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

TL;DR

This paper investigates the critical thresholds for energy-efficient repositioning of randomly placed mobile sensors on intervals and squares, identifying sharp increases in displacement costs at specific sensing and interference distances.

Contribution

It provides a detailed analysis of the thresholds affecting energy consumption in sensor displacement on both one-dimensional and two-dimensional domains.

Findings

Sharp increase in displacement cost at specific sensing radii and interference distances

Thresholds differ between interval and square sensor placements

Analytical explanation of the displacement behavior around these thresholds

Abstract

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 identical sensing range placed randomly on the unit interval and on the unit square. The main contribution is summarized as follows: If the sensors are placed on the unit interval we explain the sharp increase around the sensing radius equal to $\frac{1}{2n}$ and the interference distance equal to $\frac{1}{n}$ for the expected minimal $a$-total displacement, If the sensors are placed on the unit square we explain the sharp increase around the square sensing radius equal to $\frac{1}{2 \sqrt{n}}$ and the interference distance equal to $\frac{1}{\sqrt{n}}$ for the expected minimal $a$-total displacement.