Minimizing Energy Expense for Chain-Based Data Gathering in Wireless Sensor Networks Li-Hsing Yen...

Minimizing Energy Expense for Minimizing Energy Expense for Chain-Based Data Gathering in Chain-Based Data Gathering in

Wireless Sensor Networks Wireless Sensor Networks

Li-Hsing YenLi-Hsing YenChung Hua UniversityChung Hua University

TaiwanTaiwan

EWSN 05

22

IntroductionIntroduction

Data gatheringData gathering The process of collecting sensed data from The process of collecting sensed data from

every sensor to a distance BSevery sensor to a distance BS

Power-conserving techniquesPower-conserving techniques Data fusionData fusion Multi-hop transmissionMulti-hop transmission

PEGASIS: chain-based data gatheringPEGASIS: chain-based data gathering Data fusion & multi-hop transmissionData fusion & multi-hop transmission

33

Chain Construction in PEGASIS: Chain Construction in PEGASIS: Greedy AppendingGreedy Appending

A greedy method: append the nearest A greedy method: append the nearest non-chain node to the end of the chainnon-chain node to the end of the chain

BS

Starting withthe furthest node

44

PEGASIS: Data GatheringPEGASIS: Data Gathering

The leader collects all sensed data and The leader collects all sensed data and transmit them to the BStransmit them to the BSNodes play the role of the leader by turnsNodes play the role of the leader by turns

BS

Current leader

55

Improved Chain Construction: Improved Chain Construction: Greedy Insertion [DWZ03]Greedy Insertion [DWZ03]

Non-chain nodes can be considered Non-chain nodes can be considered inserting into any position within the chaininserting into any position within the chain

Greedy appending Greedy insertion

Time complexity: O(n2) Time complexity: O(n3)

66

Energy Dissipation ModelEnergy Dissipation Model

When When xx transmits transmits kk-bit message to -bit message to yy, , xx consumes consumes

When When yy receives receives kk-bit message, -bit message, yy consumes consumes

),( yxdkkE ampelec

eleckE

nJ/bit 50elecE pJ/bit/m 100amp

d(x, y): distance between x and y: path loss exponent

77

MMdd: Costs of Node Pairs With Direct : Costs of Node Pairs With Direct CommunicationsCommunications

Cost of every node pair (Cost of every node pair (xx, , yy)) energy consumed in delivering a energy consumed in delivering a kk-bit -bit

message between message between xx and and yy

a b

c d

2

83 912

16

If direct transmissions are used

01689160123812029320

Md

88

Optimal Chain ProblemOptimal Chain Problem

Cost of a chain = total cost of all edges in Cost of a chain = total cost of all edges in that chainthat chainGiven all node-pair costs,Given all node-pair costs,finding an energy-optimal chain finding an energy-optimal chain finding a TSP tour on a complete graph finding a TSP tour on a complete graph NP-hardNP-hard

Traveling Salesperson Problem

99

Our Idea: Virtual ChainOur Idea: Virtual Chain

every edge of the chain may correspond to every edge of the chain may correspond to aa multi-hop data propagation pathmulti-hop data propagation path rather than rather than a a direct radio transmissiondirect radio transmission

Cost of the chain= 18

12

82

416

ab

c

d

Cost of the chain= 22

edge (c, d) correspondsto path c, b, d

16

2

4

8 ab

c

dTriangle inequalitydoes not hold

1010

MMpp: Costs of Node Pairs Using: Costs of Node Pairs Using Shortest Paths Shortest Paths

a b

c d

2

83 912

16

a b

c d

2

83 95

12

01689160123812029320

012891205385029320

If shortest paths are used

MdMpMp[b, c] corresponds

to path b, a, cMp[c, d] corresponds

to path c, a, b, d

1111

Constructing Virtual ChainsConstructing Virtual Chains

MMpp can be obtained by running an can be obtained by running an all-pair shall-pair shortest path algorithmortest path algorithm on input on input MMdd

e.g., Floyd-Warshall: O(e.g., Floyd-Warshall: O(nn33) time complexity) time complexity

