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

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 $λ>0.$ 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 $\frac{1}λ.$