Modeling Data-Centric Modeling Data-Centric Routing in Wireless Sensor Routing in Wireless Sensor

NetworksNetworks

Bhaskar Krishnamachari, Deborah Bhaskar Krishnamachari, Deborah Estrin, Stephan WickerEstrin, Stephan Wicker

OUTLINEOUTLINE

IntroductionIntroduction

Routing ModelsRouting Models

Data Aggregation ModelsData Aggregation Models

Theoretical ResultsTheoretical Results

Experimental ResultsExperimental Results

ShortcomingsShortcomings

Related Work and ConclusionsRelated Work and Conclusions

INTRODUCTIONINTRODUCTION

Sensor Nets PropertiesSensor Nets Properties Reverse MulticastReverse Multicast Data RedundancyData Redundancy Sensors Not MobileSensors Not Mobile

Data Aggregation Data Aggregation Eliminate RedundancyEliminate Redundancy Minimize TransmissionsMinimize Transmissions Save EnergySave Energy

Routing ModelsRouting Models

Address CentricAddress Centric Each source independently send data to sinkEach source independently send data to sink

Data CentricData Centric Routing nodes en-route look at data sent Routing nodes en-route look at data sent

Source 2

Source 1

Sink

BA

Source 2

Source 1

Sink

BA

Routing ModelsRouting Models

SenariosSenarios All sources have different informationAll sources have different information All sources have same dataAll sources have same data Sources send Info with not deterministic Sources send Info with not deterministic

redundancy. redundancy.

1 A.C and D.C equivalent1 A.C and D.C equivalent

2.A.C can be better2.A.C can be better

3 D.C is better 3 D.C is better

DATA AGGREGATIONDATA AGGREGATION

Aggregation function is simpleAggregation function is simple Duplicate suppressionDuplicate suppression Max, min etc….Max, min etc…. Node transmits 1 packet for multiple inputsNode transmits 1 packet for multiple inputs

Optimal AggregationOptimal Aggregation Minimum Steiner tree problem (multicast tree)Minimum Steiner tree problem (multicast tree) Optimum noOptimum no . Of transmission = no. of . Of transmission = no. of

edges in the minimum Steiner tree.edges in the minimum Steiner tree. NP Hard problemNP Hard problem

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

b d g

a

e

c

h

f

5

2

5

4 1

1 2

3 2

3

2

3 1

2

1

b d g

a

e h

1

2

1 3 1

*Definition taken from the NIST site.http://www.nist.gov/dads/HTML/steinertree.html

Data AggregationData Aggregation

Suboptimal AggregationSuboptimal Aggregation Center at Nearest Source (CNS)Center at Nearest Source (CNS) Shortest Paths Tree (SPT)Shortest Paths Tree (SPT) Greedy Incremental tree (GIT)Greedy Incremental tree (GIT)

Performance measuresPerformance measures Energy savingsEnergy savings DelayDelay RobustnessRobustness

Source Placement ModelsSource Placement Models

Nodes distributed randomly per unit sq.Nodes distributed randomly per unit sq. Communication radiusCommunication radius

Event Radius ModelEvent Radius Model Single point origin of eventSingle point origin of event Data sources in Sensing Range, SData sources in Sensing Range, S

no. of data sources = no. of data sources = ππ * S * S 2 2 * n* n

Random Sources modelRandom Sources model K nodes randomly distributed act as sourcesK nodes randomly distributed act as sources

Source Placement (Event Radius)Source Placement (Event Radius)

Figure from the original paper.

Source Placement (random)Source Placement (random)

Figure from the original paper.

