& \tiny X. Deng et al. (2005)~\cite{ref133} & \OK & & \OK & & \OK & & \OK & & \OK & & & &\\
-&\textbf{\textcolor{red}{ \tiny DiLCO Protocol (2014)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & &\textbf{\textcolor{red}{\OK}} & & \\
+&\textbf{\textcolor{red}{ \tiny DiLCO Protocol (2015)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & &\textbf{\textcolor{red}{\OK}} & & \\
-&\textbf{\textcolor{red}{ \tiny MuDiLCO Protocol (2014)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} &\textbf{\textcolor{red}{\OK}} & & \\
+&\textbf{\textcolor{red}{ \tiny MuDiLCO Protocol (2015)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} &\textbf{\textcolor{red}{\OK}} & & \\
&\textbf{\textcolor{red}{ \tiny PeCO Protocol (2015)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & &\textbf{\textcolor{red}{\OK}} & & \\
\subsection{Modeling Language and Optimization Solver}
\label{ch4:sec:04:02}
-The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer 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. Obviously, It is infeasible to use GLPK on a real sensor nodes, we use it in the simulation only for simplicity. GLPK is used to compute the optimal schedule.
+The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer 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.
+%Obviously, It is infeasible to use GLPK on a real sensor nodes, we use it in the simulation only for simplicity. GLPK is used to compute the optimal schedule.
\subsection{Energy Consumption Model}
\label{ch4:sec:04:03}
\item {{\bf Energy Consumption}}
%\subsubsection{The Energy Consumption}
-We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different subregions. Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50} illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$.
+We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different subregions. Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50} illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.
\begin{figure}[h!]
\centering
\caption{Energy Consumption for $Lifetime_{95}$}
\label{Figures/ch4/R1/EC95}
\end{figure}
-
-The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.\\
As shown in Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50}, DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the computation time to solve the optimization problem, as well as the higher energy consumed during the communication.
\begin{figure}[h!]
\end{figure}
For DiLCO-2 protocol, execution times quickly become unsuitable for a sensor network, and the energy consumed during the communication, seems to be huge because it is distributed over only two subregions.
-As highlighted by figures~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases. The network lifetime also increases with the number of subregions, but only up to a given number. Thus we can see that DiLCO-16 leads to the larger lifetime improvement and not DiLCO-32. In fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.
-
-%Comparison shows that DiLCO-16 protocol, which uses 16 leaders, is the best one because it uses less number of active nodes during the network lifetime compared with DiLCO-32 protocol.
-It means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is a relevant way to maximize the lifetime of a network.
+As highlighted by figures~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases. The network lifetime also increases with the number of subregions, but only up to a given number. Thus we can see that DiLCO-16 leads to the larger lifetime improvement and not DiLCO-32. In fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions. It means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is a relevant way to maximize the lifetime of a network.
\begin{figure}[h!]
\centering
\end{figure}
As can be seen in Figure~\ref{Figures/ch4/R2/CR}, at the beginning the models which use a larger number of primary points provide slightly better coverage ratios, but latter they are the worst.
%Moreover, when the number of periods increases, coverage ratio produced by Model-9, Model-13, Model-17, and Model-21 decreases in comparison with Model-5 due to a larger time computation for the decision process for larger number of primary points.
-All models decrease, but Model-5 is the one with the slowest decrease.
+Moreover, when the number of periods increases, coverage ratio produced by all models decrease, but Model-5 is the one with the slowest decrease due to a smaller time computation of decision process for a smaller number of primary points.
As shown in Figure ~\ref{Figures/ch4/R2/CR}, coverage ratio decreases when the number of periods increases due to dead nodes. Model-5 is slightly more efficient than other models, because it offers a good coverage ratio for a larger number of periods in comparison with other models.
\item {{\bf Active Sensors Ratio}}
\contentsline {subsection}{\numberline {4.4.3}Energy Consumption Model}{81}{subsection.4.4.3}
\contentsline {subsection}{\numberline {4.4.4}Performance Metrics}{81}{subsection.4.4.4}
\contentsline {subsection}{\numberline {4.4.5}Performance Analysis for Different Number of Subregions}{83}{subsection.4.4.5}
-\contentsline {subsection}{\numberline {4.4.6}Performance Analysis for Different Number of Primary Points}{89}{subsection.4.4.6}
-\contentsline {subsection}{\numberline {4.4.7}Performance Comparison with other Approaches}{94}{subsection.4.4.7}
-\contentsline {section}{\numberline {4.5}Conclusion}{100}{section.4.5}
+\contentsline {subsection}{\numberline {4.4.6}Performance Analysis for Different Number of Primary Points}{87}{subsection.4.4.6}
+\contentsline {subsection}{\numberline {4.4.7}Performance Comparison with other Approaches}{93}{subsection.4.4.7}
+\contentsline {section}{\numberline {4.5}Conclusion}{99}{section.4.5}
\contentsline {chapter}{\numberline {5}Multiround Distributed Lifetime Coverage Optimization Protocol}{101}{chapter.5}
\contentsline {section}{\numberline {5.1}Introduction}{101}{section.5.1}
\contentsline {section}{\numberline {5.2}MuDiLCO Protocol Description}{101}{section.5.2}
