Consider n mobile sensors placed independently at random with the uniform distribution on a barrier represented as the unit line segment [0,1]. The sensors have identical sensing radius, say r. When a sensor is displaced on the line a distance equal to d it consumes energy (in movement) which is proportional to some (fixed) power a > 0 of the distance d traveled. The energy consumption of a system of n sensors thus displaced is defined as the sum of the energy consumptions for the displacement of the individual sensors.We focus on the problem of energy efficient displacement of the sensors so that in their final placement the sensor system ensures coverage of the barrier and the energy consumed for the displacement of the sensors to these final positions is minimized in expectation. In particular, we analyze the problem of displacing the sensors from their initial positions so as to attain coverage of the unit interval and derive trade-offs for this displacement as a function of the sensor range. We obtain several tight bounds in this setting thus generalizing several of the results of [10] to any power a > 0.
Consider n sensors placed randomly and independently with the uniform distribution in a d−dimensional unit cube (d ≥ 2). The sensors have identical sensing range equal to r, for some r > 0. We are interested in moving the sensors from their initial positions to new positions so as to ensure that the d−dimensional unit cube is completely covered, i.e., every point in the d−dimensional cube is within the range of a sensor. If the i-th sensor is displaced a distance d i , what is a displacement of minimum cost? As cost measure for the displacement of the team of sensors we consider the a-total movement defined as the sum, for some constant a > 0. We assume that r and n are chosen so as to allow full coverage of the d−dimensional unit cube and a > 0.The main contribution of the paper is to show the existence of a tradeoff between the d−dimensional cube, sensing radius and a-total movement. The main results can be summarized as follows for the case of the d−dimensional cube.
If the d−dimensional cube sensing radius is
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 ∈ N \ {0}. Assume n sensors are initially randomly placed in the hyperoctant [0, ∞) d according to d identical and independent Poisson processes each with arrival rate λ > 0.Let 0 < s ≤ 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 ≥ 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 n i=1 d a i (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 1 λ .
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