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Complete Optimal Deployment Patterns for Full-Coverage and k-Connectivity (k ≦ 6) Wireless Sensor Networks Xiaole Bai, Dong Xuan, Ten H. Lai, Ziqiu Yun,

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Presentation on theme: "Complete Optimal Deployment Patterns for Full-Coverage and k-Connectivity (k ≦ 6) Wireless Sensor Networks Xiaole Bai, Dong Xuan, Ten H. Lai, Ziqiu Yun,"— Presentation transcript:

1 Complete Optimal Deployment Patterns for Full-Coverage and k-Connectivity (k ≦ 6) Wireless Sensor Networks Xiaole Bai, Dong Xuan, Ten H. Lai, Ziqiu Yun, Weijia Jia Computer Science and Engineering The Ohio State University, USA Department of Mathematics Suzhou University, CHINA Department of Computer Science City University of Hong Kong, CHINA ACM International Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc 2008 YearSubmittedAccepted% Accepted 2006318319.75% 20071462718.5% 20083004414.7%

2 Outline IntroductionThe proposed patternsNumerical resultsConclusion

3 Introduction Wireless sensor networks show more and more popularity for both military and civil applications.

4 Introduction Wireless sensor networks show more and more popularity for both military and civil applications. –Noxious Gas Detection

5 Introduction Wireless sensor networks show more and more popularity for both military and civil applications. –Fire Detection

6 The deployment is a fundamental issue in Wireless Sensor Networks (WSNs) that affects many facts for these applications. There are two categories of deployments in WSNs. –Random deployment –Deterministic deployment Introduction

7 RsRs

8 Achieve 6-connectivity only when r c ≧ RsRs A

9 The work on exploring optimal patterns in WSNs is not yet complete. –3-connected –5-connected –6-connected when R c / R s < The previous exploration on optimal patterns has not yet been conducted systematically. Introduction

10 Goal Propose deployment patterns systematically. –Achieve full coverage and k-connectivity (k ≦ 6) under different ratios of sensor communication range over sensing range.

11 Deployment Patterns Universal elemental patternk=3k=4k=5k=6 k=1 or k=2

12 Deployment Patterns - Universal elemental pattern θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

13 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

14 Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s

15 Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=15, Rs=20 :  1 = 120 °,  2 = 120 °,  3 = 120 °, d 1 =15, d 2 =15 120° 15

16 Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=25, Rs=20 :  1 = 154.73 °,  2 = 102.64°,  3 = 102.64°, d 1 =25, d 2 =25 154.73° 102.64° 154.73° 102.64° 25

17 Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=28.284, Rs=20 :  1 = 180°,  2 = 90°,  3 = 90°, d 1 =28.284, d 2 =28.284 180° 90° 180°90° 28.284

18 Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 180°,  2 = 106.26°,  3 = 73.74°, d 1 = 32, d 2 = 32 180° 106.26°73.74° 180°106.26 °73.74° 32

19 Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=40, Rs=20 :  1 = 180°,  2 = 120°,  3 = 60°, d 1 = 34.641, d 2 = 34.641 180° 120°60° 180° 120 °60° 34.641

20 Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s

21 Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s ≦ √2 √2 < R c / R s < √3 √3 ≦ R c / R s 180° 90° 180°90° RcRc RcRc RcRc RcRc RcRc RcRc

22 Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 180°,  2 = 106.26°,  3 = 73.74°, d 1 = 32, d 2 = 32 180° 106.26°73.74° 180°106.26 °73.74° 32

23 Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=40, Rs=20 :  1 = 180°,  2 = 120°,  3 = 60°, d 1 = 34.641, d 2 = 34.641 180° 120°60° 180° 120 °60° 34.641

24 Deployment Patterns – 5-connectivity R c / R s ≦ √2 √2 < R c / R s < √3 √3 ≦ R c / R s θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

25 Deployment Patterns – 5-connectivity R c / R s ≦ √2 √2 < R c / R s < √3 √3 ≦ R c / R s 150° 60° 150° 60° RcRc RcRc RcRc RcRc RcRc RcRc θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

26 Deployment Patterns – 5-connectivity R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 60 °,  2 = 166.26°,  3 = 133.74°, d 1 = 32, d 2 = 32 60° 166.24° 133.74° 60° 166.26 ° 133.74° 32 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

27 Deployment Patterns – 5-connectivity R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=40, Rs=20 :  1 = 60°,  2 = 180°,  3 = 120°, d 1 = 34.641, d 2 = 34.641 60° 180° 120° 60° 180 ° 120° 34.641 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

28 Deployment Patterns – 6-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < √3 √3 ≦ R c / R s

29 Deployment Patterns – 6-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 180° 120°60° 180° 120°60° RcRc RcRc RcRc RcRc RcRc RcRc R c / R s < √3 √3 ≦ R c / R s

30 Deployment Patterns – 6-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 180° 120°60° 180° 120°60° RsRs RsRs RsRs RsRs RsRs RsRs R c / R s < √3 √3 ≦ R c / R s

31 Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s

32 Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=15, Rs=20 :  1 = 180°,  2 =78.779°,  3 =101.22°, d 1 =15, d 2 =39.263 180°78.779°101.22° 180°78.779°101.22° 15 39.263

33 Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=25, Rs=20 :  1 = 180°,  2 = 69.451°,  3 = 110.55°, d 1 =25, d 2 =37.743 180°69.450°110.55° 180° 69.451°110.55° 25 37.743

34 Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=28.284, Rs=20 :  1 = 180°,  2 = 65.53°,  3 = 114.47°, d 1 =28.284, d 2 =36.955 180°65.53°114.47° 28.284 36.955 114.47° 180° 65.53° 28.284 36.955

35 Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 180°,  2 = 60°,  3 = 120°, d 1 = 32, d 2 = 35.777 180°60°120° 32 35.777 120° 180° 60° 32 35.777

36 Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=39, Rs=20 :  1 = 180°,  2 = 37.085°,  3 = 142.91°, d 1 = 34.641, d 2 = 34.641 180° 37.085°142.91° 34.641 142.91° 180° 37.085° 34.641

37 Deployment Patterns

38 Numerical Results Parameters SimulatorUnknow Size of network1000*1000 m Sensing range30 m Communication range20~60 m

39 Numerical Results

40 Conclusion This paper propose deployment patterns systematically. –Achieve full coverage and k-connectivity (k ≦ 6) under different ratios of sensor communication range over sensing range.

41

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