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Finding Self-Similarities in Opportunistic People Networks
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Finding Self-Similarities in Opportunistic People Networks

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Opportunistic network is a type of Delay Tolerant Networks (DTN) where network communication opportunities appear opportunistic. In this study, we investigate opportunistic network scenarios based on …

Opportunistic network is a type of Delay Tolerant Networks (DTN) where network communication opportunities appear opportunistic. In this study, we investigate opportunistic network scenarios based on public network traces, and our contributions are the following: First, we identify the censorship issue in network traces that usually leads to strongly skewed distribution of the measurements. Based on this knowledge, we then apply the Kaplan-Meier Estimator to calculate the survivorship of network measurements, which is used in designing our proposed censorship removal algorithm (CRA) that is used to recover censored data. Second, we perform a rich set of analysis illustrating that UCSD and Dartmouth network traces show strong self-similarity, and can be modeled as such. Third, we pointed out the importance of these newly revealed characteristics in future development and evaluation of opportunistic networks.

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  • 1. Finding Self-similarity in Opportunistic People Networks Ling-Jyh Chen1, Yung-Chih Chen1, Tony Sun2 Paruvelli Sreedevi1, Kuan-Ta Chen1 Chen-Hung Yu3, Hao-Hua Chu3 1 Academia Sinica, Taiwan 2 UCLA, USA 3 National Taiwan University, Taiwan
  • 2. Motivation • Investigate fundamental properties of opportunistic networks • Better understand network connectivity • Solve the long been ignored censorship issue
  • 3. Contribution • Point out and recover censorship within mobility traces of opportunistic networks – Propose Censorship Removal Algorithm – Recover censored measurements • Prove the inter-contact time process as self-similar for future research on opportunistic networks
  • 4. Outline • Trace Description • Censorship Issue – Survival Analysis – Censorship Removal Algorithm • Self-similarity
  • 5. Trace Description • UCSD campus trace* – 77 days, 275 nodes involved – Client-based trace • PDAs record Wi-Fi based APs nearby • Dartmouth College trace** – 1,777 days, 5148 nodes involved – Interface-based trace • APs maintain the association log for each wireless interface – 77 days extracted for comparison *UCSD: Wireless Topology Discovery (WTD Project) **Dartmouth: RAWDAD
  • 6. Basic Terms • What is Contact ? – Two nodes are of their wireless radio range – Associated to the same AP at the same time • What is Inter-contact Time ? – Period between two consecutive contacts • Used to observe Network Connectivity – Distribution of inter-contact time • Disconnection duration • Reconnection frequency
  • 7. Basic Terms (Con’t) 1 2 3 4 5 6 7 8 9 10 11 (Weeks) Inter-contact time Case A = 3 weeks Observation End Inter-contact time Case B 7 weeks Inter-contact time ?? Case C • In the last case, the inter-contact time has been censored as 6 weeks.
  • 8. Censorship • Inter-contact time samples end after the termination of the observation. • Censored measurements are inevitable. UCSD Trace Dartmouth College Trace Censored Data Censored Data
  • 9. Survival Analysis • Important in biostatistics, medicine, … – Estimate patients’ time to live/death – Map to censored inter-contact time samples • Censored samples should have the same likelihood distribution as the uncensored’s. – Kaplan-Meier Estimator (a.k.a. Survival Function or Product Limit Estimator)
  • 10. Kaplan-Meier Estimator • Suppose there are N samples (t1<t2<t3…<tN) • At time ti : – di uncensored samples (complete samples) – ni events (censored/uncensored) • The survival function is:
  • 11. Kaplan-Meier Estimator – An Example • 10 inter-contact time samples: 1, 2+, 3+, 3.5+, 4, 5+,9, 9.5+, 10, 11+ (in weeks, + for censorship) i-c time ni di ci Survival function interval (death) (censored) S(t) 0 10 0 0 S(0)=1 (0,1] 10 1 0 S(1)= 1* 9/10=0.9 (1,4] 6 1 3 S(4)=0.9*5/6=0.75 (4,9] 4 1 1 S(9)=0.75*3/4=0.56 (9,10] 2 1 1 S(10)=0.56 *1/2=0.28 (10,11] 1 0 1 S(11)=0.28*1/1= 0.28
  • 12. Censorship Removal Algorithm • Based on the survival function S(t) – t1 < t2 < t3…<tN (N : total sample number) – Death Ratio during ti ~ ti+1: D(ti) = S(ti-1)-S(ti) S(ti) – Ci: # of censored samples at ti – Iteratively select Ci*D(ti) samples from Ci • Uniformly distribute their estimated inter-contact time by S(ti) • Mark them as uncensored samples – Terminate when all the censored samples are removed
  • 13. Censorship Removal Algorithm (Con’t) • Recovered inter-contact time measurements UCSD Trace Dartmouth Trace
  • 14. Censorship Removal Algorithm (Con’t) 1,177 days Pr (T>t) (with exact values) 77 days (with censorship) Inter-contact time • Compare the recovered values to their exact values in original trace. • 80.4% censored measurements are recovered.
  • 15. Outline • Trace Description • Censorship Issue – Survival Analysis – Censorship Removal Algorithm • Self-similarity
  • 16. Self-Similarity • What is self-similarity? – By definition, a self-similar object is exactly or approximately similar to part of itself. • In opportunistic network, we focus on the network connectivity • With recovered measurements, we prove inter- contact time series as a self-similar process – Reconnection/disconnection – Similar mobility pattern in people opp. networks
  • 17. Self-Similarity • A self-similar series – Distribution should be heavy-tailed – Examined by three statistical analyses • Variance-Time Plot, R/S Plot, Periodogram Plot • Estimated by a specific parameter : Hurst • H should be in the range of 0.5~1 – Results of three methods should be in the 95% confidence interval of Whittle estimator
  • 18. Self-Similarity (Con’t) • Previous works show inter-contact time dist. as power-law dist. • A random variable X is called heavy-tailed: – If P[X>x] ~ cx -α, with 0<α<2 as x -> ∞ – α can be found by log-log plot – Survival curves show the α for • UCSD: 0.26 • Dartmouth: 0.47
  • 19. Self-Similarity (Con’t) • Variance-Time Method – Variance decreases very slowly, even when the size grows large UCSD • The Hurst estimates are – UCSD: 0.801 – Dartmouth: 0.7973 Dartmouth
  • 20. Self-Similarity (Con’t) • Rescaled Adjusted Range (R/S) method – Keep similar properties when UCSD the dataset is divided into several sub-sets • The Hurst estimates are – UCSD:0.7472 – Dartmouth:0.7493 Dartmouth
  • 21. Self-Similarity (Con’t) • Periodogram Method – Use the slope of power spectrum of the series as frequency approaches zero UCSD • The Hurst estimates are – UCSD: 0.7924 – Dartmouth: 0.7655 Dartmouth
  • 22. Self-Similarity (Con’t) Hurst Estimate Hurst Estimate 95% Confidence Interval Aggregation level (UCSD) Aggregation level (Dartmouth) • Whittle Estimator – Usually being considered as a more robust method – Provide a confidence interval • Results of the three graphical methods are in the 95% confidence interval.
  • 23. Conclusion • Two major properties exists in modern opportunistic networks: – Censorship – Self-similarity • Using CRA, we could recover censored inter-contact time to have more accurate datasets. • With recovered datasets, we prove that inter-contact time series is self-similar.
  • 24. Thank You !