Instead of working with a continuous coverage area, we make it discrete by
considering for each sensor a set of points called primary points. Consequently,
we assume that the sensing disk defined by a sensor is covered if all of its
-primary points are covered. The choice of number and locations of primary points
-is the subject of another study not presented here.
+primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here.
%By knowing the position (point center: ($p_x,p_y$)) of a wireless
%sensor node and its $R_s$, we calculate the primary points directly
$E_{R}$ & 36 Joules\\
$R_s$ & 5~m \\
%\hline
-$W_{\Theta}$ & 1 \\
+$W_{\theta}$ & 1 \\
% [1ex] adds vertical space
%\hline
$W_{U}$ & $|P|^2$
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. The energy needed to send or receive a 1-bit
-packet is equal to $0.2575~mW$.
+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
% New version with global loops on period
\begin{equation*}
\scriptsize
- \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
+ \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M} T_m},
\end{equation*}
\end{enumerate}
-\section{Results and analysis}
+\subsection{Results and analysis}
-\subsection{Coverage ratio}
+\subsubsection{Coverage ratio}
Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
can notice that for the first thirty rounds both DESK and GAF provide a coverage
\label{fig3}
\end{figure}
-\subsection{Active sensors ratio}
+\subsubsection{Active sensors ratio}
It is crucial to have as few active nodes as possible in each round, in order to
minimize the communication overhead and maximize the network
\label{fig4}
\end{figure}
-\subsection{Stopped simulation runs}
+\subsubsection{Stopped simulation runs}
%The results presented in this experiment, is to show the comparison of our MuDiLCO protocol with other two approaches from the point of view the stopped simulation runs per round. Figure~\ref{fig6} illustrates the percentage of stopped simulation
%runs per round for 150 deployed nodes.
\label{fig6}
\end{figure}
-\subsection{Energy consumption} \label{subsec:EC}
+\subsubsection{Energy consumption} \label{subsec:EC}
We measure the energy consumed by the sensors during the communication,
listening, computation, active, and sleep status for different network densities
%In fact, a distributed optimization decision, which produces T rounds, on the subregions is greatly reduced the cost of communications and the time of listening as well as the energy needed for sensing phase and computation so thanks to the partitioning of the initial network into several independent subnetworks and producing T rounds for each subregion periodically.
-\subsection{Execution time}
+\subsubsection{Execution time}
We observe the impact of the network size and of the number of rounds on the
computation time. Figure~\ref{fig77} gives the average execution times in
-seconds (needed to solve optimization problem) for different values of $T$. The
+seconds (needed to solve optimization problem) for different values of $T$. The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the Mixed Integer Linear Program instance in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. The
original execution time is computed on a laptop DELL with Intel Core~i3~2370~M
(2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second)
rate equal to 35330. To be consistent with the use of a sensor node with Atmels
%While MuDiLCO-1, 3, and 5 solves the optimization process with suitable execution times to be used on wireless sensor network because it distributed on larger number of small subregions as well as it is used acceptable number of round(s) T. We think that in distributed fashion the solving of the optimization problem to produce T rounds in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
-\subsection{Network lifetime}
+\subsubsection{Network lifetime}
The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the
network lifetime for different network sizes, respectively for $Lifetime_{95}$
The activity scheduling in each subregion works in periods, where each period
consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii)
Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing
-Phase itself divided into T rounds.
+Phase itself divided into $T$ rounds.
Simulations results show the relevance of the proposed protocol in terms of
lifetime, coverage ratio, active sensors ratio, energy consumption, execution
