• Find regular encounter pattern from mobile users.• Regular encounter indicates an encounter trend that is repetitive

and consistent. • Using this metric can be useful in selection of relay nodes when

the encounter rate of the nodes with the target node are similar as regular nodes are likely to provide less error in encounter probability estimation.

• We propose the following methods however their validation still remains a future work.

• Select 20% of the nodes whose highest frequency magnitude is greater than rest of nodes.

• Select the nodes whose sum of three highest frequency magnitudes take up at least 30% of the total sum of frequency magnitudes.

• Figure below shows the locations where encounter events occurred according to each group selected by above methods.

• It shows different locations of encounter events by the groups of nodes.

• This indicates that regularity does not follow the general trend of encounter events. We can further infer that there can be regularly encountering nodes even at locations where number of encounter events are small.

• We look at average auto correlation coefficient that are converted to frequency domain.

• Spikes shown in the frequency component of 18 indicates that certain pattern has repeated for 18 times over 128 days, which indicates seven days interval (weekly encounter pattern). (18/128 = 7.xx)

• Weekly periodicity is noticeable from both the frequently and rarely encountering pairs with latter showing much stronger periodicity.

• This result is different from mobility diameter study, which did not observe weekly pattern in mobility of highly mobile users.

• Bluetooth traces show strong daily encounter pattern but weekly pattern could not be observed due to short duration of experiment period.

• WLAN traces: USC, UF and Montreal• Bluetooth traces: students carry PDAs (HP iPAQ & Nokia N810)

• Understanding the potential of mobile nodes is essential in use of them as message relays in DTN.

• We analyze the periodicity in encounter pattern by using power spectral analysis.

• Result: stronger periodicity (particularly weekly pattern) among rarely encounter pairs than frequently encounter pairs.

• Further utilization: we propose methods to find regularly encountering pairs.

Spectral Analysis of Periodicity and Regularity for Mobile Encounters in Delay Tolerant Networks

Computer and Information Science and Engineering Department UNIVERSITY OF FLORIDA UF

Sungwook Moon, Ahmed Helmy {smoon, helmy}@cise.ufl.edu

[1] MobiLib: USC WLAN trace and pointers to many WLAN trace archives available at http://nile.cise.ufl.edu/MobiLib.[2] CRAWDAD: A Community Resource for Archiving Wireless Data At Dartmouth. http://crawdad.cs.dartmouth.edu/index.php.[3] T. Henderson, D. Kotz and I. Abyzov, ”The Changing Usage of a Mature Campus-wide Wireless Network,” in Proceedings of ACM MobiCom 2004, September 2004. [4] W. Hsu, D. Dutta, and A. Helmy, "Extended abstract: Mining behavioral groups in large wireless LANs," in Proceedings of MOBICOM 2007. Longer version of technical report available at http://arxiv.org/abs/cs/0606002[5] W. Hsu, D. Dutta, and A. Helmy, "Profile-Cast: Behavior-Aware Mobile Networking," in Proceedings of IEEE WCNC, Las Vegas, NV, Mar. 2008. [6] U. Kumar, N. Yadav and A. Helmy, “Gender-based Grouping of Mobile Student Societies”, in MODUS workshop, St. Louis, MO, April 2008 (colocated with IPSN 2008)[7] J. Kim, Y. Du, M. Chen and A. Helmy, “Comparing Mobility and Predictability of VoIP and WLAN Traces”, in CRAWDAD workshop, Montreal QC, Canada, Sep. 2007[3] Google Earth. Download from http://earth.google.com/

More info: http://nile.cise.ufl.edu/

1. Introduction

2. Encounter Traces Analyzed

This work is supported by NSF CAREER Award 0134650 Cisco Systems, Inc.

3. Methodology

• How to analyze the periodicity of encounter pattern?– We use power spectral analysis.

• (STEP1) Process the traces to time-domain encounter traces.- Encountered pairs: nodes associated with the same access points

in the same period of time• (STEP2) Apply the auto correlation function (ACF) to find

repetitive patterns.• (STEP3) Perform discrete Fourier transform to convert the data

from time domain to frequency domain, in order to observe distinctly repeated patterns including hidden patterns.

• What do we look at?• Daily encounter rate of the entire nodes (i,j: nodes; T: total

duration; d: day; E(i,j): daily encounter of pair i,j)

• We look at the two groups of nodes: rarely encountering pairs and frequency encountering pairs

• We are more interested in the statistics of rarely encountering pairs as they have more room for improvements in choosing relay nodes.

4. Periodicity of encounter 6. Future Directions

Trace source

Trace duration

Analyzedduration

Uniqueusers

Encounter pairs

USC 2006 Jan – May2007 Jan – May2008 Jan – May

128 days 281733527442587

25354941905708931289100

UF 2007 Aug – Dec 128 days 4611550549

1249340316807427

Montreal 2004 Aug – Dec 128 days 455 2512

Bluetooth 2008 Feb – Mar2008 Nov

256 hours 1027

12771655

T

jiEjiD

T

d drate

1

0),(

),(

Figure 1. Frequency magnitude for rarely encountered pairs

Figure 2. Frequency magnitude for frequently encountered pairs

Figure 3. Frequency magnitude for Bluetooth encounter