Coverage and Connectivity Issues in Sensor Networks

1. Coverage and Connectivity Issues in Sensor Networks Ten-Hwang Lai Ohio State University

2. Outline • Introduction to Sensor Networks • Coverage, Connectivity, Density Problems

3. A Sensor Node Memory (Application) Processor Network Interface Actuator Sensor

4. Berkeley Mote: a sensor device prototype • Atmel ATMEGA103 • 4 Mhz 8-bit CPU • 128KB Instruction Memory • 4KB RAM • RFM TR1000 radio • 50 kb/s • Network programming • 51-pin connector

5. Berkeley DOT Mote • Atmel AVR 8535 • 4MHz • 8KB of Memory • 0.5KB of RAM • Low power radio • Power consumption • Active 5mA • Standby 5μA

6. Berkeley Smart Dust • bi-directional communications • sensor: acceleration and ambient light • 11.7 mm3 total circumscribed volume • 4.8 mm3 total displaced volume

7. Smart Clothing & Wearable Computing • Smart Underwear • Smart Eyeglasses • Smart Shoes • …

8. Speckled Computing • 愛丁堡大學（University of Edinburgh）科學家即將研發出大小跟灰塵差不多的超微型晶片, 這些晶片可以分散或噴灑到物體上彼此溝通、傳遞資訊。 這種名為斑點運算（speckled computing）的技術可望在三年內成為事實。 • 將晶片噴到患者的衣物上, 可監控其心跳 、呼吸與體溫。 • Source: Silicon Glen R&D Update, April, 2003  

9. Sensor Networks • Nodes: • Limited in power, computational capacity, memory, communication capacity • Prone to failures • Networks • Large scale • High density • Topology change

10. Sensor Deployment • How to deploy sensors over a field? • Planned deployment • Random deployment • What are desired properties of a “good” deployment?

11. Coverage, Connectivity, Density • Every point is covered by a sensor • K-covered • The network is connected • K-connected • Nodes are not too dense • Others

12. Coverage, Connectivity, and Density Problems • Simple coverage, k-coverage • Density control by turning on/off power • PEAS • OGDC • Topology control by adjusting power • Homogeneous • Per-node • Asymptotic connectivity/coverage

13. Covered Connected • If the covered area is convex and Rt> 2Rs Rt Rs

14. Simple Coverage Problem • Given: an area and a sensor deployment • Question: Is the entire area covered? 1 8 R 2 7 6 3 4 5

15. Is the perimeter covered? 0 360

16. K-covered 1-covered 2-covered 3-covered

17. K-Coverage Problem • Given: an area, a sensor deployment, an integer k • Question: Is the entire area k-covered? 1 8 R 2 7 6 3 4 5

18. Is the perimeter k-covered? 0 360

19. Density Control • Given: an area and a sensor deployment • Problem: turn on/off sensors to maximize the coverage time of the sensor network

20. PEAS • PEAS: A robust energy conserving protocol for long-lived sensor networks • Fan Ye, Gary Zhong, Jesse Cheng, Songwu Lu, Lixia Zhang • UCLA • ICNP 2002

21. PEAS: basic idea yes Wake up Sleep Go to Work? work no

22. Design Issues • How often to wake up? • How to determine whether to work or not? Wake-up rate? yes Wake up Sleep Go to Work? work no

23. How often to wake up? • Desired: the total wake-up rate around a node equals some given value

24. How often to wake up? • f(t) = λ exp(- λt) • exponential distribution • λ = # of times of wake-up per unit time • λ is dynamically adjusted

25. Wake-up rates A f(t) = λ exp(- λt) B f(t) = λ’ exp(- λ’t) A + B: f(t) = (λ + λ’) exp(- (λ + λ’) t)

26. Adjust wake-up rates • Working node knows • Desired wake-up rate λd • Measured wake-up rate λm • Probing node adjusts its λ by λ := λ (λd/ λm)

27. Go to work or return to sleep? • Depends on whether there is a working node nearby. Rp Go back to sleep go to work

28. Rp

29. Is the resulting network covered or connected? • If Rt ≥ (1 + √5) Rp and … • P(connected) → 1

30. OGDC: Optimal Geographical Density Control • “Maintaining Sensing Coverage and Connectivity in Large sensor networks” • Honghai Zhang and Jennifer Hou • MobiCom’03

31. Basic Idea of OGDC • Minimize T, the total amount of overlap • Equivalent to minimizing the number of working nodes • F(x) = the degree of overlap • T =∫ F(x) dx F( ) = 0 F( ) = 1 F( ) = 2

32. Minimum overlap Optimal distance = √3 R

33. Minimum overlap

34. Near-optimal

35. OGDC: the Protocol • Time is divided into rounds. In each round, each node decides whether to be active or not. • Select a starting node. Turn it on and broadcast a power-on message. • Select a node closest to the optimal position. Turn it on and broadcast a power-on message. Repeat this.

36. Selecting starting nodes • Each node volunteers with a probability p. • Backs off for a random amount of time. If hears nothing during the back-off time, then sends a power-on message carrying Sender’s position Desired direction

37. Select the next working node • On receiving a power-on messagefrom a starting node, each node sets a back-off timer inversely proportional to its deviation from the optimal position. • On receiving a power-on messagefrom a non-starting node

39. OGDC vs. PEAS

40. Coverage, Connectivity, and Density Problems • Simple coverage, k-coverage • Density control by turning on/off power • PEAS • OGDC • Topology control by adjusting power • Homogeneous • Per-node • Asymptotic connectivity/coverage

41. Power Control for Coverage and Connectivity • Randomly deploy n nodes over an area. • n: a large number. • How small can transmission power be in order to ensure coverage/connectivity with high probability?

42. Model • A: a unit area • n: number of nodes randomly deployed over A • R(n): transmission range • An edge exists between two nodes if their distance is less than R(n). • G(n): the resulting graph. • Problem: determine R(n) which guarantees G(n)’s connectivity with high probability.

43. On k- Connectivity for a Geometric Random Graph, M.D. Penrose, 1999 • R(n) = the minimum transmission range required for G(n) to have k-connectivity • R’(n) = the minimum transmission range required for G(n) to have degree k. • lim Prob( R(n) = R’(n) ) = 1, as n → infinity • R(n) ≈ R’(n) for large n

44. On the Minimum Node Degree and connectivity of a Wireless Multihop Network, C. Bettstetter, MobiHoc’02 • Prob(G(n) is of degree k) can be calculated from k, n, R’(n), node density • To determine R(n), • Choose R’(n) so that Prob(G(n) is of degree k) ≈ 1 • With this transmission range, G is of degree k with high probability • So, G is k-connected with high probability

45. Application 1 • N = 500 nodes • A = 1000m x 1000m • 3-connected required • R = ? • With R = 100 m, G has degree 3 with probability 0.99. • Thus, G is 3-connected with high probability.

46. Application 2 • A = 1000m x 1000m • R = 50 m • 3-connected required • N = ?

47. Unreliable Sensor Grid: Coverage and Connectivity, INFOCOM 2003 • Active • Dead • Be active with a prob p(n) • transmission and sense range R(n) • A necessary and sufficient condition for the network to remain covered and connected N nodes

48. Conditions for Asymptotic Coverage and Connectivity Necessary: Sufficient:

49. Individually Adjusting Power • Homogeneous transmission range • Node-based transmission range • Problem: individually adjusts the transmission range to guarantee connectivity.

50. The k-Neigh Protocol for Symmetric Topology Control in Ad Hoc Networks,MobiHoc’03 • K- neighbor graph. • Each node adjusts its transmission range so it can communicate with its k nearest neighbors • Is it connected?