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UNDERSTANDING PERIODICITY AND REGULARITY OF NODAL ENCOUNTERS IN MOBILE NETWORKS: A SPECTRAL ANALYSIS

Sungwook Moon, Ahmed Helmy

Dept. of Computer and Information Science and Engineering

University of Florida

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Contents

Introduction Data sets Methodology

Time Series Representation Auto Correlation Spectral Analysis

Periodicity in Nodal Encounter Regular Encounters Applications & Related Work Conclusions & Future Work

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Introduction

Network Environment Mobile networks

Communication via wireless signal between the mobile nodes Basic Definitions

Mobile Nodes An entity that can move around with wireless communication

devices (e.g. PDA, smartphone) Encounter (contact) [2][3]

Two mobile nodes present within the wireless communication range. (e.g. Bluetooth discovery)

Encounter and contact are used interchangeably in literatures

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Introduction

Assumption Encounter in WLAN

Mobile users using the same access points at the same time.

Commonly used assumption in other literatures [1][3]

Bluetooth encounter Detected by Bluetooth beacon signal.

[1] Augustin Chaintreau, Pan Hui, Jon Crowcroft, Christophe Diot, Richard Gass, and James Scott. Impact of human mobility on the design of opportunistic forwarding algorithms. In Proc. IEEE INFOCOM, Apr 2006. [3] W. Hsu, D. Dutta, and A. Helmy. Mining behavioral groups in large wireless lans. In Proc. ACM MobiCom, Sep 2007.

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Introduction

Motivations Efficient and intelligent deployment of mobile networks requires

deep knowledge on behavioral pattern of mobile nodes. Yet, our understanding about the behavioral pattern of mobile nodes

is mainly limited to mobility and aggregate information analysis of encounter.

Challenges Identifying the important spaces to explore among multiple

dimensions of variables to understand the behavior of mobile nodes. Processing different forms of data sets to derive generic encounter

behavior of mobile nodes.

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Overview

Problem Statement Can we identify encounter pattern of mobile users?

What are the important dimensional spaces to explore? How to analyze periodicity of mobile encounter? Can we utilize the identified characteristics of encounter

pattern?

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Introduction

Encounter Pattern Critical information for mobile networking that directly

transfers data in the event of encounter. (e.g. Bluetooth data transfer between two nodes).

No need of location information.

Type of analysis Encountered pairs (i, j)

Encounter of two mobile nodes, i and j Individual nodal encounter

Aggregate encounter information for each mobile node

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Data Sets

Trace Source Trace Duration Analyzed Duration

Collecting Devices

Encounter Pairs

USC 2006 Jan-May2007 Jan-May2008 Jan-May

128 days 28,17335,27442,587

25,359,45419,057,08931,289,100

UF 2007 Aug-Dec2008 Jan-May

128 days 46,11550,549

12,493,40316,807,427

Montreal 2004 Aug-Dec 128 days 455 2,512

Bluetooth 2008 Feb-Mar2008 Nov

256 hours 1027

1,2771,655

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Data Sets

Example trace format Processed WLAN trace format

Encounter trace format for pair (i, j)

MAC * AP Start Duration

00:aa:bb:3a:4b:5c lbw343-win-ap1200-1 1201889474 1200

MAC (i) MAC (j) Start Duration

00:aa:bb:3a:4b:5c 3c:5a:4b:de:a2:f4 1201889474 500

* MAC address is anonymized before processing.

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Contents

Introduction Data sets Methodology

Time Series Representation Auto Correlation Spectral Analysis

Periodicity in Nodal Encounter Regular Encounters Applications & Related Work Conclusions & Future Work

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Periodicity

Methodology Transform a variety of network traces to encounter

trace in a form of time series data. Analyze periodicity by applying power spectral

analysis (autocorrelation(ACF) + Fourier transform).

Practice of power spectral analysis Analysis of stock market [7]

Analysis of Network traffic [4]

[4] Alefiya Hussain, John Heidemann, and Christos Papadopoulos. Identification of repeated denial of service attacks. In Proc. IEEE INFOCOM, Apr 2006.[7] C. Chatfield. Analysis of Time Series, pages 18–24, 105–134. Chapman and Hall,1989.

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Periodicity

Time Domain Representation of Encountered Pattern Daily encounter

Binary process, = 1, for each encounter count on time d , where d = day (1,2,…T); otherwise = 0

In our extended report, we analyze about the encounter frequency and encounter duration as well.

Example time series data of daily encounter for an encounter pair (i, j)

* Sungwook Moon and Ahmed Helmy. Understanding periodicity and regularity of nodal encounters in mobile networks. Technical report, Aug 2010, arxXv:1004.4437.

