1. Minimizing Energy Consumption with Probabilistic Distance Models in Wireless Sensor Networks Yanyan Zhuang, Jianping Pan, Lin Cai University of Victoria, Canada

2. 2 Background & Related Work Clustering Schemes Cluster Head (CH) + cluster nodes two-tier hierarchical structure: simple node coordination Multi-hop: avoid long-range transmissions

3. 3 Background & Related Work (cont.)‏ Grid-Based Clustering Partition: equal-sized squares Facilitate data dissemination: sensors can transmit data without route setup in advance Manhattan Walk Diagonal-First Routing

4. 4 Background & Related Work (cont.)‏ Variable-size Clustering traffic volume highly skewed → bottleneck consume their energy much faster than other nodes → earlier breakdown of the network Existing Work time synchronization/frequent message exchanges linear network, or quasi-two-dimensional

5. 5 Distance Distribution Model Wireless Transmitter : data transmission rate : a constant related to the environment : path loss exponent [2,6]

6. 6 Distance Distribution Model Energy consumption → node distance → average distance (?) → Average Distance Model Grid structure & geometric property → probabilistic distance distribution → Distance Distribution Model

7. 7 Coordinate Distributions Two nodes in same grid (AB): U[0,1] Two nodes in diagonal grids (PQ)‏ X1, Y1 ~ U[0,1] and X2, Y2 ~ U[-1,0] Two nodes in parallel grids (RS)‏ X1, Y1, Y2 ~ U[0,1] and X2 ~ U[-1,0]

8. 8 Distance Distributions Node distance: Goal: Four step derivation Difference --> Square --> Sum --> Square Root

9. 9 Distance Distributions Node distance: Goal: Four step derivation Difference --> Square --> Sum --> Square Root

10. 10 (1) Difference distribution Example: P and Q

11. 11 (2) Square distribution Example: P and Q

12. 12 (3) Sum distribution (4) Square-root distribution

13. 13 Example: P and Q

14. 14 PDF within a Unit Grid & Polyfit

15. 15 PDF between Parallel/Diagonal Grids Parallel Diagonal

16. 16 Probabilistic Energy Optimization Simulation Setup: Friis Free Space & Two-Ray Ground cross-over distance : system loss factor : rx/tx antenna height : wavelength of the carrier signal

17. 17 Distance Verification CDF vs. Simulation One-hop Energy Consumption

18. 18 Total Energy Consumption: Distance Distribution vs. Average Model

19. 19 Improvement: Variable Size Griding P and Q X1, Y1 ~ U[0,1-q] X2, Y2 ~ U[-q(1-q),0] R X1 ~ U[-q,0], Y1 ~ U[0,1-q] S X2 ~ [-q, -q(1-q)], Y2 ~ U[-q(1-q),0]

20. 20 Distance Verification CDF vs. Simulation One-hop Energy Consumption CDF with q=0.4 and 0.7 One-Hop Energy Consumption with q=0.5

21. 21 Per-Grid/Total Energy Consumption vs. Size Ratio

22. 22 Conclusions Energy consumption model based on distance distributions Nonuniform grid-based clustering: both data traffic and energy consumption balanced The importance of grid-based clustering and the optimal grid size ratio that can balance the overall energy consumption

23. 23 Thanks! Q&A

24. 24 Coordinate Distributions Two nodes in same grid (AB): U[0,1] Two nodes in diagonal grids (PQ)‏ X1, Y1: U[0,1] and X2, Y2: U[-1,0] Two nodes in parallel grids (RS)‏ X1, Y1, Y2: U[0,1] and X2: U[-1,0]

25. 25 X1, Y1 ~ U[0,1] X2, Y2 ~ U[-1,0]

26. 26 Improvement: Variable Size Griding PQ: X1, X2 ~ U[0,1-q] and Y1, Y2 ~ U[-q(1-q),0] R: X1 ~ U[-q,0], Y1 ~ U[0,1-q] S: X2 ~ [-q, -q(1-q)], Y2 ~ U[-q(1-q),0]

27. 27 Wireless Channel Model : the data transmission rate : a constant related to the environment : path loss exponent [2,6] : distance distribution function (poly fit appx)‏