On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors

Fuchs, Michael; Kao, Louis; Wu, Wanzhen

doi:10.11650/tjm/200503

Cited by 6 publications

(6 citation statements)

References 8 publications

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“…Let T a be the displacement to the power a of Algorithm 1 in Steps ( 1)- (10). Using (A42), as well as the observation that Algorithm 1 is the sequence of the two phases A and B, we obtain the following upper bound: Claim A1.…”

Section: Appendix Fmentioning

confidence: 99%

“…(see [33], Formula 2.5.21, p. 33). Combining Equation (10) in Lemma 2 and Equation (11) in Lemma 3 leads to E(T a ) = O n 1−a . This is enough to prove the desired upper bound in the first phase.…”

Section: Appendix Fmentioning

confidence: 99%

“…In the proof of Theorem 5, we combine combinatorial techniques with the properties of the Beta distribution (see Equation (10) in Lemma 2 and Equation (11) in Lemma 3). The estimations for the Beta distribution with special positive integer parameters in Lemma 2 and Lemma 3 are new to the best of the author's knowledge.…”

mentioning

confidence: 99%

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Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors

Kapelko

2022

Sensors

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The fundamental problem of energy-efficient reallocation of mobile random sensors to provide full coverage without interference is addressed in this paper. We consider n mobile sensors with the identical sensing range placed randomly on the unit interval and on the unit square. The sensors move from their initial random positions to the final locations so that: (a) every point on the unit interval or on the unit square is within the range of a sensor; (b) each pair of sensors is at a Euclidean distance greater than or equal to s; (c) the energy consumption for the movement of the sensors to the final positions is minimized. As a cost measure for the energy in the movement of sensors, we consider a-total movement defined as the sum ∑i=1ndia, for some constant a>0, provided that the i-th sensor is displaced the distance di. The main contribution is summarized as follows: (1) if the sensors are placed on the unit interval, we explain the sharp increase around the sensing radius equal to 12n and the interference distance equal to 1n for the expected minimal a-total displacement; (2) if the sensors are placed on the unit square, we explain the sharp increase around the square sensing radius equal to 12n and the interference distance equal to 1n for the expected minimal a-total displacement. We designed and analysed three algorithms. The probabilistic analysis of our protocols is based on a novel mathematical theory of the Beta distribution.

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Section: Appendix Fmentioning

confidence: 99%

Section: Appendix Fmentioning

confidence: 99%

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Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors

Kapelko

2022

Sensors

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“…It is worth mentioning that, our work in the current paper is related to the series of papers of the autonomous sensors displacement (see [27,11,21,23,22,17,18,19,20,14,9]). It includes research on barrier and area coverage [27,23,22,19,14], on interference [11], coverage simultaneously with interference [17,18], interference simultaneously with connectivity [20] and coverage-connectivity for the range assignment [9]. In [14], the authors revisited the asymptotics of a binomial and a Poisson sum that arose as (average) displacement costs when sensors are randomly placed in anchor positions.…”

Section: Related Workmentioning

confidence: 99%

“…The novelty of the current paper lies in the introduction and investigation of the robot assisted model and comparison with the recent results for the autonomous sensor displacement (see [22,18,20,14]).…”

Section: Related Workmentioning

confidence: 99%

On the Robot Assisted Movement in Wireless Mobile Sensor Networks

Das¹,

Kapelko²

2021

Preprint

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This paper deals with random sensors initially randomly deployed on the line according to general random process and on the plane according to two independent general random processes. The mobile robot with carrying capacity k placed at the origin point is to move the sensors to achieve the general scheduling requirement such as coverage, connectivity and thus to satisfy the desired communication property in the network. We study tradeoffs between the energy consumption in robot's movement, the numbers of sensors n, the sensor range r, the interference distance s, and the robot capacity k until completion of the coverage simultaneously with interference scheduling task. In this work, we obtain upper bounds for the energy consumption in robot's movement and obtain the sharp decrease in the total movement cost of the robot so as to provide the coverage simultaneously with interference requirement.

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On the moment absolute deviation of order statistics from uniform distribution

Kapelko¹

2022

Statistics & Probability Letters

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On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors

Cited by 6 publications

References 8 publications

Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors

Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors

On the Robot Assisted Movement in Wireless Mobile Sensor Networks

On the moment absolute deviation of order statistics from uniform distribution

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