Wireless Sensor Placement for Reliable and Efficient Data Collection

1. Wireless Sensor Placementfor Reliable and Efficient Data Collection Edo Biagioni and Galen Sasaki University of Hawaii at Manoa

2. Overview • Wireless Sensor Networks • Case study: an ecological wireless sensor network • Design Considerations • Regular Deployments • Linear and other arrangements

3. Sensor Networks are Useful • Ecological study: under what conditions does the endangered species thrive? • Knowing the environment aids in setting goals or controlling processes • Many applications, including ecological, industrial, and military

4. Ad-hoc Wireless Networks • Low-power operation • Range-limited radios • Ad-hoc networking: each node forwards data for other nodes • Data may be combined en route

5. Wireless Sensor Network Design • How densely must we sample the environment? • What is the radio communications range? • How much reliability do we have, and how does it improve if we add more units? • How many units can we afford?

6. The PODS project at the University of Hawaii • Ecological sensing of Rare Plant environment • Temperature, sunlight, rainfall, humidity • High-resolution images • Kim Bridges, Brian Chee

7. Intensive deployment where the plant does grow Interested also in where the plant does not grow Connection to the internet is also a line of sensors Pod placement Sub-region

8. Practical Constraints • Higher radios have more range • Camouflage • Plant densities may vary • Different units may have different sensors • Ignored in this talk

9. Design Goals for Deployment We are given a 2-dimensional square region with total area A • Minimize the maximum distance between any point in A and the nearest sensor • Keep the distance between adjacent sensors less than r • Measure point values, compute gradients and significant thresholds

10. Design Considerations • Financial and other constraints often limit the total number of nodes, N • Failure of individual nodes should not disable the entire network • Reducing the transmission range improves the energy efficiency

11. Square, triangular, or hexagonal tiles Nodes must be within range r of their neighbors Sampling distance δ Degree 4, 6, or 3 provides redundancy Which is best? (b) Triangle tile a (a) Square tiles (c) Hexagon tile Regular Deployments

12. Computing with N, r, δ • Standard formulas for tile area (α) and for distance to the center of the tile • Distance to center < δ • Distance between nodes < r • Each node is part of c = (6, 4, or 3) tiles • N = (A/α)/c, where A/α is the number of tiles

13. Main Results for Regular Grids • N is proportional to the surface area of A • if r < δ, hexagonal deployment minimizes N, and N is inversely proportional to r2 • If δ < r, triangular deployment minimizes N, and N is inversely proportional to δ2 • Triangular, square, or hexagonal are within a factor of two of each other

14. If r < δ, we can reduce the number of nodes by going to sparse grids (sparse meshes) Communication distance remains small the number of nodes may drop substantially 3 nodes per side, s=3 Sparse Grids S=3

15. Main Results for Sparse Grids • Communication radius r, tile side a = r * s • N is inversely proportional to a and to r • The degree of most nodes is two, so reliability is reduced – the same as for linear deployments

16. 1-Dimensional Deployment • Many common applications: along streams, roads, ridges • Requires relatively few nodes • With the least number of nodes for a given r, network fails if a single node fails • How well can we do if we double the number of nodes?

17. Paired Inline Protection against node failures r r

18. Paired and Inline Performance • For inline, two successive node failures disconnect the network • For paired, failure of the two nodes of a pair disconnects the network • The former is about twice as likely

19. Sampling a Gradient • If we know the gradient, a linear deployment is sufficient • A gradient can be computed from three samples in a triangle • Variable gradients need more and longer baselines, as do threshold determinations • Grids and sparse grids measure gradients well

20. Quantifying a gradient The differences between pairs of samples help determine the gradient

21. The ultimate sparse grid: a circle Tolerates single node failures Even sampling in all directions Lines outward from the center: a star Center is well covered Star-3, Star-4, Star-5, Star-m Minimizing the number of nodes

22. Summary • Many regular deployments • Generally, N and r are given, sampling distance is allowed to vary • Tradeoff between N and redundancy: sparse grids allow large sampling distance • Lines, circles, stars are optimal when N is small, can provide information about gradients

23. Acknowledgements • Kim Bridges • Brian Chee and many students on the Pods project, including Michael Lurvey and Shu Chen • DARPA (Pods funding) • Hawaii Volcanoes National Park