0

1

d (days)1285 21 54 72

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Periodicity

Example time series data of daily encounter for an encountered pair (i, j)

0

1

d (days)1285 21 54 72

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Periodicity

Daily encounter rate Let be a daily encounter for a pair (i, j), such that

where T is the observed period. Analyzing by the encounter rate

Rarely encountering pattern takes up majority of encounter pairs; thus, may hinder other patterns in overall observation if analyzed together.

Therefore, we analyze the encounter pairs by the groups of different encounter rate. Rarely encountering pairs: (0.1 ≤ Drate < 0.2)

Frequently encountering pairs: (0.5 ≤ Drate < 0.6)

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Auto Correlation Function (ACF) Apply ACF to the time-domain representation of

encounter data to find repetitive patterns. ACF (Auto Correlation Function): a measure of how

similar the stream of data is to itself shifted in time by lag k.

k: lag, d: day; T: overall time; λ: avg. encounter rate

Periodicity

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Periodicity (encounter pairs) Various encounter pattern is showing but weekly encounter pattern

(lag = 7) shows the strongest pattern. Some of other lags (i.e. lag =14 and 21) are artifacts of a smaller lag

(i.e. lag=7)

Figure. Autocorrelation coefficient for each lag at USC encounter trace.

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Periodicity

Conversion to frequency domain representation Converting from time domain to frequency domain

shows dominant repetitive pattern more clearly while filtering out the artifacts.

Apply Fourier transform to convert time series data to the frequency domain.

c: frequency component

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Periodicity

Frequency domain graph X axis: frequency component

number of replicas over the observed period of time e.g. peak observed at 18 of the X-axis indicates that

certain pattern has repeated for 18 times over the observed period of time (128 days).

Y axis: normalized frequency magnitude in probability density.

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Contents

Introduction Data sets Methodology

Time Series Representation Auto Correlation Spectral Analysis

Periodicity in Nodal Encounter Regular Encounters Applications & Related Work Conclusions & Future Work

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Periodicity (encounter pairs) Weekly encounter pattern is very strong. (see around 18 at

frequency component)

Figure. Normalized frequency magnitude for the rarely encountering pairs (0.1 ≤ Drate < 0.2)

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Periodicity (encounter pairs)

Figure. Normalized frequency magnitude for the frequently encountering pairs (0.5 ≤ Drate < 0.6)

Weekly encounter pattern is still strong but weaker than rarely encountering pairs.

This frequency of different periodicities can be used for profiling mobile nodes.

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Periodicity (individual node) Weekly encounter pattern is stronger than encounter pairs. (see

around 18 at frequency component)

Figure. Normalized frequency magnitude for the rarely encountering nodes(0.1 ≤ Drate < 0.2)

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Periodicity (individual node) Weekly encounter pattern is stronger than encounter pairs. (see

around 18 at frequency component)

Figure. Normalized frequency magnitude for the frequently encountering nodes(0.5 ≤ Drate < 0.6)

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Periodicity (individual node) Bluetooth Encounter Daily encounter pattern is observed.

Figure. Individual Bluetooth encounter pattern for the encountered pairs at UF Bluetooth trace (hourly encounter rate)

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Contents

Introduction Data sets Methodology

Time Series Representation Auto Correlation Spectral Analysis

Periodicity in Nodal Encounter Regular Encounters Applications & Related Work Conclusions & Future Work

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Regularity

Preliminary investigation. Utilize periodic properties of encounter pairs. Regular encounter pattern is stable and consistent

pattern over the period of observed time. E.g. consistent repetition of certain pattern over time.

Discover the pairs showing regular encounter pattern from the periodicity analysis.

Trace analyzed: USC 2006 spring

0

1

d (days)128

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Regularity Knee appears in the 0.8 area Approaches to find regularly encountering pairs:

If peak frequency magnitude is in the top 20% in the group. Regularly encountering pairs show distinctly stronger periodicity with

higher frequency magnitude for their top frequency component.

Figure. Empirical CDF of the top peaks by daily encounter rate

USC 2006trace

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Regularity

Empirical heuristic approaches (preliminary) Approach #1: Extracting regularly encountering pairs.

Choose the pairs whose peak frequency magnitude (top peak) is in the top 20% for peak frequency magnitude of all the pairs. Max1 = max( ) ≥ θ, where θ is threshold for the top 20 %

peak frequency magnitude where

Approach #2: Extracting regularly encountering pairs. Pick top three magnitudes whose sum of frequency

magnitudes takes over 30% of overall sum of frequency magnitudes.

Max1 + Max2+Max3 ≥ 0.3 * sum( ), where

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Regularity

Behavioral pattern of regularly encountering pairs (on-going investigation ) Different location access pattern is observed among regularly encounter

pairs and normal pairs. Each of approach #1 and #2 show similar location access pattern.

