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

1. Using Complex Networks for Mobility Modeling and Opportunistic Networking: Part II Thrasyvoulos (Akis) Spyropoulos EURECOM

2. 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

3. Social Properties of Real Mobility Datasets • Different origins: AP associations, Bluetooth scans and self- reported • Gowalladataset • ~ 440’000 users • ~ 16.7 Mio check-ins to ~ 1.6 Mio spots • 473 “power users” who check-in 5/7 days

4. It’s a “small world” after all! • Small numbers (in parentheses) are for random graph • Clustering is high and paths are short!

5. Community Structure • Louvain community detection algorithm • All datasets are strongly modular!  clear community structure exists

6. Community Sizes

7. Contact Edge Weight Distribution

8. Degree Distribution

9. 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

10. 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

11. Library C3 Office C2 Community-based Mobility (Spatial Preference) • Multiple Communities (house, office, library, cafeteria) • Time-dependency Rest of the network p23(i) p12(i) p32(i) p21(i) p11(i) House (C1) Community (e.g. house, campus)

12. Social Networks • Graph model: Vertices = humans, Weighted Edges = strength of interaction

13. 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

14. Mapping Communities to Locations • Assume a grid with different locations of interest • Geographic consideration might gives us the candidate locations

15. pc(i) = attraction of node i to community/location c Mobility Between Communities p1(B)(t) p2(B)(t) p3(B)(t)

16. 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

17. Analysis of Epidemics: The Usual Approach Assumption 1) Underlay Graph  Fully meshed Assumption 2) Contact Process Poisson(λij), Indep. Assumption 3) Contact Rate λij= λ (homogeneous)

18. 2-hop infection Modeling Epidemic Spreading: Markov Chains (MC)

19. How realistic is this? A Poisson Graph A Real Contact Graph (ETH Wireless LAN trace)

20. Arbitrary Contact Graphs

21. 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?

22. A 2nd Bound on Epidemic Delay • Φ is a fundamental property of a graph • Related to graph spectrum, community structure

23. 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]

24. 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] [5, 3, 10, 1, 3] node i avg node i node j node j Probability Matrix P: pij Prob. (i,j) “gossip” in the next slot Connectivity Matrix

25. Distributed Estimation for Opportunistic Nets • In our network, pij depends on mobility (next contact) • Weighted contact graph W = {wij} => • Main Result: slowest convergence

26. 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

27. Backup Slides

28. 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

29. Group Mobility: Multiple Groups

30. Structural Properties of Mobility Models? Structural Properties? Mobility Model Contact Trace Community Structure?Modularity? Community Connections?Bridges? ✔ Synthetic Trace Contact Graph Contact Graph ??

31. 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 between u of X and v of Y: Strong link but neither u nor v is bridging node.

32. High spread (Bridging Nodes) Low spread (Bridging Links) Node Spread / Edge Spread • Example 3/5 3/5 2/5 MODELS TRACES ? ? Why

33. OutsideHomeLocations “At home” Location of Contacts • 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 ✔ Community home loc.: Smallest set of locations which contain 90% of intra-community contacts

34. GeometricDistribution Synchronization of Contacts • Do nodes visit the same “social” location synchronously? • Do only pairs visit social locations or larger cliques? • Detecting cliques of synchronized nodes Measured overlap of time spent at social locations by two nodes Result: many synchronized visits VS Random, independent visits

35. 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

36. TVCM:SO

37. Small Spread Evaluation • Edge spread • Original propreties MODELS TRACES ✔ ✔