On the k-coverage of line segments by a non homogeneous Poisson-Boolean model

Authors:
S. T. Aditya;Pallavi Manohar;D. Manjunath
Affiliations:
Department of Electrical Engg., IIT Bombay, Mumbai, India;Department of Electrical Engg., IIT Bombay, Mumbai, India;Department of Electrical Engg., IIT Bombay, Mumbai, India
Venue:
WiOPT'09 Proceedings of the 7th international conference on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
Year:
2009

Citing 3
Cited 0

Coverage problems for random intervals

SIAM Journal on Applied Mathematics
The physics of the Mt/G/ ∞ symbol Queue

Operations Research
Path coverage by a sensor field: The nonhomogeneous case

ACM Transactions on Sensor Networks (TOSN)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider k-coverage of a line by a two-dimensional, non homogeneous Poisson-Boolean model. This has applications in sensor networks. We extend the analysis of [1] to the case for k 1. The extension requires us to define a vector Markov process that tracks the k segments that have the longest residual coverage at a point. This process is used to determine the probability of a segment of the line being completely covered by k or more sensors. We illustrate the extension by considering the case of k = 2.