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September 2016 Sensor allocation problems on the real line
Evangelos Kranakis, Gennady Shaikhet
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J. Appl. Probab. 53(3): 667-687 (September 2016).

Abstract

A large number n of sensors (finite connected intervals) are placed randomly on the real line so that the distances between the consecutive midpoints are independent random variables with expectation inversely proportional to n. In this work we address two fundamental sensor allocation problems. The interference problem tries to reallocate the sensors from their initial positions to eliminate overlaps. The coverage problem, on the other hand, allows overlaps, but tries to eliminate uncovered spaces between the originally placed sensors. Both problems seek to minimize the total sensor movement while reaching their respective goals. Using tools from queueing theory, Skorokhod reflections, and weak convergence, we investigate asymptotic behaviour of optimal costs as n increases to ∞. The introduced methodology is then used to address a more complicated, modified coverage problem, in which the overlaps between any two sensors can not exceed a certain parameter.

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Evangelos Kranakis. Gennady Shaikhet. "Sensor allocation problems on the real line." J. Appl. Probab. 53 (3) 667 - 687, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.90080
MathSciNet: MR3570087

Subjects:
Primary: 60J20
Secondary: 68M20

Keywords: potential outflow , Queueing theory , reflected random walk , Sensor allocation , Skorokhod map , weak convergence

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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