Chapter 14 (part I) WSN: Coverage and Energy Conservation

1. Chapter 14 (part I)WSN: Coverage and Energy Conservation 國立交通大學 資訊工程系 曾煜棋教授 Prof. Yu-Chee Tseng

2. Research Issues in Sensor Networks • Hardware (2000) • CPU, memory, sensors, etc. • Protocols (2002) • MAC layers • Routing and transport protocols • Applications (2004) • Localization and positioning applications • Management (2008) • Coverage and connectivity problems • Power management • etc.

3. Coverage Problems • In general • Determine how well the sensing field is monitored or tracked by sensors. • Possible Approaches • Geometric Problems • Level of Exposure • Area Coverage • Coverage • Coverage and Connectivity • Coverage-Preserving and Energy-Conserving Problem

4. Review: Art Gallery Problem • Place the minimum number of cameras such that every point in the art gallery is monitored by at least one camera.

5. Review: Circle Covering Problem • Given a fixed number of identical circles, the goal is to minimize the radius of circles.

6. Level of Exposure • Breach and support paths • paths on which the distance from any point to the closest sensor is maximized and minimized • Voronoi diagram and Delaunay triangulation • Exposure paths • Consider the duration that an object is monitored by sensors

7. Coverage and Connectivity • Extending the coverage such that connectivity is maintained. • A region is k-covered, then the sensor network is k-connected if RC 2RS

8. Coverage-Preserving and Energy-Conserving Protocols • Sensors' on-duty time should be properly scheduled to conserve energy. • This can be done if some nodes share the common sensing region. • Question: Which sensors below can be turned off?

9. The Coverage Problems in 2D Spaces (ACM MONET, 2005)

10. Coverage Problems • In general • To determine how well the sensing field is monitored or tracked by sensors • Sensors may be randomly deployed

11. Coverage Problems • We formulate this problem as • Determine whether every point in the service area of the sensor network is covered by at least a sensors • This is called “sensor a–coverage problem”. • Why a sensors? • Fault tolerance, quality of service • applications: localization, object tracking, video surveillance

12. Is this area 1-covered? So this area is not 1-covered! This region is not covered by any sensor! This area is not only 1-covered, but also 2-covered! What is the coverage level of this area? The 2D Coverage Problem 1-covered means that every point in this area is covered by at least 1 sensor 2-covered means that every point in this area is covered by at least 2 sensors Coverage level = a means that this area is a-covered

13. Sensing and Communication Ranges 1Honghai Zhang and Jennifer C. Hou, ``On deriving the upper bound of a-lifetime for large sensor networks,'' Proc. ACM Mobihoc 2004, June 2004

14. Assumptions • Each sensor is aware of its geographic location and sensing radius. • Each sensor can communicate with its neighbors. • Difficulties: • There are an infinite number of points in any small field. • A better way: O(n2) regions can be divided by n circles • How to determine all these regions?

15. The Proposed Solution • We try to look at how the perimeter of each sensor’s sensing range is covered. • How a perimeter is covered implies how an area is covered • … by the continuity of coverage of a region • By collecting perimeter coverage of each sensor, the level of coverage of an area can be determined. • a distributed solution

16. How to calculate the perimeter cover of a sensor? Si is 2-perimeter-covered

17. Relationship between k-covered and k-perimeter-covered • THEOREM. Suppose that no two sensors are located in the same location. The whole network area A is k-coverediff each sensor in the network is k-perimeter-covered.

18. Detailed Algorithm • Each sensor independently calculates its perimeter-covered. • k = min{each sensor’s perimeter coverage} • Time complexity: nd log(d) • n: number of sensors • d: number of neighbors of a sensor

19. Simulation Results

20. A Toolkit

21. Summary • An important multi-level coverage problem! • We have proposed efficient polynomial-time solutions. • Simulation results and a toolkit based on proposed solutions are presented.

22. The Coverage Problem in 3D Spaces (IEEE Globecom 2004)

23. What is the coverage level of this 3D area? The 3D Coverage Problem

24. The 3D Coverage Problem • Problem Definition • Given a set of sensors in a 3D sensing field, is every point in this field covered by at least a sensors? • Assumptions: • Each sensor is aware of its own location as well as its neighbors’ locations. • The sensing range of each sensor is modeled by a 3D ball. • The sensing ranges of sensors can be non-uniform.

25. Overview of Our Solution • The Proposed Solution • We reduce the geometric problem • from a 3D space to one in a 2D space, • and then from a 2D space to one in a 1D space.

