Minimizing Energy Consumption with Probabilistic Distance Models in Wireless Sensor Networks

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

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

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

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

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

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

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

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

13. Example: P and Q

14. PDF within a Unit Grid & Polyfit

15. PDF between Parallel/Diagonal Grids • Parallel Diagonal

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

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

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

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. Thanks! • Q&A

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. X1, Y1 ~ U[0,1] • X2, Y2 ~ U[-1,0]

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