Theoretical ResultsTheoretical Results

Max gains sources close together, sink farMax gains sources close together, sink far

Result 1: Total no. of transmissions for A.CResult 1: Total no. of transmissions for A.C NNAA = d = d11 + d + d22 + …… + d + …… + dkk = sum(d = sum(dii) ------ ( 1 ) ) ------ ( 1 )

Result 2: optimal transmissions for D.CResult 2: optimal transmissions for D.C source nodes = Ssource nodes = S11, S, S22, …. S, …. Skk.. diameter X >= 1 diameter X >= 1

Max of the Pair-wise shortest path between nodesMax of the Pair-wise shortest path between nodes No. of Transmissions = NNo. of Transmissions = NDD

Optimal NOptimal NDD <= (k – 1)X + min(d <= (k – 1)X + min(dii) -------- ( 2 )) -------- ( 2 )

NNDD >= min(d >= min(dii) + (k - 1) ----------- ( 3 )) + (k - 1) ----------- ( 3 )

Theoretical resultsTheoretical results

Proof of 2.Proof of 2. Data aggregation tree Data aggregation tree K – 1 sources K – 1 sources source nearest sink source nearest sink No. of edges <= ( k – 1 )X + min(di) No. of edges <= ( k – 1 )X + min(di) Optimum <= No of edges Optimum <= No of edges

Proof of 3Proof of 3 Smallest possible steiner tree if X = 1Smallest possible steiner tree if X = 1

Theoretical ResultsTheoretical Results

Result 4: if X <= min(dResult 4: if X <= min(dii) then N) then NDD < N < NAA

Proof of 4:Proof of 4: NNDD < ( k – 1) X + min(d < ( k – 1) X + min(d ii) < (k)min(d) < (k)min(dii))

NNDD < sum(d < sum(dii) = N) = NA A --------------------- ---------------------

( 4 )( 4 )

Fractional Savings FSFractional Savings FS FS = ( NFS = ( NAA – N – NDD ) / ( N ) / ( NA A ) ------------------- ( 5 )) ------------------- ( 5 ) Range from 0 to 1Range from 0 to 1

Theoretical ResultsTheoretical Results

Result 5: bounds for FSResult 5: bounds for FS FS >= 1 – ((k-1)X + min(di))/sum(di) ----- ( 6 )FS >= 1 – ((k-1)X + min(di))/sum(di) ----- ( 6 ) FS <= 1-(min(di) + k – 1)/sum(di) --------- ( 7 )FS <= 1-(min(di) + k – 1)/sum(di) --------- ( 7 )

Result 6:Result 6: if min(di) = max(di) = dif min(di) = max(di) = d 1 – ((k-1)X + d)/kd <= FS <= 1-(d + k – 1)/kd ----- ( 8 )1 – ((k-1)X + d)/kd <= FS <= 1-(d + k – 1)/kd ----- ( 8 ) If X and k are constant d If X and k are constant d ∞∞

FS = 1 – 1/k -------------------------------------- ( 9 )FS = 1 – 1/k -------------------------------------- ( 9 ) If sink is far and sources close FS is k foldIf sink is far and sources close FS is k fold

4 sources FS = 1-1/4 = 75% fewer transmissions4 sources FS = 1-1/4 = 75% fewer transmissions10 sources = 90 % 10 sources = 90 %

Theoretical ResultsTheoretical Results

Result 7: if Sub-graph GResult 7: if Sub-graph G’ = (S’ = (S11 ….. S ….. Skk) is connected ) is connected data aggregation in polynomial timedata aggregation in polynomial timeProof of 7: Start GIT ( greedy incremental tree )Proof of 7: Start GIT ( greedy incremental tree )

Initialized with path from sink to nearest source.Initialized with path from sink to nearest source. New source added in each step. Since G’ is connectedNew source added in each step. Since G’ is connected No. of edges = dNo. of edges = dminmin+ k – 1 = lower bound in ( 3 )+ k – 1 = lower bound in ( 3 )

Result 8: in ER model when R > 2S optimal D.C runs in Result 8: in ER model when R > 2S optimal D.C runs in polynomial timepolynomial time

R = communication radius, S = event RadiusR = communication radius, S = event Radius

Proof of 8:Proof of 8: If R > 2S all sources are one hop of each otherIf R > 2S all sources are one hop of each other GIT and CNS result in optimal treeGIT and CNS result in optimal tree

Experimental ResultsExperimental Results

ER modelER model Sensing range S = 0.1 to 0.3Sensing range S = 0.1 to 0.3 Communication radius R = 0.15 to 0.45 incr 0.05Communication radius R = 0.15 to 0.45 incr 0.05

RS modelRS model No of sources k = 1 to 15 incr of 2No of sources k = 1 to 15 incr of 2 Communication radius same as above.Communication radius same as above.

