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                     Computer and Information Science and Engineering Department
                                      UNIVERSITY OF FLORIDA                                                                                         More info:

                         Spectral Analysis of Periodicity and Regularity for Mobile Encounters in Delay Tolerant Networks
                                                                          Sungwook Moon, Ahmed Helmy                     {smoon, helmy}

                            1. Introduction                                                       4. Periodicity of encounter                                                                          6. Future Directions
 • Understanding the potential of mobile nodes is essential in use of        • We look at average auto correlation coefficient that are                              • Find regular encounter pattern from mobile users.
   them as message relays in DTN.                                              converted to frequency domain.                                                        • Regular encounter indicates an encounter trend that is repetitive
 • We analyze the periodicity in encounter pattern by using power            • Spikes shown in the frequency component of 18 indicates that                            and consistent.
   spectral analysis.                                                          certain pattern has repeated for 18 times over 128 days, which                        • Using this metric can be useful in selection of relay nodes when
 • Result: stronger periodicity (particularly weekly pattern) among            indicates seven days interval (weekly encounter pattern). (18/128                       the encounter rate of the nodes with the target node are similar as
   rarely encounter pairs than frequently encounter pairs.                     = 7.xx)
                                                                                                                                                                       regular nodes are likely to provide less error in encounter
 • Further utilization: we propose methods to find regularly                 • Weekly periodicity is noticeable from both the frequently and                           probability estimation.
   encountering pairs.                                                         rarely encountering pairs with latter showing much stronger
                                                                               periodicity.                                                                          • We propose the following methods however their validation
                    2. Encounter Traces Analyzed                                                                                                                       still remains a future work.
                                                                             • This result is different from mobility diameter study, which did
                                                                               not observe weekly pattern in mobility of highly mobile users.                        • Select 20% of the nodes whose highest frequency magnitude is
 Trace          Trace            Analyzed         Unique   Encounter
                                                                                                                                                                       greater than rest of nodes.
 source         duration         duration         users    pairs             • Bluetooth traces show strong daily encounter pattern but weekly
 USC            2006 Jan – May   128 days         28173    2535494             pattern could not be observed due to short duration of                                • Select the nodes whose sum of three highest frequency
                2007 Jan – May                    35274    19057089            experiment period.                                                                      magnitudes take up at least 30% of the total sum of frequency
                2008 Jan – May                    42587    31289100                                                                                                    magnitudes.
 UF             2007 Aug – Dec   128 days         46115    12493403                                                                                                  • Figure below shows the locations where encounter events
                                                  50549    16807427
                                                                                                                                                                       occurred according to each group selected by above methods.
 Montreal       2004 Aug – Dec 128 days           455      2512
                                                                                                                                                                     • It shows different locations of encounter events by the groups of
 Bluetooth      2008 Feb – Mar 256 hours          10       1277                                                                                                        nodes.
                2008 Nov                          27       1655
                                                                                                                                                                     • This indicates that regularity does not follow the general trend of
 • WLAN traces: USC, UF and Montreal                                                                                                                                   encounter events. We can further infer that there can be regularly
 • Bluetooth traces: students carry PDAs (HP iPAQ & Nokia N810)                                                                                                        encountering nodes even at locations where number of encounter
                                                                                                                                                                       events are small.
                             3. Methodology
• How to analyze the periodicity of encounter pattern?                                 Figure 1. Frequency magnitude for rarely encountered pairs
   – 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?
                                                                                      Figure 2. Frequency magnitude for frequently encountered pairs
• Daily encounter rate of the entire nodes (i,j: nodes; T: total
  duration; d: day; E(i,j): daily encounter of pair i,j)

                                   d 0 Ed (i, j)
                                       T 1
                                                                                                                                                                  [1] MobiLib: USC WLAN trace and pointers to many WLAN trace archives available at
                 Drate (i, j )                                                                                                                         
                                                                                                                                                                  [2] CRAWDAD: A Community Resource for Archiving Wireless Data At Dartmouth.
                                                                                                                                                                  [3] T. Henderson, D. Kotz and I. Abyzov, ”The Changing Usage of a Mature Campus-wide Wireless Network,”
• We look at the two groups of nodes: rarely encountering pairs and                                                                                               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
  frequency encountering pairs                                                                                                                                    Proceedings of MOBICOM 2007. Longer version of technical report available at
• We are more interested in the statistics of rarely encountering pairs                                                                                           [5] W. Hsu, D. Dutta, and A. Helmy, "Profile-Cast: Behavior-Aware Mobile Networking," in Proceedings of
                                                                                                                                                                  IEEE WCNC, Las Vegas, NV, Mar. 2008.
  as they have more room for improvements in choosing relay nodes.                                                                                                [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)
                                                                                      Figure 3. Frequency magnitude for Bluetooth encounter                       [7] J. Kim, Y. Du, M. Chen and A. Helmy, “Comparing Mobility and Predictability of VoIP and WLAN Traces”,
This work is supported by NSF CAREER Award 0134650                                                                                                                in CRAWDAD workshop, Montreal QC, Canada, Sep. 2007
                            Cisco Systems, Inc.                                                                                                                   [3] Google Earth. Download from

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