\subsection{Centralized approaches}
The major approach is to divide/organize the sensors into a suitable number of
-set covers where each set completely covers an interest region and to activate
-these set covers successively. The centralized algorithms always provide nearly
+cover sets where each set completely covers an interest region and to activate
+these cover sets successively. The centralized algorithms always provide nearly
or close to optimal solution since the algorithm has global view of the whole
network. Note that centralized algorithms have the advantage of requiring very
low processing power from the sensor nodes, which usually have limited
%heterogeneous energy wireless sensor networks.
%In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions.
-The works presented in \cite{Bang, Zhixin, Zhang} focuses on coverage-aware,
+The works presented in \cite{Bang, Zhixin, Zhang} focuse on coverage-aware,
distributed energy-efficient, and distributed clustering methods respectively,
-which aims to extend the network lifetime, while the coverage is ensured. More
+which aim to extend the network lifetime, while the coverage is ensured. More
recently, Shibo et al. \cite{Shibo} have expressed the coverage problem as a
minimum weight submodular set cover problem and proposed a Distributed Truncated
Greedy Algorithm (DTGA) to solve it. They take advantage from both temporal and
%heterogeneous energy wireless sensor networks.
%In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions.
-The works presented in \cite{Bang, Zhixin, Zhang} focuses on coverage-aware,
+The works presented in \cite{Bang, Zhixin, Zhang} focuse on coverage-aware,
distributed energy-efficient, and distributed clustering methods respectively,
-which aims to extend the network lifetime, while the coverage is ensured. S.
+which aim to extend the network lifetime, while the coverage is ensured. S.
Misra et al. \cite{Misra} have proposed a localized algorithm for coverage in
sensor networks. The algorithm conserve the energy while ensuring the network
coverage by activating the subset of sensors with the minimum overlap area. The
\item LISTENING: sensor node is waiting for a decision (to be active or not);
\item COMPUTATION: sensor node has been elected as leader and applies the
optimization process;
-\item ACTIVE: sensor node participate to the monitoring of the area;
+\item ACTIVE: sensor node is participating to the monitoring of the area;
\item SLEEP: sensor node is turned off to save energy;
\item COMMUNICATION: sensor node is transmitting or receiving packet.
\end{enumerate}
undercoverage. The weights $W_\theta$ and $W_U$ must be properly chosen so as
to guarantee that the maximum number of points are covered during each round.
%% MS W_theta is smaller than W_u => problem with the following sentence
-In our simulations priority is given to the coverage by choosing $W_{\theta}$ very
-large compared to $W_U$.
+In our simulations priority is given to the coverage by choosing $W_{U}$ very
+large compared to $W_{\theta}$.
%The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase.
\subsection{Sensing phase}
25 runs.
%Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions.
We performed simulations for five different densities varying from 50 to
-250~nodes. Experimental results are obtained from randomly generated networks in
-which nodes are deployed over a $50 \times 25~m^2 $ sensing field. More
+250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
precisely, the deployment is controlled at a coarse scale in order to ensure
that the deployed nodes can cover the sensing field with the given sensing
range.
\cite{raghunathan2002energy}. Each of the first three subsystems can be turned
on or off depending on the current status of the sensor. Energy consumption
(expressed in milliWatt per second) for the different status of the sensor is
-summarized in Table~\ref{table4}. The energy needed to send or receive a 1-bit
-packet is equal to $0.2575~mW$.
+summarized in Table~\ref{table4}.
\begin{table}[ht]
\caption{The Energy Consumption Model}
and 24~bits respectively. The value of energy spent to send a 1-bit-content
message is obtained by using the equation in ~\cite{raghunathan2002energy} to
calculate the energy cost for transmitting messages and we propose the same
-value for receiving the packets.
+value for receiving the packets. The energy needed to send or receive a 1-bit
+packet is equal to $0.2575~mW$.
The initial energy of each node is randomly set in the interval $[500;700]$. A
sensor node will not participate in the next round if its remaining energy is
or $5$ seems bearable, but for $T=7$ they become quickly unsuitable for a sensor
node, especially when the sensor network size increases. Again, we can notice
that if we want to schedule the nodes activities for a large number of rounds,
-we need to choose a relevant number of subregion in order to avoid a complicated
+we need to choose a relevant number of subregions in order to avoid a complicated
and cumbersome optimization. On the one hand, a large value for $T$ permits to
reduce the energy-overhead due to the three pre-sensing phases, on the other
hand a leader node may waste a considerable amount of energy to solve the
