Modeling Data-Centric Routing in Wireless Sensor Networks

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Modeling Data-Centric Routing in Wireless Sensor
Networks

• Bhaskar Krishnamachari, Deborah Estrin, Stephan
  Wicker

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OUTLINE

• Introduction
• Routing Models
• Data Aggregation Models
• Theoretical Results
• Experimental Results
• Shortcomings
• Related Work and Conclusions

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INTRODUCTION

• Sensor Nets Properties
• Reverse Multicast
• Data Redundancy
• Sensors Not Mobile
• Data Aggregation
• Eliminate Redundancy
• Minimize Transmissions
• Save Energy

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Routing Models

• Address Centric
• Each source independently send data to sink
• Data Centric
• Routing nodes en-route look at data sent

Source 2
Source 2
Source 1
Source 1
B
A
B
A
Sink
Sink
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Routing Models

• Senarios
• All sources have different information
• All sources have same data
• Sources send Info with not deterministic
  redundancy.
• 1 A.C and D.C equivalent
• 2.A.C can be better
• 3 D.C is better

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DATA AGGREGATION

• Aggregation function is simple
• Duplicate suppression
• Max, min etc.
• Node transmits 1 packet for multiple inputs
• Optimal Aggregation
• Minimum Steiner tree problem (multicast tree)
• Optimum no . Of transmission no. of edges in
  the minimum Steiner tree.
• NP Hard problem

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Steiner Trees

• A minimum-weight tree connecting a designated
  set of vertices, called terminals, in a weighted
  graph or points in a space. The tree may include
  non- terminals, which are called Steiner vertices
  or Steiner points

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2
2
b
d
g
b
d
g
3
1
3
1
1
4
1
5
2
1
e
h
e
h
1
2
2
1
a
c
f
a
3
2
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Definition taken from the NIST
site. http//www.nist.gov/dads/HTML/steinertree.ht
ml
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Data Aggregation

• Suboptimal Aggregation
• Center at Nearest Source (CNS)
• Shortest Paths Tree (SPT)
• Greedy Incremental tree (GIT)
• Performance measures
• Energy savings
• Delay
• Robustness

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Source Placement Models

• Nodes distributed randomly per unit sq.
• Communication radius
• Event Radius Model
• Single point origin of event
• Data sources in Sensing Range, S
• no. of data sources p S 2 n
• Random Sources model
• K nodes randomly distributed act as sources

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Source Placement (Event Radius)
Figure from the original paper.
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Source Placement (random)
Figure from the original paper.
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Theoretical Results

• Max gains sources close together, sink far
• Result 1 Total no. of transmissions for A.C
• NA d1 d2 dk sum(di) ------ ( 1 )
• Result 2 optimal transmissions for D.C
• source nodes S1, S2, . Sk.
• diameter X gt 1
• Max of the Pair-wise shortest path between nodes
• No. of Transmissions ND
• Optimal ND lt (k 1)X min(di) -------- ( 2 )
• ND gt min(di) (k - 1) ----------- ( 3 )

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Theoretical results

• Proof of 2.
• Data aggregation tree
• K 1 sources ? source nearest sink
• No. of edges lt ( k 1 )X min(di)
• Optimum lt No of edges
• Proof of 3
• Smallest possible steiner tree if X 1

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Theoretical Results

• Result 4 if X lt min(di) then ND lt NA
• Proof of 4
• ND lt ( k 1) X min(di) lt (k)min(di)
• ? ND lt sum(di) NA --------------------- ( 4 )
• Fractional Savings FS
• FS ( NA ND ) / ( NA ) ------------------- ( 5
  )
• Range from 0 to 1

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Theoretical Results

• Result 5 bounds for FS
• FS gt 1 ((k-1)X min(di))/sum(di) ----- ( 6 )
• FS lt 1-(min(di) k 1)/sum(di) --------- ( 7 )
• Result 6
• if min(di) max(di) d
• 1 ((k-1)X d)/kd lt FS lt 1-(d k 1)/kd
  ----- ( 8 )
• If X and k are constant d ? 8
• FS 1 1/k -----------------------------------
  --- ( 9 )
• If sink is far and sources close FS is k fold
• 4 sources FS 1-1/4 75 fewer transmissions
• 10 sources 90

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Theoretical Results

• Result 7 if Sub-graph G (S1 .. Sk) is
  connected ? data aggregation in polynomial time
• Proof of 7 Start GIT ( greedy incremental tree )
• Initialized with path from sink to nearest
  source.
• New source added in each step. Since G is
  connected
• No. of edges dmin k 1 lower bound in ( 3 )
• Result 8 in ER model when R gt 2S optimal D.C
  runs in polynomial time
• R communication radius, S event Radius
• Proof of 8
• If R gt 2S all sources are one hop of each other
• GIT and CNS result in optimal tree

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Experimental Results

• ER model
• Sensing range S 0.1 to 0.3
• Communication radius R 0.15 to 0.45 incr 0.05
• RS model
• No of sources k 1 to 15 incr of 2
• Communication radius same as above.
• N 100 nodes randomly placed / unit area
• NEXT EXPERIMENTAL RESULTS

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Ideal A.C for E-R model
Figure from the original paper.
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Ideal A.C for R-S model
Figure from the original paper.
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A.C Model

• Cost highest when
• More sources
• Communication range low
• Reasoning
• More sources more transmissions
• More hops between sink and sources

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Energy Costs E-R model
Figure from the original paper.
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Energy Costs E-R model

• GITDC coincides with optimal
• Even Moderate S ? connected subgraph
• Result 7 holds
• As R increases ? CNSDC optimal
• Result 8 holds

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Energy Costs R-S model
Figure from the original paper.
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Energy Costs R-S model

• As R increases GITDS is best
• SPTDS, CNSDS and AC
• CNSDC is poor
• Sources are random
• No point aggregating near the sink

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No of sources varied
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No of sources varied

• ER model
• CNSDC poor
• e.g s 0.3 nearly 1/3 of all nodes are sources
• Route directly to sink is faster
• R-S model
• GITDC performance significantly better

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Delay due to D.C

• With Aggregation
• Delay proportional to the between sink and
  furthest source
• Difference between these distances
• Greatest distance when
• Communication radius is low
• No. of sources is high

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Communication radius varied
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No. of sources varied
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Robustness

• Lower cost of adding nodes
• E.g. GITDC cost is shortest path of new node from
  tree
• A.C cost is path to sink
• For given energy budget
• More sources in D.C than A.C
• More robustness if only fraction of sources
  accurate

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Robustness graph
E-R model
R-S model
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Shortcomings

• Overly simplistic A.C vs D.C
• Not considered overhead costs of routing
• Routing specific
• Delay considered only specific to aggregation
• Processing delay, congestion
• Single sink

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Related work

• Smart dust motes
• TinyOS
• PicoRadio
• Directed diffusion

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Conclusion

• Gains from D.C most when sources clustered
  together and far from sink
• Robustness increase
• Latency can be no negligible