Pallavi Manohar
Abstract
We analyze the statistical properties of the coverage of a one-dimensional path induced by a two-dimensional nonhomogeneous random sensor network. Sensor locations form a nonhomogeneous Poisson process and sensing area for the sensors are circles of random independent and identically distributed radii. We first characterize the coverage of a straight-line path by the nonhomogeneous one-dimensional Boolean model. We then obtain an equivalent Mt/Gt/∞, queue whose busy period statistics is the same as the coverage statistics of the line. We obtain k-coverage statistics for an arbitrary point and a segment on the x-axis. We provide upper and lower bounds on the probability of complete k-coverage of a segment. We illustrate all our results for the case of the sensor deployment having a “Laplacian” intensity function.
- de Silva, V., Ghrist, R., and Muhammad, A. 2005. Blind swarms for coverage in 2-d. In Proceeding of the Conference Robotics Systems and Science.Google Scholar
- Eick, S., Massey, W. A., and Whitt, W. 1993a. Mt/G/∞ queues with sinusoidal arrival rates. Management Sci. 39, 241--252. Google ScholarCross Ref
- Eick, S., Massey, W. A., and Whitt, W. 1993b. The physics of Mt/G/∞ queue. Oper. Res. 41, 4, 731--742. Google ScholarCross Ref
- Ghrist, R. and Muhammad, A. 2005. Coverage and hole detection in sensor networks via homology. In Proceedings of the International Symposium on Information Processing in Sensor Networks (IPSN). Google ScholarDigital Library
- Green, L. and Kolesar, P. 1991. The pointwise stationary approximation for queues with nonstationary arrivals. Management Sci. 37, 84--97. Google ScholarDigital Library
- Grimmett, G. R. 1999. Percolation, 2nd ed. Vol. 321. Springer.Google Scholar
- Hall, P. 1988. Intoduction to the Theory of Coverage Process. John Wiley and Sons.Google Scholar
- Kumar, S., Lai, T. H., and Balogh, J. 2004. On k-coverage in a mostly sleeping sensor network. In Proceedings of the ACM Annual International Conference on Mobile Computing and Networks. (MobiCom). Google ScholarDigital Library
- Lazos, L. and Poovendran, R. 2006. Stochastic coverage in heterogeneous sensor networks. ACM Trans. Sensor Netw. 2, 3, 325--358. Google ScholarDigital Library
- Li, X. Y., Wan, P. J., and Frieder, O. 2003. Coverage in wireless ad-hoc sensor networks. IEEE Trans. Comput. 52, 6, 753--763. Google ScholarDigital Library
- Liu, B. and Towsley, D. 2003. On the coverage and detectability of wireless sensor networks. In Proceedings of the Conference on WiOpt'03 Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks.Google Scholar
- Liu, B. and Towsley, D. 2004. A study on the coverage of large-scale sensor networks. In 1st IEEE International Conference on Mobile Ad-hoc and Sensors.Google Scholar
- Megerian, S., Koushanfar, F., and Potkonjak, M. 2005. Worst and best-case coverage in sensor networks. IEEE Trans. Mobile Comput. 4, 84--92. Google ScholarDigital Library
- Meguerdichian, S., Koushanfar, F., Qu, G., and Potkonjak, M. 2001. Coverage problems in wireless ad-hoc sensor networks. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
- Meguerdichian, S., Koushanfar, F., Qu, G., and Potkonjak, M. 2002. Exposure in wireless sensor networks: Theory and practical solutions. J. Wireless Netw. 8. Google ScholarDigital Library
- Ram, S. S., Iyer, S. K., Manjunath, D., and Yogeshwaran, D. 2007. On the path coverage properties of random sensor networks. IEEE Trans. Mobile Comput. 6, 494--506. Google ScholarDigital Library
- Ram, S. S., Manjunath, D., and Borkar, V. B. 2006. A note on busy period statistics for Mt/Gt/∞ queues. www.ifp.uiuc.edu/ssriniv5/Files/mtgt.pdf.Google Scholar
- Ross, S. M. 1996. Stochastic Processes, 2nd ed. John Wiley and Sons.Google Scholar
- Ross, S. M. 2003. Introduction to Probability Models, 8th ed. Academic Press. Google ScholarDigital Library
- Shakkotai, S., Srikant, R., and Shroff, N. 2003. Unreliable sensor grids: Coverage, connectivity and diameter. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
- Stadje, W. 1989. Coverage problems for random intervals. SIAM J. Appl. Math. 49, 1538--1551. Google ScholarDigital Library
- Wan, P. J. and Yi, C. W. 2006. Coverage by randomly deployed wireless sensor networks. IEEE/ACM Trans. Netw. 14, 2658--2669. Google ScholarDigital Library
- Whitt, W. 1991. The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increase. Management Sci. 37, 307--314. Google ScholarDigital Library
Index Terms
- Path coverage by a sensor field: The nonhomogeneous case
Recommendations
Coverage enhancement by using the mobility of mobile sensor nodes
Coverage is a fundamental problem in sensor networks. Sensor coverage, which reflects how well a sensor network is monitored by sensors, is an important measure for the quality of service (QoS) that a sensor network can provide. In mobile sensor ...
Extending k-Coverage Lifetime of Wireless Sensor Networks Using Mobile Sensor Nodes
WIMOB '09: Proceedings of the 2009 IEEE International Conference on Wireless and Mobile Computing, Networking and CommunicationsOne of the important issues in wireless sensor network (WSN) is to k-cover the target sensing field and to extend its lifetime. We propose a method to k-cover the field and maximize the WSN lifetime by moving mobile sensor nodes to appropriate positions ...
The coverage problem in a wireless sensor network
One of the fundamental issues in sensor networks is the coverage problem, which reflects howwell a sensor network is monitored or tracked by sensors. In this paper, we formulate this problem as a decision problem, whose goal is to determine whether ...
Comments