1. Optimizing Lifetime for Continuous Data Aggregation With Precision Guarantees in Wireless Sensor Networks Xueyan Tang and Jianliang Xu IEEE/ACM TRANSACTIONS ON NETWORKING, AUGUST 2008

2. 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

3. Introduction (1/2) Wireless Sensor Networks

4. Introduction (2/2) Data Aggregation 20221820 221820 1822 AVERAGE 20 221820 221820 1822 MAX 22 20 22

5. Data Aggregation with Precision-Guarantee Query Example “ average temperature reading of all sensor nodes within an error bound of 3 o C. ” 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 | X t+1 – X t | > 0.5 o C

6. Data Aggregation with Precision-Guarantee 20->20.222 18->19 20->19.8 20221920 1822 AVERAGE 2020.3 20221820 221820 1822 Time t 20 Time t+1 Total Error bound: 3 o C Error bound of each sensor : 0.5 o C 20 Approximate: 20.15 Real: 20.16

7. 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 e1e1 e2e2 e3e3 e4e4 e5e5 e6e6 Objective: Maximize network lifetime Subject to:

8. Precision Allocation in Single- Hop Networks 123n Given the error bound: E e1e1 e2e2 e n-1 enen Objective: Maximize network lifetime Subject to: …

9. Precision Allocation in Single- Hop Networks Network lifetime Objective: Maximize Subject to: p i : residual energy u i (e i ) : rate-error function s i : energy cost per data transmission

10. Optimal Precision Allocation l1l1 l2l2 l3l3 l4l4 Minimum lifetime for sensor i

11. Optimal Precision Allocation l1l1 l2l2 l3l3 l4l4 Minimum lifetime for sensor i e1*e1* l*l* e2*e2* e3*e3* e 4 * = 0 e 1 * + e 2 * + e 3 * + e 4 * = E Maximum lifetime = l*

12. Optimal Precision Allocation proof

13. Candidate Error Bounds - Continuous v.s. Discrete l2l2 l3l3 l4l4 l1l1 e 11 e 12 e 13 e 14 e 21 e 22 e 23 e 24 e 31 e 32 e 33 e 34 e 41 e 42 e 43 e 44

14. Candidate-Based Precision Allocation - Optimal Candidate Precision Allocation l2l2 l3l3 l4l4 l1l1 e 11 e 12 e 13 e 14 e 21 e 22 e 23 e 24 e 31 e 32 e 33 e 34 e 41 e 42 e 43 e 44 1 2 3 4 5 6 7

15. Precision Allocation in Multi- Hop Networks Given the error bound: E e1e1 e2e2 e3e3 e4e4 e5e5 e6e6 20->20.222 18->19 20->19.8 20221920 1822 2020.3 Approximate: 20.15 Real: 20.16

16. Precision Allocation in Multi- Hop Networks Network lifetime Objective: Minimize Subject to: p i : residual energy u i, xi : rate-error function s i : energy cost per data transmission v i : energy cost per data receiving NP-Hard!!!!!

17. Distributed Suboptimal Candidate Precision Allocation 3 1 2 e 11, e 12,…, e 1m u 11, u 12,…, u 1m e 11, e 12,…, e 1m u 11, u 12,…, u 1m Threshold: T 31, T 32,…, T 3m Optimal allocation: A 31, A 32,…, A 3m Gross error bound: E 31, E 32,…, E 3m Example: For A 31 Find an optimal allocation is e 1p, e 2q Such that E 31 = e 31 + e 1p + e 2q  T 31 e 31, e 32,…, e 3m u 31, u 32,…, u 3m

18. Distributed Suboptimal Candidate Precision Allocation 3 1 2 E 31, E 32,…, E 3m U 31, U 32,…, U 3m 7 6 54 E 61, E 62,…, E 6m U 61, U 62,…, U 6m Threshold: T 71, T 72,…, T 7m Optimal allocation: A 71, A 72,…, A 7m Gross error bound: E 71, E 72,…, E 7m e 71, e 72,…, e 7m u 71, u 72,…, u 7m For A 71 Find an optimal allocation is E 3p, E 6q Such that E 71 = e 71 + E 3p + E 6q  T 71

20. Performance Evaluation Simulation Setup Energy cost in transmitting a message s : message size  : distance-independent term (50 nj/b)  : coefficient (100 pj/b/m 2 ) q: distance-dependent term ( 2) d: distance Energy cost in receiving a message  is set at 50 nJ/b

21. Network Layout

23. Performance Evaluation

24. Single-Hop Network

26. Multi-Hop Network

28. 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.