1. T IME SERIES MODELING OF TEMPORAL NETWORK Sandipan Sikdar CNeRG Retreat 14 1

2. T EMPORAL NETWORK Network that changes with time Nodes and edges entering or leaving the system dynamically Example: Human communication network, mobile call network 2

3. T EMPORAL NETWORK AS TIME SERIES 3

4. 4 Time series of some of the properties

5. P ROPERTIES OF TIME SERIES Stationarity ADF test KPSS test Trend Periodicity Seasonality 5

6. F ORECASTING USING T IME SERIES Selecting a window Auto-correlation ARIMA (auto-regressive-integrated-moving-average) 6 Auto-correlation function plots

7. R ESULTS AND DISCUSSIONS Datasets: INFOCOM 06 Human communication network collected at IEEE INFOCOM 2006 SIGCOMM 09 Human communication network collected at SIGCOMM 2009 Resolution – 5 minutes. 7

8. A CCURACY OF PREDICTION 8

9. S PECTROGRAM ANALYSIS Short term Fourier transform The whole series is divided into equal-sized windows and discrete Fourier transform is applied on this windowed data. We are able to get a view of the local frequency spectrum. 9

10. S PECTROGRAM ANALYSIS We use spectrograms for two purposes Determining predictability of a property We look into the spectrogram of the whole series. Determining the goodness of prediction at any time point We look into the spectrogram of the series formed by the previous few points. 10

11. S PECTROGRAM ANALYSIS 11 Spectrograms for (a)no of nodes and (b)betweenness centrality

12. S PREADING IN TEMPORAL NETWORKS 12

13. D ELAY - TOLERANT NETWORKS (DTN) Very sparse node population Unequal delay associated between the occurrence and reoccurrence of a link Lack of full network connectivity at virtually all points in time Eventual packet delivery achieved through node mobility 13

14. B ROADCAST /S PREADING IN DTN Challenges: o Distributed System o No global information o Unstable links Routing mechanisms: o Spray and wait o Two-hop spreading 14

15. T HE OVERALL SETUP Agent configuration and network Message configuration Transfer protocol Push Pull (restricted) Metrics of interest Delay Wastage 15

16. A COMBINED STRATEGY Push strategy works best at the start Pull strategy works best towards the end Can we combine the two strategies to improve broadcast time? Can we modify the strategies to reduce wastage? 16

17. T HE X % STRATEGY Switch from push to pull when x% of the nodes have been covered Significant improvement in broadcast delay and wastage Need for a global information and also spread the information to all the nodes 17

18. A NOTHER STRATEGY Interleave between push and pull A node starts the broadcast Capable nodes push for a preset number of time- steps Number of steps changes dynamically Nodes with partial segment tries to pull in the next few steps 18

19. R EDUCE WASTAGE Keeping some history information at each node An array which keeps track of the last k contact opportunities If last k transactions were unsuccessful, we turn off the node with some probability Reduces wastage But convergence? 19

20. T HANK YOU …… 20