Coverage problems for random intervals
SIAM Journal on Applied Mathematics
The pointwise stationary approximation for M1/M1/s
Management Science
Mt/G/∞ queues with sinusoidal arrival rates
Management Science
The physics of the Mt/G/ ∞ symbol Queue
Operations Research
Exposure in wireless sensor networks: theory and practical solutions
Wireless Networks
On k-coverage in a mostly sleeping sensor network
Proceedings of the 10th annual international conference on Mobile computing and networking
Worst and Best-Case Coverage in Sensor Networks
IEEE Transactions on Mobile Computing
Coverage and hole-detection in sensor networks via homology
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Coverage by randomly deployed wireless sensor networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Stochastic coverage in heterogeneous sensor networks
ACM Transactions on Sensor Networks (TOSN)
Introduction to Probability Models, Ninth Edition
Introduction to Probability Models, Ninth Edition
On the Path Coverage Properties of Random Sensor Networks
IEEE Transactions on Mobile Computing
Coverage in wireless ad hoc sensor networks
IEEE Transactions on Computers
On the coverage process of a moving point target in a non-uniform dynamic sensor field
IEEE Journal on Selected Areas in Communications - Special issue on stochastic geometry and random graphs for the analysis and designof wireless networks
On the k-coverage of line segments by a non homogeneous Poisson-Boolean model
WiOPT'09 Proceedings of the 7th international conference on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
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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.