N = 100 nodes randomly placed / unit areaN = 100 nodes randomly placed / unit area

NEXT EXPERIMENTAL RESULTSNEXT EXPERIMENTAL RESULTS

Ideal A.C for E-R modelIdeal A.C for E-R model

Figure from the original paper.

Ideal A.C for R-S modelIdeal A.C for R-S model

Figure from the original paper.

A.C ModelA.C Model

Cost highest when Cost highest when More sources More sources Communication range lowCommunication range low

ReasoningReasoning More sources more transmissionsMore sources more transmissions More hops between sink and sourcesMore hops between sink and sources

Energy Costs E-R modelEnergy Costs E-R model

Figure from the original paper.

Energy Costs E-R modelEnergy Costs E-R model

GITDC coincides with optimalGITDC coincides with optimal Even Moderate S Even Moderate S connected subgraph connected subgraph

Result 7 holdsResult 7 holds

As R increases As R increases CNSDC optimal CNSDC optimalResult 8 holdsResult 8 holds

Energy Costs R-S modelEnergy Costs R-S model

Figure from the original paper.

Energy Costs R-S modelEnergy Costs R-S model

As R increases GITDS is bestAs R increases GITDS is best SPTDS, CNSDS and ACSPTDS, CNSDS and AC

CNSDC is poorCNSDC is poor Sources are random Sources are random No point aggregating near the sinkNo point aggregating near the sink

No of sources variedNo of sources varied

No of sources variedNo of sources varied

ER modelER model CNSDC poorCNSDC poor

e.g s = 0.3 nearly 1/3 of all nodes are sourcese.g s = 0.3 nearly 1/3 of all nodes are sources

Route directly to sink is fasterRoute directly to sink is faster

R-S model R-S model GITDC performance significantly betterGITDC performance significantly better

Delay due to D.CDelay due to D.C

With AggregationWith Aggregation Delay proportional to the between sink and Delay proportional to the between sink and

furthest sourcefurthest source Difference between these distancesDifference between these distances

Greatest distance whenGreatest distance when Communication radius is lowCommunication radius is low No. of sources is highNo. of sources is high

Communication radius variedCommunication radius varied

No. of sources variedNo. of sources varied

RobustnessRobustness

Lower cost of adding nodesLower cost of adding nodes E.g. GITDC cost is shortest path of new node E.g. GITDC cost is shortest path of new node

from treefrom tree A.C cost is path to sinkA.C cost is path to sink

For given energy budget For given energy budget More sources in D.C than A.CMore sources in D.C than A.C More robustness if only fraction of sources More robustness if only fraction of sources

accurateaccurate

Robustness graphRobustness graph

E-R model R-S model

ShortcomingsShortcomings

Overly simplistic A.C vs D.COverly simplistic A.C vs D.C

Not considered overhead costs of routingNot considered overhead costs of routing Routing specificRouting specific

Delay considered only specific to Delay considered only specific to aggregationaggregation Processing delay, congestionProcessing delay, congestion

Single sinkSingle sink

Related workRelated work

Smart dust motesSmart dust motes

TinyOSTinyOS

PicoRadioPicoRadio

Directed diffusionDirected diffusion

ConclusionConclusion

Gains from D.C most when sources Gains from D.C most when sources clustered together and far from sinkclustered together and far from sink

Robustness increaseRobustness increase

Latency can be no negligibleLatency can be no negligible