  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 $\frac{1}{\lambda}.$
