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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 (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
e1*
l*
e2*
e3*
e4* = 0
e1*+ e2
*+ e3*+ e4
* = E
Maximum lifetime = l*
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
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.
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