Modeling Data-Centric
Routing in Wireless Sensor
Networks
Bhaskar Krishnamachari, Deborah
Estrin, Stephan Wicker
OUTLINE
Introduction
Routing Models
Data Aggregation Models
Theoretical Results
Experimental Results
Shortcomings
Related Work and Conclusions
INTRODUCTION
Sensor Nets Properties
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Reverse Multicast
Data Redundancy
Sensors Not Mobile
Data Aggregation
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Eliminate Redundancy
Minimize Transmissions
Save Energy
Routing Models
Address Centric
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Each source independently send data to sink
Data Centric
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Routing nodes en-route look at data sent
Source 2
Source 1
Source 2
Source 1
A
B
Sink
A
B
Sink
Routing Models
Senarios
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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
DATA AGGREGATION
Aggregation function is simple
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Duplicate suppression
Max, min etc….
Node transmits 1 packet for multiple inputs
Optimal Aggregation
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Minimum Steiner tree problem (multicast tree)
Optimum no . Of transmission = no. of edges
in the minimum Steiner tree.
NP Hard problem
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
5
2
b
4
d
g
3
1
2
b
1
d
1
5
g
3
1
2
1
e
1
a
h
2
3
e
2
c
1
f
2
h
a
3
*Definition taken from the NIST site.
http://www.nist.gov/dads/HTML/steinertree.html
Data Aggregation
Suboptimal Aggregation
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Center at Nearest Source (CNS)
Shortest Paths Tree (SPT)
Greedy Incremental tree (GIT)
Performance measures
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Energy savings
Delay
Robustness
Source Placement Models
Nodes distributed randomly per unit sq.
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Communication radius
Event Radius Model
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Single point origin of event
Data sources in Sensing Range, S
no. of data sources = π * S 2 * n
Random Sources model
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K nodes randomly distributed act as sources
Source Placement (Event Radius)
Figure from the original paper.
Source Placement (random)
Figure from the original paper.
Theoretical Results
Max gains sources close together, sink far
Result 1: Total no. of transmissions for A.C
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NA = d1 + d2 + …… + dk = sum(di) ------ ( 1 )
Result 2: optimal transmissions for D.C
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source nodes = S1, S2, …. Sk.
diameter X >= 1
Max of the Pair-wise shortest path between nodes
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No. of Transmissions = ND
Optimal ND <= (k – 1)X + min(di) -------- ( 2 )
ND >= min(di) + (k - 1) ----------- ( 3 )
Theoretical results
Proof of 2.
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Data aggregation tree
K – 1 sources  source nearest sink
No. of edges <= ( k – 1 )X + min(di)
Optimum <= No of edges
Proof of 3
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Smallest possible steiner tree if X = 1
Theoretical Results
Result 4: if X <= min(di) then ND < NA
Proof of 4:
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ND < ( k – 1) X + min(di) < (k)min(di)
 ND < sum(di) = NA --------------------- ( 4 )
Fractional Savings FS
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FS = ( NA – ND ) / ( NA ) ------------------- ( 5 )
Range from 0 to 1
Theoretical Results
Result 5: bounds for FS
 FS >= 1 – ((k-1)X + min(di))/sum(di) ----- ( 6 )
 FS <= 1-(min(di) + k – 1)/sum(di) --------- ( 7 )
Result 6:
 if min(di) = max(di) = d
 1 – ((k-1)X + d)/kd <= FS <= 1-(d + k – 1)/kd ----- ( 8 )
 If X and k are constant d  ∞
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 %
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 )
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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 > 2S optimal D.C runs in
polynomial time
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R = communication radius, S = event Radius
Proof of 8:
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If R > 2S all sources are one hop of each other
GIT and CNS result in optimal tree
Experimental Results
ER model
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Sensing range S = 0.1 to 0.3
Communication radius R = 0.15 to 0.45 incr 0.05
RS model
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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
Ideal A.C for E-R model
Figure from the original paper.
Ideal A.C for R-S model
Figure from the original paper.
A.C Model
Cost highest when
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More sources
Communication range low
Reasoning
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More sources more transmissions
More hops between sink and sources
Energy Costs E-R model
Figure from the original paper.
Energy Costs E-R model
GITDC coincides with optimal
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Even Moderate S  connected subgraph
Result 7 holds
As R increases  CNSDC optimal
Result 8 holds
Energy Costs R-S model
Figure from the original paper.
Energy Costs R-S model
As R increases GITDS is best
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SPTDS, CNSDS and AC
CNSDC is poor
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Sources are random
No point aggregating near the sink
No of sources varied
No of sources varied
ER model
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CNSDC poor
e.g s = 0.3 nearly 1/3 of all nodes are sources
Route directly to sink is faster
R-S model
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GITDC performance significantly better
Delay due to D.C
With Aggregation
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Delay proportional to the between sink and
furthest source
Difference between these distances
Greatest distance when
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Communication radius is low
No. of sources is high
Communication radius varied
No. of sources varied
Robustness
Lower cost of adding nodes
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E.g. GITDC cost is shortest path of new node
from tree
A.C cost is path to sink
For given energy budget
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More sources in D.C than A.C
More robustness if only fraction of sources
accurate
Robustness graph
E-R model
R-S model
Shortcomings
Overly simplistic A.C vs D.C
Not considered overhead costs of routing
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Routing specific
Delay considered only specific to
aggregation
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Processing delay, congestion
Single sink
Related work
Smart dust motes
TinyOS
PicoRadio
Directed diffusion
Conclusion
Gains from D.C most when sources
clustered together and far from sink
Robustness increase
Latency can be no negligible