Adaptive Data Collection Strategies for Lifetime-Constrained Wireless Sensor Networks Xueyan Tang Jianliang Xu Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore; Parallel and Distributed Systems, IEEE Transactions on June 2008

Outline Introduction Problem Formulation Single-hop networks Optimal Data Update Solution (Off-line) Adaptive Data Update Strategy (On-line) Adaptive Aggregate Data Update Multi-hop networks Performance Evaluation Conclusion

Data Report Problem (1/3) - Single-hop Networks Consider 10 solar radiation readings 369, 330, 264, 266, 274, 279, 260, 233, 225 Assume the total energy budget of a sensor is three updates (i.e., send only three updates) Periodically update strategy Sends the 1-th, 4-th, and 7-th readings 369, skip, skip, 266, skip, skip, 260, skip, skip Approximate readings 369, 369, 369, 266, 266, 266, 260, 260, 260 Reconstructed data

Data Report Problem (2/3) - Single-hop Networks Data Error (Deviation) Exact readings : 369, 330, 264, 266, 274, 279, 260, 233, 225 Approximate readings: 369, 369, 369, 266, 266, 266, 260, 260, 260 Error = = 227. error

Data Report Problem (3/3) - Single-hop Networks Better Update Strategy sends the 1-th, 4-th, and 8-th readings 369, skip, skip, 266, skip, skip, skip, 233, skip approximate readings 369, 369, 369, 266, 266, 266, 266, 233, 233 Error = ?+0+ 8 = 78 error

Problem Formulation (1/3) - Single-hop Networks Problem: Exact readings : 369, 330, 264, 266, 274, 279, 260, 233, 225 ………… Find M updates such that root-mean-square of collected data error is minimized.

Problem Formulation (2/3) - Single-hop Networks Assume Exact readings (T: given network lifetime): d 1, d 2, …, d T Energy budget (at most): M updates Data updates at times: v 1 =1, v 2, v 3, …, v M Ex: v 1 =1  1-th reading (first update) v 2 =3  3-th reading (second update) Approximate readings:

Problem Formulation (3/3) - Single-hop Networks Find v 1 =1, v 2, v 3, …, v M such that is minimized. where

Optimal Data Update Solution (Off-line Version) Assume that all sensor readings are known a priori Exact readings d 1, d 2, …, d T are known Solve by a dynamic programming algorithm.

Dynamic Programming (1/4) Let be an optimal solution to the (t, m)-optimization problem. Claim: must be an optimal solution to the (t -1, m -1)-optimization problem.

Dynamic Programming (2/4) Proof Assume there exists a better solution

Dynamic Programming (3/4)

Dynamic Programming (4/4) Let A(t, m) be the minimal achievable total square error to the (t, m)-optimization problem. Let B(t, m) be the time of the last data update in the optimal solution.

Adaptive Data Update Strategy (On-line Version) Idea Let the sensor node update a new reading with the base station only when the new reading substantially differs from the last update. i.e., update only if Example: W = , 330, 264, 266, 274, 310, 260, 233, 225

Adaptive Data Update Strategy (On-line Version) Issues The number of updates are decided by W How to dynamically adjust W Assume that the energy budgets: 3 updates Expected data update period : Once every 3 time units 369, 330, 264, 266, 274, 279, 260, 233, 225

Adaptive Data Update Strategy (On-line Version) Measure the data update period every time a new reading is updated. Estimate of data update period Compare with the expected data update period I E :

Adaptive Data Update Strategy (Algorithm) Initialization

Adaptive Data Update Strategy (Algorithm)

Adaptive Aggregate Data Update - Multi-hop networks Problem in multi-hop networks bottleneck Node A : receive 6 updates sends 3 updates

Adaptive Aggregate Data Update - Multi-hop networks Node A : receive 6 updates sends 8 updates Node A : receive 6 updates sends 3 updates

Allocating Number of Updates The number of updates that node can send is bottleneck send receive Total energy

Allocating Number of Updates -Idea Round tRound t+1 Assume thresholds W A = 3, W B =2, W C = |22-19| > W B |21-20| < W C | | < W A

Goal The objective is to let the sensor nodes send as many updates as possible subject to the energy constraints

Update Allocation Algorithm - An Example u i : unused energy budget x i : min(x i, x pi ) c i : allocated number of updates Assume that s = 1 units (send) and v = 1 units (receive) u i /x i /c i A: u i = 12 (initial) x i = 12/(2+1) = 4 c i = min(4, ∞ )=4 Round 1

Update Allocation Algorithm - An Example u i : unused energy budget x i : min(x i, x pi ) c i : allocated number of updates Assume that s = 1 units (send) and v = 1 units (receive) u i /x i /c i B: u i = 12 (initial) x i = 12/(3+1) = 3 c i = min(4, 3 ) = 3 Round 1

Update Allocation Algorithm - An Example u i : unused energy budget x i : min(x i, x pi ) c i : allocated number of updates Round 2 A: u i = = 2 x i = 2/(0+1) = 2 c i = min(2, ∞ )+4=6

Update Allocation Algorithm

Performance Evaluation Experimental Setup

Performance Evaluation - Single-hop (without aggregation )

Performance for Parameter Settings

Performance Evaluation - Multi-hop (MAX Aggregation)

Performance Evaluation - Multi-hop (Average Aggregation)

Conclusion This paper developed adaptive strategies for both individual and aggregate data collections to make full use of the energy budgets of sensor nodes. Experimental results show that, compared to the periodic strategy, adaptive strategies significantly improve the accuracy of collected data.