26. Reduction Technique (I) • 3D => 2D • To determine whether the whole sensing field is sufficiently covered, we look at the spheres of all sensors • Theorem 1: If each sphere is a-sphere-covered, then the sensing field is a-covered. • Sensor si isa-sphere-covered if all points on its sphere are sphere-covered by at least a sensors, i.e., on or within the spheres of at least a sensors.

27. Reduction Technique (II) • 2D => 1D • To determine whether each sensor’s sphere is sufficiently covered, we look at how each spherical cap and how each circle of the intersection of two spheres is covered. • (refer to the next page) • Corollary 1: Consider any sensor si. If each point on Si is a-cap-covered, then sphere Si is a-sphere-covered. • A point p is a-cap-covered if it is on at least a caps.

28. Cap and Circle

29. k-cap-covered • p is 2-cap-covered(by Cap(i, j) and Cap(i, k)).

30. Reduction Technique (III) • 2D => 1D • Theorem 2: Consider any sensor si and each of its neighboring sensor sj. If each circle Cir(i, j) is a-circle-covered, then the sphere Si is a-cap-covered. • A circle is a-circle-covered if every point on this circle is covered by at least a caps.

31. k-circle-covered • Cir(i, j) is 1-circle-covered(by Cap(i, k)). Cap(i, k) Cir(i, j)

32. Reduction Technique (IV) • 2D => 1D • By stretching each circle on a 1D line, the level of circle coverage can be easily determined. • This can be done by our 2-D coverage solution.

33. Reduction Example =>

34. Reduction Example =>

35. Calculating the Circle Coverage

36. Calculating the Circle Coverage =>

37. Calculating the Circle Coverage =>

38. Calculating the Circle Coverage =>

39. The Complete Algorithm • Each sensor si independently calculates the circle coverage of each of the circle on its sphere. • sphere coverage of si = min{ circle coverage of all circles on Si } • overall coverage = min{ sphere coverage of all sensors }

40. Complexity • To calculate the sphere coverage of one sensor: O(d2logd) • d is the maximum number of neighbors of a sensor • Overall: O(nd2logd) • n is the number of sensors in this field

41. Short Summary • We define the coverage problem in a 3D space. • Proposed solution • 3D => 2D => 1D • Network Coverage => Sphere Coverage => Circle Coverage • Applications • Deploying sensors • Reducing on-duty time of sensors

42. A Decentralized Energy-Conserving, Coverage-Preserving Protocol (IEEE ISCAS 2005)

43. Overview • Goal: prolong the network lifetime • Schedule sensors’ on-duty time • Put as many sensors into sleeping mode as possible • Meanwhile active nodes should maintain sufficient coverage • Two protocols are proposed: • basic scheme (by Yan, He, and Stankovic, in ACM SenSys 2003) • energy-based scheme (by Tseng, IEEE ISCAS 2005)

44. Basic Scheme • Two phases • Initialization phase: • Message exchange • Calculate each sensor’s working schedule in the next phase • Sensing phase: • This phase is divided into multiple rounds. • In each round, a sensor has its own working schedule. • Reference time: • Each sensor will randomly generate a number in the range [0, cycle_length] as its reference time.

45. Structure of Sensors’ Working Cycles • Theorem: • If each intersection point between any two sensors’ boundaries is always covered, then the whole sensing field is always covered. • Basic Idea: • Each sensor i and its neighbors will share the responsibility, in a time division manner, to cover each intersection point.

46. Ref a Ref b Ref c Ref d c b a d 聯集: a’s final on-duty time in round i An Example (to calculate sensor a’s working schedule) ……… Round 1 Round 2 Round n Initial phase Sensing phase Initial phase Round i

47. more details … • The above will also be done by sensors b, c, and d. • This will guarantee that all intersection points of sensors’ boundaries will be covered over the time domain.

48. Energy-Based Scheme • goal: based on remaining energy of sensors • Nodes with more remaining energies should work longer. • Each round is logically separated into two zones: • larger zone: 3T/4 • smaller zone: T/4. • Reference time selection: • If a node’s remaining energy is larger than ½ of its neighbors‘, randomly choose a reference time in the larger zone. • Otherwise, choose a reference time in the smaller zone. • Work schedule selection: • based on energy (refer to the next page)

49. Ref a Ref b Ref c Ref d Energy-Based Scheme (cont.) • Frontp,i and Backp,i are also selected based on remaining energies. richer rich poor Round i

50. Two Enhancements • k-Coverage-Preserving Protocol • (omitted) • active time optimization • Longest Schedule First (LSF) • Shortest Lifetime First (SLF)