maximization of system lifetime for data-centric wireless sensor networks 指導教授：林永松...

Maximization of System Lifetime for Data-Centric Wireless Sensor Networks

指導教授：林永松博士

具資料集縮能力無線感測網路系統生命週期之最大化

研究生：郭文政

國立臺灣大學資訊管理學研究所碩士論文審查

民國 95年 7月 27 日

2

Outline

Introduction Background Motivation

Problem Description & Formulation Solution Approach

Lagrangean Relaxation method Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work

3

Introduction

Wireless sensor networks Sensing Computation Communication

4

Introduction (cont’d)

Issues End-to-end delay Coverage Lifetime (Energy Consumption)

Data Aggregation treesClusteringSpanning trees

5

Background

Clustering LEACH (Low- Energy Adaptive Clustering Hierarchy) *

Set-up phase Steady state phase

Spanning trees PEDAP(Power Efficient Data gathering and Aggregation Protocol) **

Minimum cost spanning tree: Prim’s algorithm PEDAP-PA (Power Efficient Data gathering and Aggregation Protocol- Po

wer Aware) Remaining energy concept

* W. Heinzelman, A. Chandrakasan and H. Balakrishnan, "Energy-Efficient Communication Protocol for Wireless Microsensor Networks", the 33rd Hawaii International Conference on System Sciences, Jan. 2000.

** H. O. Tan and I. Korpeoglu, “Power Efficient Data Gathering and Aggregation in Wireless Sensor Networks”, ACM SIGMOD Record, vol. 32, no. 4, pp. 66-71, 2003

6

Motivation

How to energy-efficient construct the data aggregation trees to reduce the power consumption and further prolong the system lifetime?

Event

Source node

Relay node

Sink node

7

Problem Description

Source node

Relay node

Sink node

Event

In the WSN, each event must be monitored by one awake data source node and the nodes transmit the sensed data to the sink node through aggregation trees.

Each aggregation tree is used for one or more rounds. The goal is to maximize the system lifetime under energy capacity constraints.

8

Problem Description (cont’d)

25 Rounds

11 Rounds 16 Rounds

52 Rounds

9


Assumption Heterogeneous network Fixed sensing range and fixed transmission range Bidirectional links Error-free transmission within the transmission radius The sink node knows nodes all a priori

Given The network topology includes node set and link set The set of data source nodes The set of events The sink node Capacity for each node evaluated by residual power lifetime Transmission cost of each link with respect to energy consumption

10


Objective To maximize the system lifetime of the sensor network

Subject to Event constraint: Each event must be monitored by one awake data

source node and the awake data source nodes sense and transmit the sensed data to the sink node.

Battery constraint: The total power consumption of a node can not exceed its initial energy level.

To determine The number of times that tree t is used

11

Problem Formulation

12

Problem Formulation (cont’d)

Objective Function

max (IP) subject to:

tt T

r

w

pr wrp P

x

w

pr pl lrp P

x y

1lr

l o

y

wr lr

l w

y

w W r R

l L r Rw W

o N W r R

w W r R

(IP 1)

(IP 2)

(IP 3)

(IP 4)

1wr iww W

e

i V r R

(IP 5)1lr

l s

y

r R (IP 6)

lr tl trt T

y z

w

pr pn nrp P

x

n N r R w W

l L r R (IP 7)

(IP 8)

Eventconstraints

Treeconstraints

13


1trt T

z

tr t

r R

z r

q wr m s w

r R r R

E E E C

q nr r s n

r R r R

E E E C

r R

t T

w W

n N

(IP 9)

(IP 10)

(IP 11)

(IP 12)

wr

nr

trz

lry

{0,1,2,..., }t tr Mprx

w W r R

n N

t T

l L

wp P w W

r R

r R

r R

r R

.t T

(IP 13)

(IP 14)

(IP 15)

(IP 16)

(IP 17)

(IP 18)

