On the Levy-walk Nature of Human Mobility

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• 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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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
Synthetic 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 walks

No existing work on analyzing the statistical
patterns of human mobility.
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Objective Outline

• Human walk measurement methodology.
• Human mobility pattern analysis.
• Impact on mobile network performance.
• Conclusions

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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.

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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 a?
• 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
Levy Walks (randomly generate)
NCSU
KAIST
Disney World
NYC (Manhattan)
State Fair
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PDF
CCDF
NCSU
KAIST
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PDF
CCDF
NYC
Disney World
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PDF
CCDF
State fair
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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
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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

• Diffusion matters!

ICT
DTN routing delay using two hop relay algorithm
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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.

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Thank you and Questions?