysis for Opportunistic Networks

2


Social Properties of Real Mobility Datasets Different origins: AP associations, Bluetooth scans

and self- reported

Gowalla dataset

~ 440’000 users

~ 16.7 Mio check-ins to ~ 1.6 Mio spots

473 “power users” who check-in 5/7 days3


It’s a “small world” after all!

Small numbers (in parentheses) are for random graph Clustering is high and paths are short!

4


Community Structure Louvain community detection algorithm

All datasets are strongly modular! clear community structure exists

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Community Sizes

6


Contact Edge Weight Distribution

7


Degree Distribution

8


Outline Motivation






9


Mobility Models with the “Right” Social Structure

Q: Do existing models create such (social) macroscopic structure?A: Not really

Q: How can we create/modify models to capture correctly?A: The next part of the lesson

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Community-based Mobility (Spatial Preference) Multiple Communities (house, office, library, cafeteria) Time-dependency

House(C1)

Community (e.g. house, campus)

p11(i)

p12(i)

Rest of the network

p21(i)

OfficeC2

LibraryC3

p23(i)

p32(i)

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Social Networks Graph model: Vertices = humans, Weighted Edges =

strength of interaction

12


Local trips: inside community Roaming/Remote trips: towards another community TVCM (left): local and roaming trips based on simple

2-state Markov Chain. HCMM (right): roaming trips (direction and frequency)

dependent on where your “friends” are13


Mapping Communities to Locations Assume a grid with different locations of interest

Geographic consideration might gives us the candidate locations

14


Mobility Between Communities

C}{j

wp Cj

ij(i)C

pc(i) = attraction of node i to community/location c

p2(B)(t)

p1(B)(t)

p3(B)(t)

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Outline Motivation






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Assumption 1) Underlay Graph Fully meshedAssumption 2) Contact Process Poisson(λij), Indep.Assumption 3) Contact Rate λij = λ (homogeneous)

Nln(N)

λ1ETdst

Analysis of Epidemics: The Usual Approach

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Modeling Epidemic Spreading: Markov Chains (MC)

2-hop infection

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How realistic is this?A Poisson Graph

A Real Contact Graph(ETH Wireless LAN trace)

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Arbitrary Contact Graphs

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aaa

aa

a

aaCjCiijC

CjCiij

C

CjCiij

akk CTE

,,,

1,

min

11max1][

Bounding the Transition Delay

What are we really saying here?? Let a = 3 how can split the graph

into a subgraph of 3 and a subgraph of N-3 node, by removing a set of edges whose weight sum is minimum?

21


A 2nd Bound on Epidemic Delay

NN

aNaaNaDE

N

a

N

a aepid

ln1)(

1)(

1][11

)(

minmin ,

aNaaa

a CjCiijC

a

Φ is a fundamental property of a graphRelated to graph spectrum, community structure

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Distributed Estimation and Optimization

Distributed Estimation Central problem in many (most?) DTN problems Routing [Spyropoulos et al. ‘05] : estimate total number of nodes Buffer Management [Balasubramanian et al. ‘07] : estimate number

of replicas of a message General Framework [Guerrieri et al. ‘09]: study of pair-wise and population

methods for aggregate parameters Distributed Optimization

Most DTN algorithms are heuristics; no proof of convergence or optimality

Markov Chain Monte Carlo (MCMC): sequence of local (randomized) actions converging (in probability) to global optimal

Successfully applied to frequency selection [Infocom’07] and content placement [Infocom’10]

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Distributed Estimation – A Case Study Analytical Framework: S. Boyd, A. Ghosh, B. Prabhakar, D.

Shah, “Randomized Gossip Algorithms”, Trans. on Inform. Theory, 2006.

Gossip algorithm to calculate aggregate parameters average, cardinality, min, max connected network (P2P, sensor net, online social net)

Initial node values [5, 4, 10, 1, 2]

Connectivity Matrix

0 0 0.15 0 0.12

0 0 0.2 0.18 0.2

0.15 0.2 0 0 0.15

0 0.18 0 0 0

0.12 0.2 0.15 0 0

1 0 1 0 1

0 1 1 1 1

1 1 1 0 1

0 1 0 1 0

1 1 1 0 1

node i node i

node

j no

de

j

Probability Matrix P: pijProb. (i,j) “gossip” in the next

slot

[5, 3, 10, 1, 3]

avg

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Distributed Estimation for Opportunistic Nets In our network, pij depends on mobility (next contact)

Weighted contact graph W = {wij} =>

Main Result:

slowest convergence

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Lessons Learnt Human Mobility is driven by Social Networking factors

Mobility Models can be improved by taking social networking properties into account

Better protocols can be designed by considering the position/role of nodes on the underlying social/contact graph

Mobility datasets, seen as complex networks, also exhibit the standard complex network properties: small world path, high clustering coefficient, skewed degree distribution

26

Eurecom, Sophia-AntipolisThrasyvoulos Spyropoulos / [email protected]

Backup Slides

27


III. Reference Point Group Mobility (RPGM) Nodes are divided into groups Each group has a leader The leader’s mobility follows random way point The members of the group follow the leader’s mobility

closely, with some deviation Examples:

Group tours, conferences, museum visits Emergency crews, rescue teams Military divisions/platoons

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Group Mobility: Multiple Groups

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Structural Properties of Mobility Models?

Mobility Model

??

Synthetic Trace

Contact Graph

Contact Trace

Contact Graph

Community Structure?Modularity?Community Connections?Bridges?

Structural Properties?

✔

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Community Connections Distribution of community connection among links and

nodes

Implications for networking! (Routing, Energy, Resilience)

Which mobility processes create these?

Bridging node u of community X:Strong links to many nodes of Y.

Bridging link betweenu of X and v of Y:Strong link but neitheru nor v is bridging node.

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Node Spread / Edge Spread Example

2/5

3/5

TRACES MODELSLow spread(Bridging Links)

High spread(Bridging Nodes)

3/5

Why? ?32


Difference in mobility processes (intuition) Mobility Models: Nodes visit other communities Reality/Traces: Nodes of different communities meet outside

the context and location of their communities

Location of Contacts

OutsideHomeLocations

“At home”

✔Community home loc.: Smallest set of locations which contain 90% of intra-community contacts

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Do nodes visit the same “social” location synchronously?

Do only pairs visit social locations or larger cliques? Detecting cliques of synchronized nodes

Synchronization of Contacts

GeometricDistribution

Measured overlap of time spent at social locations by two nodes

Random, independent visitsVS

Result: many synchronized visits

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Social Overlay

Hypergraph G(N, E) Arbitrary number of nodes per Hyperedge Represent group behavior

Calibration from measurements # Nodes per edge # Edges per node

Adapted configuration model

Drive different mobility models TVCM:SO HCMM:SO

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TVCM:SO

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Evaluation Edge spread

Original propreties

Small Spread

MODELS TRACES

✔

✔37

Using Complex Networks for Mobility Modeling and Opportunistic Networking: Part II

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