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TIME SERIES MODELING OF TEMPORAL NETWORK

Sandipan Sikdar

CNeRG Retreat ‘14

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TEMPORAL NETWORK

Network that changes with time

Nodes and edges entering or leaving the system dynamically

Example: Human communication network, mobile call network

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TEMPORAL NETWORK AS TIME SERIES

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TEMPORAL NETWORK AS TIME SERIES

Time series of some of the properties

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PROPERTIES OF TIME SERIES

Stationarity ADF test KPSS test

Trend

Periodicity

Seasonality

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FORECASTING USING TIME SERIES

Selecting a window

Auto-correlation ARIMA (auto-regressive-integrated-moving-

average)

Auto-correlation function plots

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RESULTS AND DISCUSSIONS

Datasets:

INFOCOM ’06Human communication network collected at IEEE INFOCOM 2006

SIGCOMM ’09Human communication network collected at SIGCOMM 2009

Resolution – 5 minutes.

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ACCURACY OF PREDICTION

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SPECTROGRAM 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.

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SPECTROGRAM 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.

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SPECTROGRAM ANALYSIS

Spectrograms for (a)no of nodes and (b)betweenness centrality

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SPREADING IN TEMPORAL NETWORKS

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DELAY-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

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BROADCAST/SPREADING IN DTN

Challenges:o Distributed Systemo No global informationo Unstable links

Routing mechanisms:o Spray and waito Two-hop spreading

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THE OVERALL SETUP

Agent configuration and network

Message configuration

Transfer protocol Push Pull (restricted)

Metrics of interest Delay Wastage

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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?

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THE 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

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ANOTHER 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

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REDUCE 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?

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THANK YOU……