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Critical Sensor Density

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Coverage Control in Sensor Networks

Part of the book series: Computer Communications and Networks ((CCN))

Abstract

Before network deployment, one may want to know how many sensor nodes are needed such that every point of the sensor field can be covered by at least one sensor. Sensor density is defined as the number of nodes per unit area. In a homogeneous sensor network, the critical sensor density (CSD) provides an insight on the minimal number of nodes required for complete area coverage. In deterministic sensor placement, it is desirable to know not only the minimal number of nodes but also their locations. For a homogeneous network, a basic placement pattern can be repeated to tile-up the whole sensor field. A placement pattern is optimal if it requires the minimal number of nodes to completely cover the sensor field, and an optimal placement pattern determines the CSD for deterministic sensor placements. In random sensor deployments, the analysis for CSD often applies an asymptotic approach, but its result provides a lower bound of CSD for a sensor field with finite area: The number of nodes should be no smaller than the area of the sensor field times the critical sensor density to ensure complete area coverage (almost surely) in each deployment. In particular, the following questions are addressed in this chapter:

What is the optimal placement pattern in deterministic node deployments and how to derive the critical sensor density for random node deployments?

We first introduce the optimal placement pattern for deterministic node placement and then review existing approaches for CSD analysis in random network deployment.

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References

  1. Adlakha, S., Srivastava, M.: Critical density thresholds for coverage in wireless sensor networks. In: IEEE Wireless Communications and Networking Conference (WCNC) vol. 3, pp. 1615–1620 (2003)

    Google Scholar 

  2. Akyildiz, I.F., Pompili, D., Melodia, T.: Underwater acoustic sensor networks: Research challenges. Ad Hoc Networks (Elsevier) 3(2), 257–279 (2005)

    Google Scholar 

  3. Alam, S.N., Haas, Z.J.: Coverage and connectivity in three-dimensional networks. In: ACM the 12th Annual International Conference on Mobile Computing and Networking (MobiCom), pp. 346–357 (2006)

    Google Scholar 

  4. Alon, N., Spencer, J.: The Probabilistic Method. Wiley, New York (2000)

    Book  MATH  Google Scholar 

  5. Bai, X., Kumar, S., Xuan, D., Yun, Z., Lai, T.H.: Deploying wireless sensors to achieve both coverage and connectivity. In: ACM the 7th International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 131–142 (2006)

    Google Scholar 

  6. Bai, X., Xuan, D., Yun, Z., Lai, T.H., Jia, W.: Complete optimal deployment patterns for full-coverage and k-connectivity (k≤6) wireless sensor networks. In: ACM the 9th International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 401–410 (2008)

    Google Scholar 

  7. Bai, X., Yun, Z., Xuan, D., Lai, T.H., Jia, W.: Deploying four-connectivity and full-coverage wireless sensor networks. In: IEEE the 27th Conference on Computer Communications (Infocom), pp. 906–914 (2008)

    Google Scholar 

  8. Bai, X., Zhang, C., Xuan, D., Teng, J., Jia, W.: Low-connectivity and full-coverage three dimensional wireless sensor networks. In: ACM the 10th International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 145–154 (2009)

    Google Scholar 

  9. Grimmett, G.: Percolation. Springer, Berlin (1999)

    MATH  Google Scholar 

  10. Hall, P.: Introduction to the Theory of Coverage Processes. Wiley, New York (1988)

    MATH  Google Scholar 

  11. Han, X., Cao, X., Lloyd, E.L., Shen, C.C.: Deploying directional sensor networks with guaranteed connectivity and coverage. In: IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks (SECON), pp. 153–160 (2008)

    Google Scholar 

  12. Kar, K., Banerjee, S.: Node placement for connected coverage in sensor networks. In: International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt) (2003)

    Google Scholar 

  13. Sir Thomson, W. (Lord Kelvin): On the division of space with minimum partitional area. Philosophical Magazine 24(151), 503–514 (1887). URL: http://zapatopi.net/kelvin/papers/on_the_division_of_space.html

    Google Scholar 

  14. Kershner, R.: The number of circles covering a set. American Journal of Mathematics 61(3), 665–671 (1939)

    Article  MathSciNet  Google Scholar 

  15. Kim, J.E., Yoon, M.K., Han, J., Lee, C.G.: Sensor placement for 3-coverage with minimum separation requirements. In: The 4th IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS), pp. 266–281 (2008)