Virtual chains can be constructed by running Virtual chains can be constructed by running any chain construction algorithmany chain construction algorithm on input on input MMpp

Virtualchain

Greedy appendingGreedy appending

or insertionor insertionMd Mp

Floyd-WarshallFloyd-Warshall

or any otheror any other

O(n3)

1212

MMtt: Node-Pair Costs Based on MST: Node-Pair Costs Based on MST

Getting Getting MMpp is somewhat time expensive is somewhat time expensiveAn alternativeAn alternative

Md MSTMinimum-costMinimum-costspanning treespanning tree

algorithmalgorithmMt

Traverse alongTraverse alongthe MSTthe MST

Virtualchain

ChainChainconstructionconstructionalgorithmalgorithm

O(n2)

Mt[i, j] is the cost of theunique path from i to j

in the MST

O(n2)

1313

Triangle Inequality Property (TIP) of Triangle Inequality Property (TIP) of Node Cost PairsNode Cost Pairs

TIP does not hold in TIP does not hold in MMdd

MMdd[[ii, , jj]] may be larger than may be larger than MMdd[[ii, , kk] + ] + MMdd[[kk, , jj]] due to non-linear signal attenuationdue to non-linear signal attenuation

TIP does hold in TIP does hold in MMpp

due to the property of shortest pathsdue to the property of shortest paths

TIP does hold in TIP does hold in MMtt

proof is in our paperproof is in our paper

1414

MST-Based Chain ConstructionMST-Based Chain Construction

Used as an approximation to TSP problemUsed as an approximation to TSP problem

With TIP, the cost of the chain is no more than With TIP, the cost of the chain is no more than twicetwice of the MST of the MSTWithout TIP Without TIP No algorithm with constant No algorithm with constant performance ratioperformance ratio

Md, Mp, or Mt

MSTMinimum-costMinimum-costspanning treespanning tree

algorithmalgorithm

Virtualchain

Traverse the treeTraverse the treein prefix orderin prefix order

O(n2) O(n2)

1515

All Possible Cost Matrix/Chain All Possible Cost Matrix/Chain Construction CombinationsConstruction Combinations

Chain construc-Chain construc-tiontion

Cost matrixCost matrix

Greedy Greedy appendingappending

Greedy Greedy insertioninsertion

MST MST traversetraverse

MMdd PEGASISPEGASIS Direct-Direct-insertioninsertion**

Direct-Direct-MSTMST

MMpp Shortest-Shortest-appendingappending

Shortest-Shortest-insertioninsertion

Shortest-Shortest-MSTMST

MMtt MST-MST-appendingappending

MST-MST-insertioninsertion

MST-MST-MSTMST++

* [DWZ03] + can be further simplified (MST-reduced)

1616

Time Complexity of All MethodsTime Complexity of All Methods

MethodMethod Cost matrix Cost matrix computationcomputation

Chain Chain constructionconstruction

OverallOverall

PEGASISPEGASIS O(O(nn22)) O(O(nn22)) O(O(nn22))

Direct-insertion [DWZ03]Direct-insertion [DWZ03] O(O(nn22)) O(O(nn33)) O(O(nn33))

Direct-MSTDirect-MST O(O(nn22)) O(O(nn22)) O(O(nn22))

Shortest-appendingShortest-appending O(O(nn33)) O(O(nn22)) O(O(nn33))

Shortest-insertionShortest-insertion O(O(nn33)) O(O(nn33)) O(O(nn33))

Shortest-MSTShortest-MST O(O(nn33)) O(O(nn22)) O(O(nn33))

MST-appendingMST-appending O(O(nn22)) O(O(nn22)) O(O(nn22))

MST-insertionMST-insertion O(O(nn22)) O(O(nn33)) O(O(nn33))

MST-reducedMST-reduced O(O(nn22)) O(O(nn22)) O(O(nn22))

