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1 Outline Background static average aggregation in sensor - - PowerPoint PPT Presentation

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LiMoSense Live Monitoring in Dynamic Sensor Networks Ittay Eyal, Idit Keidar, Raphi Rom Technion, Israel Israeli Networking Day. March 2011 1 Outline Background static average aggregation in sensor networks. LiMoSense

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1

LiMoSense – Live Monitoring in Dynamic Sensor Networks

Ittay Eyal, Idit Keidar, Raphi Rom Technion, Israel Israeli Networking Day. March 2011

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2 Outline

  • Background – static average

aggregation in sensor networks.

  • LiMoSense – Live and robust.
  • Correctness.
  • Convergence.
  • Dynamic behavior.
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3 Sensors Read values and communicate. Light-weight, little energy, error prone.

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4 Sensor Network Many sensors (at least thousands). Limited topology. Similar scenario in cloud monitoring

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5 Average Aggregation Target: Average of read values. Reason: Environmental monitoring. Cloud computing load monitoring. Challenge: Cannot collect the values. Solution: In-network aggregation. Hierarchical solution? Not robust.

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6 Static error-free aggregation [1,2] Bidirectional communication gossip

1.

  • D. Kempe, A. Dobra, and J. Gehrke. Gossip-based computation of aggregate information. In FOCS, 2003.

2.

  • S. Nath, P. B. Gibbons, S. Seshan, and Z. R. Anderson. Synopsis diffusion for robust aggregation in sensor networks.

In SenSys, 2004.

8 2 3 5 5 3 5 4 4 t=1 t=2 t=3

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7 Static error-free aggregation [1,2] Unidirectional communication gossip

1.

  • D. Kempe, A. Dobra, and J. Gehrke. Gossip-based computation of aggregate information. In FOCS, 2003.

2.

  • S. Nath, P. B. Gibbons, S. Seshan, and Z. R. Anderson. Synopsis diffusion for robust aggregation in sensor networks.

In SenSys, 2004.

5, 1 3, 1 4.3, 1.5 3, 0.5

Send half:

A B

v w

in in in B B B B

w v w v v w w   

 

1 2

,

A A

v w

(3, 0.5)

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8 Static error-free aggregation [1,2] Unidirectional communication gossip

1.

  • D. Kempe, A. Dobra, and J. Gehrke. Gossip-based computation of aggregate information. In FOCS, 2003.

2.

  • S. Nath, P. B. Gibbons, S. Seshan, and Z. R. Anderson. Synopsis diffusion for robust aggregation in sensor networks.

In SenSys, 2004.

5, 1 3, 1 4, y 4, x

A B

v w

(3, 0.5)

t  

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9 Static error-free aggregation Realistic?

  • Monitoring  Dynamic input! (restart?)
  • Cheap sensors  Crashes.
  • Limited battery 

Link failure and message loss

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10

LiMoSense – Live Monitoring in Dynamic Sensor Networks

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11 Live error-free aggregation Observation: Invariant: read sum = Weighted sum

5, 1 3, 1 4.3, 3/2 3, 1/2

A B

3 1 5 1 8     3 1 / 2 4.3 3 / 2 8    

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12 Live error-free aggregation Observation: Invariant: read sum = Weighted sum Goal: Maintain the invariant after input changes.

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13 Live error-free aggregation Each node stores:

  • 1. Current weighted estimation.
  • 2. Previously read value.

On read change: update weighted estimation to fix invariant.

 

1 new R ead prevR ead

i i i i i

est est w   

Weight unchanged.

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14 Live error-free aggregation

 

1 new R ead prevR ead

i i i i i

est est w   

Case 1: Case 2: Example: read value 0  1

3, 1 3, 2 4, 1 3.5, 2

Before After

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15 Live robust aggregation

Lost messages  lost weight  broken Invariant:

3, 1

(3, 0.5)

3, 0.5

(3, 0.25)

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16 Live robust aggregation Solution: Send summary, not diff:

3, 1

(3, 0.5)

3, 0.5

(3, 0.25)

3, 1

(3, 0.5)

3, 0.5

(3, 0.75)

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17 Live robust aggregation Solution: Send summary, not diff:

  • Lost message:

Fix on next one.

