On the Energy Efficient Displacement of Random Sensors for Interference and Connectivity

TL;DR

This paper studies how to reallocate randomly placed sensors in a high-dimensional space to minimize energy use while maintaining interference-free communication, revealing threshold phenomena at specific distances.

Contribution

It introduces a model for sensor displacement with energy costs and identifies a sharp threshold behavior related to interference and connectivity distances.

Findings

Expected minimal total movement exhibits sharp threshold behavior at s,v = 1/λ.

Displacement cost sharply declines or increases around the threshold.

The model provides insights into energy-efficient sensor network reallocation.

Abstract

This paper investigates the problem of the minimilization of energy consumption in reallocation of wireless mobile sensors network (WMSN) to assure good communication without interference. Fix $d\in\mathbb{N}\setminus\{0\}.$ Assume $n$ sensors are initially randomly placed in the hyperoctant $[0,\infty)^d$ according to $d$ identical and independent Poisson processes each with arrival rate $\lambda>0.$ Let $0< s \le v$ be given real numbers. We are allowed to move the sensors, so that every two consecutive sensors are placed at distance greater than or equal to $s$ and less than or equal to $v.$ Fix $a\ge 1.$ Assume that $i-$th sensor is displaced a distance equal to $m(i).$ The cost measure for the displacement of the team of sensors is the sum $\sum_{i=1}^{n}d_i^a$ ($a-$total movement). In this work, we discover and explain a sharp decline and a sharp increase (a threshold phenomena) in the expected minimal $a-$total movement around the interference-connectivity distances $s,v$ equal to $\frac{1}{\lambda}.$