On the Range Assignment in Wireless Sensor Networks for Minimizing the Coverage-Connectivity Cost

This article deals with reliable and unreliable mobile sensors having identical sensing radius r, communication radius R, provided that r≤ R and initially randomly deployed on the plane by dropping them from an aircraft according to general random process. The sensors have to move from their initial random positions to the final destinations to provide greedy path k₁-coverage simultaneously with k₂-connectivity. In particular, we are interested in assigning the sensing radius r and communication radius R to minimize the time required and the energy consumption of transportation cost for sensors to provide the desired k₁-coverage with k₂-connectivity. We prove that for both of these optimization problems, the optimal solution is to assign the sensing radius equal to r = k₁||E[S]||/2 and the communication radius R = k₂||E[S]||/2, where ||E[S]|| is the characteristic of general random process according to which the sensors are deployed. When r< k₁||E[S]||/2 or R< k₂||E[S]||/ 2, and sensors are reliable, we discover and explain the sharp increase in the time required and the energy consumption in transportation cost to ensure the desired k₁-coverage with k₂-connectivity.