  • Failed link:

Transfer undo.

3, 1

(3, 0.5)

3, 0.5

(3, 0.75)

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18 Live robust aggregation Solution: Send summary, not diff:

3, 1

(3, 0.5)

3, 0.5

(3, 0.75)

3, 0.25 3, 1

Link fail Undo

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19 Live robust aggregation Challenge: weight  infinity Solution: Hybrid push-pull: Ask neighbor to send back inverse.

3, 1

(3, 0.5)

3, 0.5

(3, 0.75)

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20 Live robust aggregation Challenge: weight  infinity Solution: Hybrid push-pull: Ask neighbor to send back inverse.

3, 1

(3, 0.5)

3, 0.5

(3, -0.5) pull

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21 Live robust aggregation Crashed node  lost links.

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22

Co Correctness ectness

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23 Correctness - Safety Theorem 1: The invariant always holds.

  • 1. On message send/receive.
  • 2. After value change.
  • 3. After add/remove neighbor.
  • 4. After node removal/addition.
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24 Correctness - Liveness Theorem 2: After GST, all estimations converge to the average.

  • 1. Quantization constant and fairness.
  • 2. Value propagation.
  • 3. Convergence.
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25 Correctness - Liveness

  • 1. Quantization constant and fairness.

Weight is transferred in multiples of q. Note – This does not effect accuracy. Each node eventually succeeds to send a push message to all of its neighbors.

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26 Correctness - Liveness

  • 2. Value propagation.

Lemma: For any time t >= GST and node i, there exists a time t’ > t after which every node j has a component of i with a weight larger than some bound (the bound is dependent on n and q)

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27

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28 Correctness - Liveness

  • 3. Convergence.

Define a series GST =t0, t1, t2, ... Where at ti each node has a bounded- from-below portion from each node at ti-1. At each ti, the largest error is smaller than in ti-1, because it's mixed with other values.

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29

Co Converg ergence ence Rate ate

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30 Convergence Static convergence rate (exchange gossip):

  • Static input (after GST).
  • Dense topology.
  • Synchronous uniform runs.
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31 Convergence Static convergence rate (exchange gossip): Assumption: normal distribution of estimations.

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32 Convergence Static convergence rate (exchange gossip):

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33

Dy Dyna namic mic Beh ehavior vior

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34 Step Function 100 nodes. Standard Normal distribution 10 nodes change Values (+10)

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35 Step Function 100 nodes. Standard Normal distribution 10 nodes change Values (+10)

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36 Step Function 100 nodes. Standard Normal distribution 10 nodes change Values (+10)

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37 Creeping Value Change 100 nodes. Standard Normal distribution Every 10 steps, 10 nodes change Values (+0.01)

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38 Creeping Value Change 100 nodes. Standard Normal distribution Every 10 steps, 10 nodes change Values (+0.01)

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39 100 nodes. Standard Normal distribution Every 10 steps, 10 nodes change Values (+0.01) Creeping Value Change

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40 100 nodes. Standard Normal distribution 10 nodes change Values (+10) for 100 steps Response to Step Function

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41 Response to Step Function 100 nodes. Standard Normal distribution 10 nodes change Values (+10) for 100 steps

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42 Dynamic Network Disc Graph t=2500: 10 nodes range decay, 7 lost links t=5000: Node crash.

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43 Summary

  • LiMoSense – Live Average Monitoring in

error prone dynamic sensor networks.

  • Live: aggregate dynamic data reads.
  • Fault tolerant: Message loss, link failure

and node crash.

  • Correctness in dynamic asynchronous

settings.

  • Exponential convergence after GST.
  • Quick dynamic behavior.

Ittay Eyal, Idit Keidar, Raphael Rom. LiMoSense - Live Monitoring in Dynamic Sensor Networks, Technion technical report CCIT #786 March 2011EE.

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44

Go Good

  • d Qu

Ques estions tions

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45 Convergence Static convergence rate (push gossip):