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On the Levy-walk Nature of Human Mobility

On the Levy-walk Nature of Human Mobility. Injong Rhee, Minsu Shin and Seongik Hong NC State University. Kyunghan Lee and Song Chong KAIST. Motivations. Mobility models for mobile networks Realistic mobility models required for Realistic network simulation.

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On the Levy-walk Nature of Human Mobility

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  1. On the Levy-walk Nature of Human Mobility Injong Rhee, Minsu Shin and Seongik Hong NC State University Kyunghan Lee and Song Chong KAIST

  2. Motivations • Mobility models for mobile networks • Realistic mobility models required for • Realistic network simulation. • Accurate understanding of the protocol performance. • Many existing models • Random Way Point (RWP), Random Direction (RD), Brownian (BM), Group mobility model, Manhattan model, …but • Existing models reflect realistic patterns of human mobility? • No existing work on empirical analysis of human flight length / pause time distribution. • Understanding human mobility patterns isimportant for mobile network simulation because many mobile network devices are attached to humans.

  3. RWP RD Manhattan model Group mobility model Existing Models Synthetic model! Context model! (based on strong assumptions)

  4. Moving patterns of animals • Statistical patterns are analyzed from the data obtained from electronic devices attached to animals • Flight lengths of foraging animals such as spider monkeys, albatrosses (seabirds) and jackals follow Levy walks No existing work on analyzing the statistical patterns of human mobility.

  5. Objectives • To extract mobility patterns from real human trace data. • To make a realistic mobility model for human driven mobile networks. • To evaluate their impact on networking performance. Objective & Outline • Human walk measurement methodology. • Human mobility pattern analysis. • Impact on mobile network performance. • Conclusions

  6. Human movement Data Collection • Daily mobility traces are collected from 5 different sites. • Currently, 198 daily traces (98 participants) for 2 years. • http://netsrv.csc.ncsu.edu • Handheld GPS receivers are used. • position accuracy of better than three meters.

  7. Sample traces • We could gather a variety of traces!

  8. Trace analysis Rectangular model Pause Participant moves less than r meters during 30 second period. Flight length All sampled points are inside of the rectangle formed by two end points and width w • Angle model • Merges similar direction flights in the rectangular model if • No pause occurs between consecutive flights • Relative angle between two consecutive flights is less than αθ • Prevents a trip from being broken into small flights

  9. Flight length/Pause time distribution Maximum Likelihood Estimation (MLE) result Various distributions such as Truncated Pareto, exponential, lognormal distributions are tested. Best fit with the truncated Pareto distribution Human flight length/pause time have long tails; but they are truncated at some points Levy walks also have power-law flight lengths! Human walk traces have similar characteristics. (Flight length) (Pause time)

  10. A Picture worth thousand wordsMobility traces from five different locations Levy Walks (randomly generate) NCSU KAIST NYC (Manhattan) Disney World State Fair

  11. PDF CCDF NCSU KAIST

  12. PDF CCDF NYC Disney World

  13. PDF CCDF State fair

  14. Diffusion • Mean Squared Displacement (MSD) : (position of a random walker after time t)2 • Normal diffusion (BM): • Super-diffusion (Levy walk): Levy walks have faster diffusion rates We verified that human walk traces have gamma larger than one….meaning that they have super-diffusion (results in the paper). Levy Walks Brownian move faster than normal RWP

  15. Impact of Levy Walk on Inter Contact Times Inter Contact Time (ICT) Time period between two successive contacts of the same two nodes Empirical ICT CCDF distribution is known to show dichotomy (Power law head + exponential tail) Generated ICT by Levy Walks Same pattern as measured (UCSD) Dichotomy Normal diffusive small flights make power law head Super diffusive long flights make exponential decay ICT

  16. Impact to DTN routing • Diffusion matters! ICT DTN routing delay using two hop relay algorithm

  17. Conclusions Human walks have similar statistical features of Levy walks. • Heavy-tail flight length distribution • Heavy-tail pause time distribution • Super diffusion rate But they are NOT Levy walks. • Human walks clearly not random walks. • Then what make human walks have such tendency? Future Work.

  18. Thank you and Questions?

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