Eurecom, Sophia-Antipolis Thrasyvoulos Spyropoulos / Using Complex Networks for Mobility Modeling and Opportunistic Networking: Part II Thrasyvoulos (Akis) Spyropoulos EURECOM

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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 days 3

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Small numbers (in parentheses) are for random graph  Clustering is high and paths are short! 4

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Louvain community detection algorithm  All datasets are strongly modular!  clear community structure exists 5

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Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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 9

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis 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 10

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Multiple Communities (house, office, library, cafeteria)  Time-dependency House (C 1 ) Community (e.g. house, campus) p 11 (i) p 12 (i) Rest of the network p 21 (i) Office C 2 Library C 3 p 23 (i) p 32 (i) 11

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Graph model: Vertices = humans, Weighted Edges = strength of interaction 12

Thrasyvoulos Spyropoulos / 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” are 13

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Assume a grid with different locations of interest  Geographic consideration might gives us the candidate locations 14

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  p c (i) = attraction of node i to community/location c p 2 (B) (t) p 1 (B) (t) p 3 (B) (t) 15

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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 16

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis Assumption 1) Underlay Graph  Fully meshed Assumption 2) Contact Process  Poisson(λ ij ), Indep. Assumption 3) Contact Rate  λ ij = λ (homogeneous) Analysis of Epidemics: The Usual Approach 17

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis 2-hop infection 18

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis A Poisson Graph A Real Contact Graph (ETH Wireless LAN trace) 19

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Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis 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

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis A 2 nd Bound on Epidemic Delay  Φ is a fundamental property of a graph  Related to graph spectrum, community structure 22

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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] 23

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Analytical Framework: S. Boyd, A. Ghosh, B. Prabhakar, D. Shah, “Randomized Gossip Algorithms”, Trans. on Inform. Theory,  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 node i node j Probability Matrix P: p ij Prob. (i,j) “gossip” in the next slot [5, 3, 10, 1, 3] avg 24

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  In our network, p ij depends on mobility (next contact)  Weighted contact graph W = {w ij } =>  Main Result: slowest convergence 25

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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

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Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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 28

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Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis Mobility Model ?? Synthetic Trace Contact Graph Contact Trace Contact Graph Community Structure? Modularity? Community Connections? Bridges? Structural Properties? ✔ 30

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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 between u of X and v of Y: Strong link but neither u nor v is bridging node. 31

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Example 2/5 3/5 TRACES MODELS Low spread (Bridging Links) High spread (Bridging Nodes) 3/5 Why?? 32

Thrasyvoulos Spyropoulos / 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 Outside Home Locations “At home” ✔ Community home loc.: Smallest set of locations which contain 90% of intra-community contacts 33

Thrasyvoulos Spyropoulos / 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 Geometric Distribution Measured overlap of time spent at social locations by two nodes Random, independent visits VS Result: many synchronized visits 34

Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  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 35

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Thrasyvoulos Spyropoulos / Eurecom, Sophia-Antipolis  Edge spread  Original propreties Small Spread MODELSTRACES ✔ ✔ 37