= 0 or 1

= 0 or 1

= 0 or 1

= 0 or 1

= 0 or 1

Energy constraints

14

Lagrangean Relaxation Method

Relax Constraints (3) 、 (5) 、 (7) 、 (8) 、 (11) 、 (12) and we can obtain the following Lagrangean relaxation problem (LR)

Primal Problem

LagrangeanRelaxation

Problem

prxwr lry trz tr nr

LagrangeanDual

Problem

OptimalSolution

OptimalSolution

OptimalSolution

OptimalSolution

Adjust Multipliers

15

Subproblem 1 (related to decision variable )prxwr

1 2 3 6

1 3 2 5

min

min

w w

w

lrw pr pl wr wr nrw pr pn wr wr m sl L r R w W p P w W r R n N r R w W p P w W r R

lrw pl nrw pn pr wr w m s wrw W r R p P l L n N w W r R

x x E E

x E E

w

pr wrp P

x

subject to:

1wr iww W

e

wr

prx

= 0 or 1

= 0 or 1

w W r R

w W r R

w W r R

wp P w W .r R

(Sub1 1.1)

(Sub1 1.2)

(Sub1 1.3)

(Sub1 1.4)

Firstly, set the decision variable to be 1 or 0 according to the corresponding coefficient. Then, solve the shortest path problem by Dijkstra’s algorithm if the decision variable is 1.

wr

wrTime complexity: 2

O W N

16

Subproblem 2 (related to decision variable )

1 2 4

4 1 2

min lrw lr wr lr lr lrl L r R w W w W r R l L r Rl w

lr lrw wr lrr R l L w W w Wl w

y y y

y

1lrl o

y

1lrl s

y

lry

subject to:

o N W r R

r R

l L .r R

lry

(Sub2 2.1)

(Sub2 2.2)

(Sub2 2.3)= 0 or 1

Compute the coefficient of each link. Pick up at most one outgoing link of each node and at least one incoming link of the sink node according to the corresponding coefficient.

Time complexity: O W

17

Subproblem 3 (related to decision variable )trz tr

4

4

min t lr tl trt T l L r R t T

t lr tl trt T r R t T l L

r z

r z

1trt T

z

trz

tr tr R

z r

{0,1,2,..., }t tr M

r R

= 0 or 1 t T r R

t T

.t T

(Sub3 3.1)

(Sub3 3.2)

(Sub3 3.3)

(Sub3 3.4)

subject to:

Firstly, solve the spanning tree problem by Prim’s algorithm. Th

en, calculate the sum of the rounds each tree t is used. Time complexity: 2

O W N

18

Subproblem 4 (related to decision variable )nr

3 7

6 3

min

min

nrw nr nr nr r sn N r R w W n N r R

n r s nrw nrn N r R w W

E E

E E

nr

subject to:

= 0 or 1 n N .r R (Sub4 4.1)

Set the decision variable to be 1 or 0 according to the corresponding coefficient.

nr

Time complexity: O W

19

Getting Primal Feasible Solutions

By applying Lagrangean Relaxation method and the subgradient method to solve the problem, we can obtain

A theoretical lower bound of the primal problem Some hints to get a feasible solution to the primal problem

Two major primal decision variables wr trz

20

Getting Primal Feasible Solution

(Tree1)

(Tree2)

(Tree3)

22 Rounds31 Rounds43 Rounds55 Rounds

21

Experiment Scenarios

Random network Grid network

22

Evaluation of Lifetime (Random Network)

Evaluation of Lifetime (Rounds) (Small Network, No. of Nodes = 25)

Random Network

0

20

40

60

80

100

2 5 10

Number of source nodes

Lifet

ime

(Rou

nds)

LR

SA1

SA2

23


Evaluation of Lifetime (Rounds) (Medium Network, No. of Nodes = 49)

Random Network

0

20

40

60

80

100

2 5 10 20


Lifet

ime

(Rou

nds)

