using complex networks for mobility modeling and opportunistic networking: part ii
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Using Complex Networks for Mobility Modeling and Opportunistic Networking: Part II. Thrasyvoulos ( Akis ) Spyropoulos EURECOM. Outline. Motivation Introduction to Mobility Modeling Complex Network Analysis for Opportunistic Routing Complex Network Properties of Human Mobility - PowerPoint PPT PresentationTRANSCRIPT
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
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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
Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
It’s a “small world” after all!
Small numbers (in parentheses) are for random graph Clustering is high and paths are short!
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Community Structure Louvain community detection algorithm
All datasets are strongly modular! clear community structure exists
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Contact Edge Weight Distribution
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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
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Social Networks Graph model: Vertices = humans, Weighted Edges =
strength of interaction
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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
Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Mapping Communities to Locations Assume a grid with different locations of interest
Geographic consideration might gives us the candidate locations
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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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
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Modeling Epidemic Spreading: Markov Chains (MC)
2-hop infection
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
How realistic is this?A Poisson Graph
A Real Contact Graph(ETH Wireless LAN trace)
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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?
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Group Mobility: Multiple Groups
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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Node Spread / Edge Spread Example
2/5
3/5
TRACES MODELSLow spread(Bridging Links)
High spread(Bridging Nodes)
3/5
Why? ?32
Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
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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Thrasyvoulos Spyropoulos / [email protected] Eurecom, Sophia-Antipolis
Evaluation Edge spread
Original propreties
Small Spread
MODELS TRACES
✔
✔37