Exposure In Wireless Ad-Hoc Sensor Networks

1. Exposure In Wireless Ad-Hoc Sensor Networks Seapahn Meguerdichian Computer Science Department University of California, Los Angeles Farinaz Koushanfar Department of EE and CS University of California Berkeley Gang Qu Electrical and Computer Engineering Department University of Maryland Miodrag Potkonjak Computer Science Department University of California Los Angeles

2. Embedded CPU Memory Battery Sensor(s) Radio Tx/Rx Courtesy: www.rockwellscientific.com GATEWAY MAIN SERVER CONTROL CENTER Wireless Ad-Hoc Sensor Networks

3. Wireless Ad-Hoc Sensor Networks GATEWAY MAIN SERVER CONTROL CENTER

4. Sensor Coverage • Given: • Field A • N sensors How well can the field be observed ? • Closest Sensor (minimum distance) only • Worst Case Coverage: Maximal Breach Path • Best Case Coverage: Maximal Support Path • Multiple Sensors: speed and path considered Minimal Exposure Path

5. Talk Organization • Related work • Introduce Exposure • Preliminaries and problem formulation • Special cases • Exposure calculation algorithm • Experimental results • Open problems and research directions • Conclusion

6. Related Work • Sensor Networks Communications of the ACM, vol. 43, May 2000. • Proactive ComputingD. Tennenhouse. • Embedding The Internet: IntroductionD. Estrin, R. Govindan, J. Heidemann. • Location Discovery ACM SIGMOBILE 2001 (same session) • Dynamic Fine-Grained Localization in Ad-Hoc Networks of SensorsA. Savvides, C. Han, M. Srivastava • Coverage Proceedings of IEEE Infocom, vol. 3, April 2001. • Coverage Problems in Wireless Add-Hoc Sensor NetworksS. Meguerdichian, F. Koushanfar, M. Potkonjak, M. Srivastava

7. Exposure: An Introduction

8. Exposure - Semantics • Likelihood of detection by sensors function of time interval and distance from sensors. • Minimal exposure paths indicate the worst case scenarios in a field: • Can be used as a metric for coverage • Sensor detection coverage • Wireless (RF) transmission coverage • For RF transmission, exposure is a potential measure of quality of service along a specific path.

9. Preliminaries: Sensing Model Sensing model S at an arbitrary point p for a sensor s : where d(s,p) is the Euclidean distance between the sensor s and the point p, and positive constants  and K are technology- and environment-dependent parameters.

10. Preliminaries: Intensity Model(s) Effective sensing intensity at point p in field F : All Sensors Closest Sensor • K Closest Sensors • K=3 for Trilateration

11. Definition: Exposure The Exposure for an object O in the sensor field during the interval [t1,t2]along the path p(t) is:

12. Exposure – Coverage Problem Formulation Given: • Field A • N sensors • Initial and final points I and F Problem: Find the Minimal Exposure Path PminE in A, starting in I and ending in F. PminE is the path in A, along which the exposure is the smallest among all paths from I to F.

13. Special Case – One Sensor Minimal exposure path for one sensor in a square field:

14. General Exposure Computations • Analytically intractable. • Need efficient and scalable methods to approximate exposure integrals and search for Minimal Exposure Paths. • Use a grid-based approach and numerical methods to approximate Exposure integrals. • Use existing efficient graph search algorithms to find Minimal Exposure Paths.

15. Minimal Exposure Path Algorithm • Use a grid to approximate path exposures. • The exposure (weight) along each edge of the grid approximated using numerical techniques. • Use Dijkstra’s Single-Source Shortest Path Algorithm on the weighted graph (grid) to find the Minimal Exposure Path. • Can also use Floyd-Warshall All-Pairs Shortest Paths Algorithm to find PminEbetween arbitrary start and end points.

16. Rectilinear Grids – Not Good Enough Square Equilateral Triangle L Line lengths: Black=Red=Yellow=Blue= 2 xGreen = 2 x L LengthRed=LengthBlue

17. Generalized Grid Generalized Grid – 1st order, 2nd order, 3rd order … More movement freedom  more accurate results Approximation quality improves by increasing grid divisionswith higher costs of storage and run-time.

18. Minimal Exposure Path Algorithm Complexity • Single Source Shortest Path (Dijkstra) • Each point is visited once in the worst case. • For an nxn grid with m divisions per edge:n2(2m-1)+2nm+1 total grid points. • Worst case search: O(n2m) • Dominated by grid construction. • 1GHz workstation with 256MB RAM requires less than 1 minute for n=32, m=8 grids. • All-Pairs Shortest Paths (Floyd-Warshall) • Has a average case complexity of O(p3). • Dominated by the search: O((n2m)3) • Requires large data structures to store paths.

19. 8x8 m=1 Exposure: 0.7079 Length: 1633.9 16x16 m=2 Exposure: 0.6976 Length: 1607.7 32x32 m=8 Exposure: 0.6945 Length: 1581.0 PminE – Uniform Random Deployment Minimal exposure path for 50 randomly deployed sensors using the All-Sensor intensity model (IA).

20. Exposure – Statistical Behavior Diminishing relative standard deviation in exposure for 1/d2 and 1/d4 sensor models.

21. Sensors Cross Triangle Hexagon Exposure Level (compared to Square) ~20 6x 3x 1.5x ~120 30x 1.5x 1.5x PminE– Deterministic Deployment Minimal exposure path under the All-Sensor intensity model (IA) and deterministic sensor deployment schemes. Cross Square Triangle Hexagon

22. Exposure – Research Directions • Localized implementations • Performance and cost studies subject to • Wireless Protocols (MAC, routing, etc) • Errors in measurements • Locationing • Sensing • Numerical errors • Computation based on incomplete information • Not every node will know the exact position and information about all other nodes

23. Summary • Exposure: • Definition • Efficient Algorithm • Centralized Implementation • Algorithm: • Generalized grid approximation • Application of graph search algorithms • Ad-hoc wireless sensor networks: • Coverage • Quality of Service • Research: • Numerous interesting open problems