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1
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?