\dfrac{\eta}{n_i^\alpha l(e_i,r_i)^\beta} * W + z & \mbox{if $e_i \geq e_{threshold}$} \\
W & \mbox{otherwise,}\\
\end{array} \right.
-%\label{eq12}
\notag
\end{equation}
\noindent We consider a sensor network composed of static nodes distributed independently and uniformly at random. A high-density deployment ensures a high coverage ratio of the interested area at the start. The nodes are supposed to have homogeneous characteristics from a communication and a processing point of view, whereas they have heterogeneous energy provisions. Each node has access to its location thanks, either to a hardware component (like a GPS unit) or a location discovery algorithm. Furthermore, we assume that sensor nodes are time synchronized in order to properly coordinate their operations to achieve complex sensing tasks~\cite{ref157}. Two sensor nodes are supposed to be neighbors if the euclidean distance between them is at most equal to 2$R_s$, where $R_s$ is the sensing range.
-\indent We consider a boolean disk coverage model which is the most widely used sensor coverage model in the literature. Thus, since a sensor has a constant sensing range $R_s$, every space points within a disk centered at a sensor with the radius of the sensing range is said to be covered with this sensor. We also assume that the communication range $R_c$ is at least twice the sensing range $R_s$ (i.e., $R_c \geq 2R_s$). In fact, Zhang and Hou~\cite{ref126} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode. we consider multi-hop communication.
+\indent We consider a boolean disk coverage model which is the most widely used sensor coverage model in the literature. Thus, since a sensor has a constant sensing range $R_s$, each space point within a disk centered at a sensor with the radius of the sensing range is said to be covered with this sensor. We also assume that the communication range $R_c$ is at least twice the sensing range $R_s$ (i.e., $R_c \geq 2R_s$). In fact, Zhang and Hou~\cite{ref126} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode. we consider multi-hop communication.
%We assume that each sensor node can directly transmit its measurements toward a mobile sink node.
%For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. The mobile sink node collects the measurements and transmits them to the base station.
\subsubsection{Decision phase}
\label{ch4:sec:02:03:03}
-The leader will solve an integer program (see section~\ref{ch4:sec:03}) to select which sensors will be activated in the following sensing phase to cover the subregion. It will send ActiveSleep packet to each sensor in the subregion based on the algorithm's results.
+The leader will solve an integer program (see section~\ref{ch4:sec:03}) to select which sensors will be activated in the following sensing phase to cover the subregion. It will send an ActiveSleep packet to each sensor in the subregion based on the algorithm's results.
%($RE_j$) corresponds to its remaining energy) to be alive during the selected periods knowing that $E_{th}$ is the amount of energy required to be alive during one period.
-\begin{figure}[h!t]
+\begin{figure}[t]
\centering
\includegraphics[scale=0.8]{Figures/ch4/R1/T.pdf}
\caption{Execution Time (in seconds)}
& \mbox{is not covered during round $t$,}\\
\left( \sum_{j \in J} \alpha_{jp} * X_{tj} \right)- 1 & \mbox{otherwise.}\\
\end{array} \right.
-\label{eq13}
+\label{eq133}
\end{equation}
More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
minus one that cover the primary point $p$ during round $t$. The
1 &\mbox{if the primary point $p$ is not covered during round $t$,} \\
0 & \mbox{otherwise.}\\
\end{array} \right.
-\label{eq14}
+\label{eq1114}
\end{equation}
Our coverage optimization problem can then be formulated as follows
\end{frame}
\subsection{Results Analysis and Comparison }
-\label{ch5:sec:04:02}
+\label{ch5:sec:04:03}
\begin{enumerate}[i)]
%% CHAPTER 06 %%
%% %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \chapter{ Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}
+ \chapter{ Perimeter-based Coverage Optimization to Improve Lifetime in WSNs}
\label{ch6}
\fi
\section*{3. Main Contributions of this Dissertation}
- \addcontentsline{toc}{section}{4. Main Contributions of this Dissertation}
+ \addcontentsline{toc}{section}{3. Main Contributions of this Dissertation}
%The coverage problem in WSNs is becoming more and more important for many applications ranging from military applications such as battlefield surveillance to the civilian applications such as health-care surveillance and habitant monitoring.
The main contributions in this dissertation concentrate on designing distributed optimization protocols to extend the lifetime of WSNs. We summarize the main contributions of our research as follows:
% \section{ Refereed Journal and Conference Publications}
\section*{4. Dissertation Outline}
-\addcontentsline{toc}{section}{5. Dissertation Outline}
+\addcontentsline{toc}{section}{4. Dissertation Outline}
The dissertation is organized as follows: the next chapter presents a scientific background about wireless sensor networks. Chapter 2 states a review of the related literatures to the coverage problem in WSNs, prior works and current works. Evaluation tools and optimization solvers are investigated in chapter 3. Chapter 4 describes the proposed DiLCO protocol, while chapter 5 and 6 respectively present the MuDiLCO and PeCO protocols. Finally, we conclude our work in chapter 7.
\chapter*{Résumé \markboth{Résumé}{Résumé}}
-\label{cha}
+\label{cha1}
\addcontentsline{toc}{chapter}{Résumé}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% The content of the PhD thesis
\begin{document}
+
% set the page numbers to be arabic, starting at page 1 %
\setcounter{page}{1}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
+
%% Introduction générale
\include{INTRODUCTION}
\contentsline {chapter}{Introduction }{19}{chapter*.8}
\contentsline {section}{1. General Introduction }{19}{section*.9}
\contentsline {section}{2. Motivation of the Dissertation }{20}{section*.10}
-\contentsline {section}{4. Main Contributions of this Dissertation}{20}{section*.11}
-\contentsline {section}{5. Dissertation Outline}{21}{section*.12}
+\contentsline {section}{3. Main Contributions of this Dissertation}{20}{section*.11}
+\contentsline {section}{4. Dissertation Outline}{21}{section*.12}
\contentsline {part}{I\hspace {1em}Scientific Background}{23}{part.1}
\contentsline {chapter}{\numberline {1}Wireless Sensor Networks}{25}{chapter.1}
\contentsline {section}{\numberline {1.1}Introduction}{25}{section.1.1}
\contentsline {subsection}{\numberline {5.4.2}Metrics}{105}{subsection.5.4.2}
\contentsline {subsection}{\numberline {5.4.3}Results Analysis and Comparison }{106}{subsection.5.4.3}
\contentsline {section}{\numberline {5.5}Conclusion}{112}{section.5.5}
-\contentsline {chapter}{\numberline {6} Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}{113}{chapter.6}
+\contentsline {chapter}{\numberline {6} Perimeter-based Coverage Optimization to Improve Lifetime in WSNs}{113}{chapter.6}
\contentsline {section}{\numberline {6.1}Introduction}{113}{section.6.1}
\contentsline {section}{\numberline {6.2}The PeCO Protocol Description}{113}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}Assumptions and Models}{113}{subsection.6.2.1}
