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.

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On the Levy-walk Nature On the Levy-walk Nature of Human Mobilityof Human Mobility

Injong Rhee, Minsu Shin and Seongik Hong

NC State University

Kyunghan Lee and Song Chong

KAIST

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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.

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Existing Models

RWP RD

Synthetic model!

Group mobility model Manhattan model

Context model!(based on strong assumptions)

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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 walksNo existing work on analyzing the statistical patterns

of human mobility.

)1(~)( llp20

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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.

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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.

Site# of

participants# of daily

tracesAvg. duration

(Hours)Avg. maximum distance (Km)

Campus I (NCSU) 20 35 10.2 3.6

Campus II (KAIST) 34 76 10.6 2.6

New York City 9 32 9.3 8.4

Disney World 18 38 8.7 3.4

State fair 17 17 2.6 0.6

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Sample traces We could gather a variety of traces!

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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

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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)

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A Picture worth thousand wordsMobility traces from five different locations

KAIST

Disney WorldNYC (Manhattan)

NCSU

State Fair

Levy Walks(randomly generate)

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KAIST

NCSUPDF CCDF

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NYC

Disney World

PDF CCDF

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Statefair

PDF CCDF

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Diffusion Mean Squared Displacement (MSD) : (position of a random

walker after time t)2

Normal diffusion (BM): Super-diffusion (Levy walk):

1,~MSD t1,~MSD t

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).

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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

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Impact to DTN routing

DTN routing delay using two hop relay algorithm

ICT

Diffusion matters!

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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.

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Thank you and Questions?