1717

Leader SchedulingLeader Scheduling

determine which node plays the role of determine which node plays the role of leader in each round of data collectionsleader in each round of data collectionsThe goal is to maximize the number of The goal is to maximize the number of data collection roundsdata collection roundsleader scheduling in PEGASISleader scheduling in PEGASIS round-robin (RR)round-robin (RR) An improvement: nodes are not allowed to be An improvement: nodes are not allowed to be

leaders if their distances to neighbors are leaders if their distances to neighbors are beyond some thresholdbeyond some threshold

1818

Formulating the ProblemFormulating the Problem

NotationNotation eeii: energy consumed by node : energy consumed by node ii in transmits a in transmits akk-bit message to the BS-bit message to the BS

ii,,jj: energy consumed by : energy consumed by ii in transmitting to in transmitting to jj eerr: energy consumed by : energy consumed by ii in receiving a msg in receiving a msg EEii: the amount of energy : the amount of energy ii initially has initially has xxii: the number of times : the number of times ii has been selected to has been selected to

be the leaderbe the leader

1919

Optimal Leader SchedulingOptimal Leader Scheduling

Find positive integer values of Find positive integer values of xxii’s as to’s as tomaximizemaximize xxiisubject tosubject to

nnrnnnnnnn

rrrr

rrrr

r

E

EEE

x

xxx

ee

eeeeeeeeee

ee

3

2

1

3

2

1

1,1,1,

4,332,32,3

3,23,221,2

2,12,12,11

22

A Linear Programming Problem

2020

MRPF: MRPF: Maximum Residual Power FirstMaximum Residual Power First

In each round of data collection, selects In each round of data collection, selects the node that has the maximum residual the node that has the maximum residual power to be the leaderpower to be the leaderResidual power information is Residual power information is piggybacked with data message as a part piggybacked with data message as a part of the aggregated dataof the aggregated dataEach node compares its power level with Each node compares its power level with that attached with incoming data message that attached with incoming data message and sends only the larger oneand sends only the larger one

2121

Simulation Results: Number of Simulation Results: Number of Rounds Before 1st Node DiesRounds Before 1st Node Dies

02000400060008000

100001200014000

50 100 200Number of nodes

Rou

nds

PEGASIS

Direct-MST

Others

02000400060008000

100001200014000

50 100 200

Number of nodes

Rou

nds

PEGASIS

Direct-MSTOthers

50 x 50 network 100 x 100 network

BS is located at (50, 150)

2222

Number of Rounds BeforeNumber of Rounds Before1st Node Dies (Cont.)1st Node Dies (Cont.)

0

1000

2000

3000

4000

5000

6000

7000

50 100 200

Number of nodes

Roun

ds

PEGASIS

Direct-MST

Others

0

1000

2000

3000

4000

5000

6000

7000

50 100 200

Number of nodes

Roun

ds

PEGASIS

Direct-MST

Others

50 x 50 network 100 x 100 network

BS is located at (50, 200)

2323

Number of Rounds BeforeNumber of Rounds Before1st Node Dies (Cont.)1st Node Dies (Cont.)

0200400600800

100012001400160018002000

50 100 200

Number of nodes

Rou

nds

PEGASIS

Direct-MST

Others

0200

400600800

1000

120014001600

18002000

50 100 200

Number of nodes

Rou

nds

PEGASIS

Direct-MST

Others

BS is located at (50, 300)

50 x 50 network 100 x 100 network

2424

Performance of Leader Scheduling Performance of Leader Scheduling Algorithms (50x50 Network)Algorithms (50x50 Network)

BS is located at (25, 150) BS is located at (25, 250)

2525

Variance of Residual PowerVariance of Residual PowerWhen 1st Node DiesWhen 1st Node Dies

BS is located at (25, 150) BS is located at (25, 250)

2626

ConclusionsConclusions

Optimal chain problem is NP-hardOptimal chain problem is NP-hardMST-appending and MST-reduced both MST-appending and MST-reduced both have the merits of lower time cost and have the merits of lower time cost and better resultsbetter resultsOptimal leader scheduling is a linear Optimal leader scheduling is a linear programming problemprogramming problemMRPF performs nearly the same as the MRPF performs nearly the same as the optimal schedulingoptimal scheduling