Figure. Location (AP) access preference by general pairs vs regular pairs (approach #1 = top 20 percent, approach #2 = top 3 frequency magnitudes)

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Contents

Introduction Data sets Methodology

Time Series Representation Auto Correlation Spectral Analysis

Periodicity in Nodal Encounter Regular Encounters Applications & Related Work Conclusions & Future Work

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Application

Develop realistic encounter model. Profiling mobile nodes based on periodic

property and embed profile to simulated node or robot node to emulate human behavior. *

* Sungwook Moon and Ahmed Helmy. Mobile Testbeds with an Attitude. IEEE GlobeCom, Demo session, Dec 2010.

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Application

Classify the mobile users by regularity to create a stable overlay networks.

A

DB

C

E

F

ε (BD)

ε (BE)

ε (EF)

ε (BC)

ε (AB)

ε (AC)

ε (CD)

ε (CF)

Regular encounter

Non-Regular encounter

ε: regularity metric

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Related Work

Periodicity Spectral analysis is used in network traffic analysis

to discover similar footprints of DDOS attack. [4]

Periodicity study for activities at APs discovers strong periodicity from aggregate APs access pattern and mobility diameter of mobile nodes. [5]

[4] Alefiya Hussain, John Heidemann, and Christos Papadopoulos. Identification of repeated denial of service attacks. In Proc. IEEE INFOCOM, Apr 2006.[5] Minkyong Kim and David F. Kotz. Periodic properties of user mobility and access-point popularity. Personal and Ubiquitous Computing, Springer-Verlag, 11, Aug 2007.

Our work is unique in that we use spectral analysis to analyze encounter pairs and individual encounter pattern.

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Related Work

Encounter: Inter-contact time follows power-law distribution from an analysis of 200 mobile users. [2]

Regularity: Researchers indicate that discovering regular pattern can be useful in predicting behaviors to help routing decision. [6]

[2] Thomas Karagiannis, Jean-Yves Le Boudec, and Milan Vojnovic. Power law and exponential decay of inter contact times between mobile devices. In Proc. ACM MobiCom, Sep 2007.[6] Pan Hui and Jon Crowcroft. Human mobility models and opportunistic communication system design. Royal Society Philosophical Transactions, (366):1872, Jun 2008.

We analyze the extensive network trace with diverse set of mobile users.Our regularity analysis can help to make an informed decision in predicting encounter behavior.

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Contents

Introduction Data sets Methodology

Time Series Representation Auto Correlation Spectral Analysis

Periodicity in Nodal Encounter Regular Encounters Applications & Related Work Conclusions & Future Work

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Conclusions

Contribution Analyze the encounter pattern for extensive network traces

for more than 50,000 mobile users and find mathematical methodology to study periodicity of encounter pattern.

Observe strong periodicity, particularly weekly encounter pattern, for rarely encountering pairs and individual encounter pattern.

Propose two empirical heuristic approaches to discover regularly encounter pattern, and discover regularly encountering pairs show different location visiting behavior than normal pairs.

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Future Work

Analyze periodicity of inter-contact time and location access pattern.

Investigation and validation of the methods to discover regular encounter pattern on the diverse set of traces.

Classifying the encountered pairs by periodicity to use in profiling and modeling encounter pattern.

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References

[1] Augustin Chaintreau, Pan Hui, Jon Crowcroft, Christophe Diot, Richard Gass, and James Scott. Impact of human mobility on the design of opportunistic forwarding algorithms. In Proc. IEEE INFOCOM, Apr 2006.[2] Thomas Karagiannis, Jean-Yves Le Boudec, and Milan Vojnovic. Power law and exponential decay of inter contact times between mobile devices. In Proc. ACM MobiCom, Sep 2007.[3] W. Hsu, D. Dutta, and A. Helmy. Mining behavioral groups in large wireless lans. In Proc. ACM MobiCom, Sep 2007.[4] Alefiya Hussain, John Heidemann, and Christos Papadopoulos. Identification of repeated denial of service attacks. In Proc. IEEE INFOCOM, Apr 2006.[5] Minkyong Kim and David F. Kotz. Periodic properties of user mobility and access-point popularity. Personal and Ubiquitous Computing, Springer-Verlag, 11, Aug 2007.[6] Pan Hui and Jon Crowcroft. Human mobility models and opportunistic communication system design. Royal Society Philosophical Transactions, (366):1872, Jun 2008.[7] C. Chatfield. Analysis of Time Series, pages 18–24, 105–134. Chapman and Hall,1989.[8] Sungwook Moon and Ahmed Helmy. Understanding periodicity and regularity of nodal encounters in mobile networks. Technical report, Aug 2010, arxXv:1004.4437.[9] Sungwook Moon and Ahmed Helmy. Mobile Testbeds with an Attitude. IEEE GlobeCom, Demo session, Dec 2010.

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Questions

Thank you.