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 is important for mobile network simulation because many mobile network devices are attached to humans.

3 Existing Models RWP RD Synthetic model! Group mobility model Manhattan 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 Objective & Outline  Human walk measurement methodology.  Human mobility pattern analysis.  Impact on mobile network performance.  Conclusions  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.

6 Human movement Data Collection  Daily mobility traces are collected from 5 different sites.  Currently, 198 daily traces (98 participants) for 2 years.   Handheld GPS receivers are used.  position accuracy of better than three meters. Site # of participants # of daily traces Avg. duration (Hours) Avg. maximum distance (Km) Campus I (NCSU) Campus II (KAIST) New York City Disney World State fair

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 α θ  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 words Mobility traces from five different locations KAIST Disney WorldNYC (Manhattan) NCSU State Fair Levy Walks (randomly generate)

11 KAIST NCSU PDFCCDF

12 NYC Disney World PDFCCDF

13 State fair PDFCCDF

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 move faster than normal Brownian RWP Levy Walks We verified that human walk traces have gamma larger than one….meaning that they have super- diffusion (results in the paper).

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 DTN routing delay using two hop relay algorithm ICT  Diffusion matters!

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

18 Thank you and Questions?