Optimizing Lifetime for Continuous DataAggregation With Precision Guarantees in Wireless Sensor Networks

Xueyan Tang and Jianliang Xu

IEEE/ACM TRANSACTIONS ON NETWORKING, AUGUST 2008

Outline Introduction Data Aggregation with Precision-Guarantees

Quality-Guarantees Quality-aware

Precision Allocation in Single-Hop Networks Precision Allocation in Multi-Hop Networks Performance Evaluation Conclusion

Introduction (1/2)

Wireless Sensor Networks

Introduction (2/2) Data Aggregation

20 22 18 20

20 22 18 20

18 22

AVERAGE

20 20

20 22 18 20

20 22 18 20

18 22

MAX

22 22

20 22

Data Aggregation with Precision-Guarantee Query Example

“average temperature reading of all sensor nodes within an error bound of 3 oC.”

Idea: the sensor nodes do not have to report all

readings to the base station. Only the updates necessary to guarantee

the desired level of precision For example, send if | Xt+1 – Xt| > 0.5 oC

Data Aggregation with Precision-Guarantee

20->20.2

22 18->19 20->19.8

20 22 19 20

18 22

AVERAGE

20 20.3

20 22 18 20

20 22 18 20

18 22

Time t

20 20

Time t+1

Total Error bound: 3 oC Error bound of each sensor : 0.5 oC

20

Approximate: 20.15

Real: 20.16

Data Aggregation with Precision-Guarantee The problem is:

How to allocate user-specified precision among sensor nodes such that the network lifetime is maximized?Given the error bound: E

e1 e2

e3 e4 e5 e6

Objective:

Maximize network lifetime

Subject to:

6

1i

i

e E

Precision Allocation in Single-Hop Networks

1 2 3 n

Given the error bound: E

e1 e2 en-1 en

Objective:

Maximize network lifetime

Subject to:

1

n

ii

e E

…

Precision Allocation in Single-Hop Networks

Network lifetime

Objective: Maximize

Subject to:

1

n

ii

e E

pi : residual energy

ui(ei) : rate-error function

si : energy cost per data

transmission

Optimal Precision Allocation

l1

l2

l3

l4

Minimum lifetime for sensor i

Optimal Precision Allocation

l1

l2

l3

l4

Minimum lifetime for sensor i

e1*

l*

e2*

e3*

e4* = 0

e1*+ e2

*+ e3*+ e4

* = E

Maximum lifetime = l*

Optimal Precision Allocation

proof

Candidate Error Bounds- Continuous v.s. Discrete

l2

l3

l4

l1

e11

e12

e13

e14

e21

e22

e23

e24

e31

e32

e33

e34

e41

e42

e43

e44

Candidate-Based Precision Allocation- Optimal Candidate Precision Allocation

l2

l3

l4

l1

e11

e12

e13

e14

e21

e22

e23

e24

e31

e32

e33

e34

e41

e42

e43

e44

12

3

45 6

7

Precision Allocation in Multi-Hop Networks

Given the error bound: E

e1 e2

e3 e4 e5 e620->20.2

22 18->19 20->19.8

20 22 19 20

18 22

20 20.3

Approximate: 20.15

Real: 20.16

6

1i

i

e E

Precision Allocation in Multi-Hop Networks

Network lifetime

Objective:Minimize

Subject to:

,1

i

n

i xi

e E

pi : residual energy

ui , xi : rate-error function

si : energy cost per data

transmission

vi : energy cost per data

receiving

NP-Hard!!!!!

Distributed Suboptimal Candidate Precision Allocation

3

1 2

e11, e12,…, e1m

u11, u12,…, u1m

e11, e12,…, e1m

u11, u12,…, u1m

Threshold: T31, T32,…, T3m

Optimal allocation: A31, A32,…, A3m

Gross error bound: E31, E32,…, E3m

Example:For A31

Find an optimal allocation is e1p , e2q

Such that

E31 = e31 + e1p + e2q T31

e31, e32,…, e3m

u31, u32,…, u3m

Distributed Suboptimal Candidate Precision Allocation

3

1 2

E31, E32,…, E3m

U31, U32,…, U3m

7

6

54

E61, E62,…, E6m

U61, U62,…, U6m

Threshold: T71, T72,…, T7m

Optimal allocation: A71, A72,…, A7m

Gross error bound: E71, E72,…, E7m

e71, e72,…, e7m

u71, u72,…, u7m

For A71

Find an optimal allocation is E3p , E6q

Such that

E71 = e71 + E3p + E6q T71

Performance Evaluation Simulation Setup

Energy cost in transmitting a message

s : message size : distance-independent term (50 nj/b) : coefficient (100 pj/b/m2) q: distance-dependent term ( 2) d: distance

Energy cost in receiving a message is set at 50 nJ/b

Network Layout

Network Layout

Performance Evaluation

Single-Hop Network

Single-Hop Network

Multi-Hop Network

Multi-Hop Network

Conclusion This paper proposes an adaptive precision

allocation to differentiate the quality of data collected from different sensors, thereby balancing their energy consumption.

Experimental results show that (1) tolerating just a small degree of inaccuracy

prolongs network lifetime (2) uniform allocation does not perform well even if

the readings at all nodes follows similar changing pattern

(3) the proposed schemes significantly outperform existing methods.