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Path coverage by a sensor field: The nonhomogeneous case

Authors:

Pallavi Manohar,

S. Sundhar Ram,

D. ManjunathAuthors Info & Claims

ACM Transactions on Sensor Networks (TOSN), Volume 5, Issue 2

Article No.: 17, Pages 1 - 26

https://doi.org/10.1145/1498915.1498923

Published: 03 April 2009 Publication History

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 M_t/G_t/∞, 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.

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Cited By

Shamoun SAbdelzaher TBar-Noy ALoureiro AKanhere SBellavista P(2019)Maximum Gaps in Path CoverageProceedings of the 22nd International ACM Conference on Modeling, Analysis and Simulation of Wireless and Mobile Systems10.1145/3345768.3355940(109-112)Online publication date: 25-Nov-2019
https://dl.acm.org/doi/10.1145/3345768.3355940
Shamoun SAbdelzaher TBar-Noy AHansdah RKrishnaswamy DVaidya N(2019)Dynamic sensor selection for path coverageProceedings of the 20th International Conference on Distributed Computing and Networking10.1145/3288599.3288627(277-281)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1145/3288599.3288627
Shamoun SMei JAbdelzaher TBar-Noy A(2018)Leveraging Knowledge for Path Exposure2018 14th International Conference on Distributed Computing in Sensor Systems (DCOSS)10.1109/DCOSS.2018.00021(103-110)Online publication date: Jun-2018
https://doi.org/10.1109/DCOSS.2018.00021
Show More Cited By

Index Terms

Path coverage by a sensor field: The nonhomogeneous case
1. Mathematics of computing
  1. Probability and statistics
    1. Stochastic processes

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Published In

cover image ACM Transactions on Sensor Networks

ACM Transactions on Sensor Networks Volume 5, Issue 2

March 2009

284 pages

ISSN:1550-4859

EISSN:1550-4867

DOI:10.1145/1498915

Issue’s Table of Contents

Copyright © 2009 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Journal Family

ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 03 April 2009

Accepted: 01 June 2008

Revised: 01 June 2008

Received: 01 September 2007

Published in TOSN Volume 5, Issue 2

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Cited By

Shamoun SAbdelzaher TBar-Noy ALoureiro AKanhere SBellavista P(2019)Maximum Gaps in Path CoverageProceedings of the 22nd International ACM Conference on Modeling, Analysis and Simulation of Wireless and Mobile Systems10.1145/3345768.3355940(109-112)Online publication date: 25-Nov-2019
https://dl.acm.org/doi/10.1145/3345768.3355940
Shamoun SAbdelzaher TBar-Noy AHansdah RKrishnaswamy DVaidya N(2019)Dynamic sensor selection for path coverageProceedings of the 20th International Conference on Distributed Computing and Networking10.1145/3288599.3288627(277-281)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1145/3288599.3288627
Shamoun SMei JAbdelzaher TBar-Noy A(2018)Leveraging Knowledge for Path Exposure2018 14th International Conference on Distributed Computing in Sensor Systems (DCOSS)10.1109/DCOSS.2018.00021(103-110)Online publication date: Jun-2018
https://doi.org/10.1109/DCOSS.2018.00021
Schwarz JSelinka GStolletz R(2016)Performance analysis of time-dependent queueing systems: Survey and classificationOmega10.1016/j.omega.2015.10.01363(170-189)Online publication date: Sep-2016
https://doi.org/10.1016/j.omega.2015.10.013
Dong DLiao XLiu KLiu YXu W(2012)Distributed Coverage in Wireless Ad Hoc and Sensor Networks by Topological Graph ApproachesIEEE Transactions on Computers10.1109/TC.2011.14961:10(1417-1428)Online publication date: 1-Oct-2012
https://dl.acm.org/doi/10.1109/TC.2011.149
Decreusefond LFerraz E(2011)On the One Dimensional Poisson Random Geometric GraphJournal of Probability and Statistics10.1155/2011/3503822011:1Online publication date: 11-Oct-2011
https://doi.org/10.1155/2011/350382
Molina GLuna FNebro AAlba E(2011)An efficient local improvement operator for the multi-objective wireless sensor network deployment problemEngineering Optimization10.1080/0305215X.2010.54684043:10(1115-1139)Online publication date: Oct-2011
https://doi.org/10.1080/0305215X.2010.546840
Li LZhang BZheng J(2011) A study on one‐dimensional k ‐coverage problem in wireless sensor networks Wireless Communications and Mobile Computing10.1002/wcm.108713:1(1-11)Online publication date: 24-Jan-2011
https://doi.org/10.1002/wcm.1087
Manohar PVereshchaka MManjunath D(2010)Survivability analysis under non-uniform stochastically dependent node damages2010 National Conference On Communications (NCC)10.1109/NCC.2010.5430150(1-5)Online publication date: Jan-2010
https://doi.org/10.1109/NCC.2010.5430150
Wang BWang B(2010)Find Penetration PathsCoverage Control in Sensor Networks10.1007/978-1-84996-059-5_10(187-200)Online publication date: 12-Jan-2010
https://doi.org/10.1007/978-1-84996-059-5_10
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