LR

SA1

SA2

24


Evaluation of Lifetime (Rounds) (Large Network, No. of Nodes = 81)

Random Network

0

20

40

60

80

100

2 5 10 20 30 40


Lifet

ime

(Rou

nds)

LR

SA1

SA2

25

Evaluation of Lifetime (Grid Network)

Evaluation of Lifetime (Rounds) (Small Network, No. of Nodes = 25)

Grid Network

0

20

40

60

80

100

2 5 10


Lifet

iem

(Rou

nds)

LR

SA1

SA2

26

Evaluation of Lifetime(Grid Network)

Evaluation of Lifetime (Rounds) (Medium Network, No. of Nodes = 49)

Grid Network

0

20

40

60

80

100

2 5 10 20


Lifet

ime

(Rou

nds)

LR

SA1

SA2

27

Evaluation of Lifetime(Grid Network)

Evaluation of Lifetime (Rounds) (Large Network, No. of Nodes = 81)

Grid Network

0

20

40

60

80

100

2 5 10 20


Lifet

ime

(Rou

nds)

LR

SA1

SA2

28

Discussion

The bottleneck of system lifetime The relay nodes around the sink node The source nodes Articulation points

Source node

Relay node

Sink node

Event

29

Conclusion

Contribution Propose a mathematical formulation to model

this complicated problem Devise a simple heuristic algorithm to obtain

good solutions which outperforms PEDAP and PEDAP-AP

Bottleneck of System Lifetime

30

Future Work

End-to-end Delay

Clustering

31

Q & A

-Thanks for your listening

32

Problem Formulation

la

33


34


35

Getting Primal Feasible Solution

The proposed heuristic algorithm is described as follows Step 1: Construct candidate trees based on the solutions to (Sub3) and

select the data source nodes to transmit sensed data based on the solutions to (Sub1).

Step 2: Sort the candidate trees in ascending order with the cost, the total energy consumption in the aggregation tree.

Step 3: Use the tree to transmit the sensed data to the sink node from candidate trees, if satisfied with all constraints, if not, select another tree from the candidate trees. Repeat step2 until the candidate trees are exhausted.

Step 4: Construct a new tree to transmit the sensed data to the sink node based on remaining energy of nodes. Repeat step3 until we can not construct a tree.

Step 5: Compute the lifetime

36

Lagrangean Relaxation method

Relax Constraints (3) 、 (5) 、 (7) 、 (8) 、 (11) 、 (12) and we can obtain the following Lagrangean relaxation problem (LR)

1 2 3 4 5 61 , , , , ,LRz

1

2

3

4

5

6

min

( )

( )

( )

(

w

w

tt T

lrw pr pl lrl L r R w W p P

wr wr lrw W r R l w

nrw pr pn nrn N r R w W p P

lr lr tl trl L r R t T

w q wr m s ww W r R r R

n q nr R sr R r R

r

x y

y

x

y z

E E E C

E E E

)nn N

C

(LR)

37

Lagrangean Relaxation method (cont’d)

w

pr wrp P

x

1lr

l o

y

w W r R

o N W r R

1wr iww W

e

i V r R

1lrl s

y

r R

1trt T

z

tr t

r R

z r

r R

t T

subject to:

(LR 1)

(LR 3)

(LR 4)

(LR 5)

(LR 6)

(LR 2)

38

Lagrangean Relaxation method (cont’d)

wr

nr

trz

lry

{0,1,2,..., }t tr Mprx

w W r R

n N

t T

l L

wp P w W

r R

r R

r Rr R

.t T

(LR 7)

(LR 8)

(LR 9)

(LR 10)

(LR 11)

(LR 12)

= 0 or 1

= 0 or 1

= 0 or 1

= 0 or 1

= 0 or 1

We can decomposed this LR problem into 4 subproblems.

maximization of system lifetime for data-centric wireless sensor networks 指導教授：林永松...

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