    Google Scholar 

  16. Kim, J.E., Han, J., Lee, C.G.: Optimal 3-coverage with minimum separation requirements for ubiquitous computing environments. Mobile Networks and Applications (Springer) (2009). doi:10.1007/s11036-008-0122-9

  17. Kumar, S., Lai, T.H., Balogh, J.: On k-coverage in a mostly sleeping sensor network. In: ACM International Conference on Mobile Computing and Networking (MobiCom), pp. 114–158 (2004)

    Google Scholar 

  18. Kumar, S., Lai, T.H., Balogh, J.: On k-coverage in a mostly sleeping sensor network. Wireless Networks (Springer) 14(3), 277–294 (2008)

    Article  Google Scholar 

  19. Lazos, L., Poovendran, R.: Stochastic coverage in heterogeneous sensor networks. ACM Transactions on Sensor Network (ToSN) 2(3), 325–358 (2006)

    Article  Google Scholar 

  20. Liu, B., Towsley, D.: A study of the coverage of large-scale sensor networks. In: IEEE International Conference on Mobile Ad-hoc and Sensor Systems (MASS), pp. 475–483 (2004)

    Google Scholar 

  21. Lyengar, R., Kar, K., Banerjee, S.: Low-coordination topologies for redundancy in sensor networks. In: ACM the 6th International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 332–342 (2005)

    Google Scholar 

  22. Mo, W., Qiao, D., Wang, Z.: Mostly-sleeping wireless sensor networks: Connectivity, k-coverage, and α-lifetime. In: The 43rd Annual Allerton Conference on Communication, Control, and Computing (2005)

    Google Scholar 

  23. Mo, W., Qiao, D., Wang, Z.: Lifetime maximization of sensor networks under connectivity and k-coverage constraints. In: International Conference on Distributed Computing in Sensor Systems (DCOSS), pp. 422–442 (2006)

    Google Scholar 

  24. Paillard, G., Ravelomanana, V.: Limit theorems for degree of coverage and lifetime in large sensor networks. In: IEEE Infocom, pp. 106–110 (2008)

    Google Scholar 

  25. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives. Gordon and Breach, Yverdon (1993), p. 9

    MATH  Google Scholar 

  26. Santalo, L.A.: Integral Geometry and Geometric Probability, 2nd Edition. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  27. Wan, P.J., Yi, C.W.: Coverage by randomly deployed wireless sensor networks. IEEE Transactions on Information Theory 52(6), 2658–2669 (2006)

    Article  MathSciNet  Google Scholar 

  28. Wang, Y.C., Hu, C.C., Tseng, Y.C.: Efficient deployment algorithms for ensuring coverage and connectivity of wireless sensor networks. In: IEEE International Conference on Wireless Internet, pp. 114–121 (2005)

    Google Scholar 

  29. Wang, B., Chua, K.C., Srinivasan, V., Wang, W.: Information coverage in randomly deployed wireless sensor networks. IEEE Transactions on Wireless Communications 6(8), 2994–3004 (2007)

    Article  Google Scholar 

  30. Yates, R.D., Goodman, D.J.: Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers. Wiley, New York (1999)

    MATH  Google Scholar 

  31. Yen, L.H., Yu, C.W., Cheng, Y.M.: Expected k-coverage in wireless sensor networks. Elsevier Ad Hoc Networks 4(5), 636–650 (2006)

    Article  Google Scholar 

  32. Zhang, H., Hou, J.: On deriving the upper bound of α-lifetime for large sensor networks. In: ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 121–132 (2004)

    Google Scholar 

  33. Zhang, H., Hou, J.C.: On the upper bound of α-lifetime for large sensor networks. ACM Transactions on Sensor Networks (ToSN) 1(2), 272–300 (2005)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Intelligent Systems Centre, Nanyang Technological University, 50 Nanyang Drive Research Techno Plaza, Level 7, Singapore, 637553, Singapore

    Dr. Bang Wang

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  1. Dr. Bang Wang
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Correspondence to Bang Wang .

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Wang, B. (2010). Critical Sensor Density. In: Coverage Control in Sensor Networks. Computer Communications and Networks. Springer, London. https://doi.org/10.1007/978-1-84996-059-5_6

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  • DOI: https://doi.org/10.1007/978-1-84996-059-5_6

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-058-8

  • Online ISBN: 978-1-84996-059-5

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