Update by Ali today

diff --git a/ACRONYMS.tex b/ACRONYMS.tex
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diff --git a/Abstruct.tex b/Abstruct.tex
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diff --git a/CHAPITRE_01.tex b/CHAPITRE_01.tex
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diff --git a/CHAPITRE_02.tex b/CHAPITRE_02.tex
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diff --git a/CHAPITRE_03.tex b/CHAPITRE_03.tex
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diff --git a/CHAPITRE_04.tex b/CHAPITRE_04.tex
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index 2df2e9e..6365fb8
--- a/CHAPITRE_04.tex
+++ b/CHAPITRE_04.tex
@@ -145,8 +145,6 @@ The  leader will  solve an  integer  program (see  section~\ref{ch4:sec:03}) to
 \label{ch4:sec:02:03:04}
 Active  sensors  in the  round  will  execute  their sensing  task  to preserve maximal  coverage in the  region of interest. We  will assume that the cost  of keeping a node awake (or asleep)  for sensing task is the same for all wireless sensor  nodes in the  network.  Each sensor will receive  an ActiveSleep  packet from the leader  informing it to stay awake or to go to sleep for a time  equal to the round of sensing until starting a new period.
 
 \label{ch4:sec:02:03:04}
 Active  sensors  in the  round  will  execute  their sensing  task  to preserve maximal  coverage in the  region of interest. We  will assume that the cost  of keeping a node awake (or asleep)  for sensing task is the same for all wireless sensor  nodes in the  network.  Each sensor will receive  an ActiveSleep  packet from the leader  informing it to stay awake or to go to sleep for a time  equal to the round of sensing until starting a new period.
 

-An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO} which describes the execution of a period  by a node (denoted by $s_j$  for a sensor  node indexed by  $j$). In  the beginning,  a node  checks whether  it has enough energy to stay active during the next sensing phase (i.e., the remaining energy ($RE_j$) $\geq$ $E_{th}$ (the  amount of energy required to be alive during one round)). If yes, it exchanges information  with  all the  other nodes belonging to the same subregion:  it collects from each node its position coordinates, remaining energy ($RE_j$), ID, and  the number  of  one-hop neighbors  still  alive. Once  the  first phase  is completed, the nodes  of a subregion choose a leader to  take the decision based on  the  following  criteria   with  decreasing  importance:  larger  number  of neighbors, larger remaining energy, and  then in case of equality, larger index. After that,  if the sensor node is  leader, it will execute  the integer program algorithm (see Section~\ref{ch4:sec:03})  which provides a set of  sensors planned to be active in the next sensing phase. As leader, it will send an Active-Sleep packet to each sensor  in the same subregion to  indicate it if it has to  be active or not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the Active-Sleep packet to know its state for the coming sensing phase.
-

 \begin{algorithm}[h!]                
 
   \BlankLine
 \begin{algorithm}[h!]                
 
   \BlankLine


@@ -185,6 +183,7 @@ An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO}
 
 \end{algorithm}
 
 
 \end{algorithm}
 

+An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO} which describes the execution of a period  by a node (denoted by $s_j$  for a sensor  node indexed by  $j$). In  the beginning,  a node  checks whether  it has enough energy to stay active during the next sensing phase (i.e., the remaining energy ($RE_j$) $\geq$ $E_{th}$ (the  amount of energy required to be alive during one round)). If yes, it exchanges information  with  all the  other nodes belonging to the same subregion:  it collects from each node its position coordinates, remaining energy ($RE_j$), ID, and  the number  of  one-hop neighbors  still  alive. Once  the  first phase  is completed, the nodes  of a subregion choose a leader to  take the decision based on  the  following  criteria   with  decreasing  importance:  larger  number  of neighbors, larger remaining energy, and  then in case of equality, larger index. After that,  if the sensor node is  leader, it will execute  the integer program algorithm (see Section~\ref{ch4:sec:03})  which provides a set of  sensors planned to be active in the next sensing phase. As leader, it will send an Active-Sleep packet to each sensor  in the same subregion to  indicate it if it has to  be active or not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the Active-Sleep packet to know its state for the coming sensing phase.

 
 %Primary Points based 
 \section{Coverage Problem Formulation}
 
 %Primary Points based 
 \section{Coverage Problem Formulation}


@@ -281,7 +280,7 @@ large compared to $W_{\theta}$.
 \section{Simulation Results and Analysis}
 \label{ch4:sec:04}
 
 \section{Simulation Results and Analysis}
 \label{ch4:sec:04}
 

-\subsection{Simulation Framework}  %%% 
+\subsection{Simulation Framework}  

 \label{ch4:sec:04:01}
 
 To assess the performance of DiLCO protocol, we have used the discrete event simulator OMNeT++ \cite{ref158} to run different series of simulations. Table~\ref{tablech4} gives the chosen parameters setting.
 \label{ch4:sec:04:01}
 
 To assess the performance of DiLCO protocol, we have used the discrete event simulator OMNeT++ \cite{ref158} to run different series of simulations. Table~\ref{tablech4} gives the chosen parameters setting.


@@ -368,8 +367,9 @@ COMPUTATION & on & on & on & 26.83 \\
 % is used to refer this table in the text
 \end{table}
 
 % is used to refer this table in the text
 \end{table}
 

-\indent For the sake of simplicity we ignore  the energy needed to turn on the radio, to start up the sensor node, to move from one status to another, etc. Thus, when a sensor becomes active (i.e., it has already received its status from leader), it can turn  its radio  off to  save battery. The value of energy spent to send a 1-bit-content message is  obtained by using  the equation in ~\cite{ref112} 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 $0.2575~mW$.
-
+\indent For the sake of simplicity we ignore  the energy needed to turn on the radio, to start up the sensor node, to move from one status to another, etc. Thus, when a sensor becomes active (i.e., it has already received its status from leader), it can turn  its radio  off to  save battery. DiLCO uses two types of packets
+for communication. The size of the INFO packet and Active-Sleep packet
+are 112 bits and 16 bits respectively. The value of energy spent to send a 1-bit-content message is  obtained by using  the equation in ~\cite{ref112} 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 $0.2575~mW$.

 
 %We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}. 
 
 
 %We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}. 
 


@@ -399,7 +399,7 @@ the efficiency of our approach:
   coverage ratio: 
 \begin{equation*}
 \scriptsize
   coverage ratio: 
 \begin{equation*}
 \scriptsize

-\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
+\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100,

 \end{equation*}
 where  $n$ is  the number  of covered  grid points  by active  sensors  of every
 subregions during  the current  sensing phase  and $N$ is the total number  of grid
 \end{equation*}
 where  $n$ is  the number  of covered  grid points  by active  sensors  of every
 subregions during  the current  sensing phase  and $N$ is the total number  of grid


@@ -425,13 +425,13 @@ in  order to  minimize  the communication  overhead  and maximize  the
 network lifetime. The Active Sensors Ratio is defined as follows:
 \begin{equation*}
 \scriptsize
 network lifetime. The Active Sensors Ratio is defined as follows:
 \begin{equation*}
 \scriptsize

-\mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$J$}} \times 100 .
+\mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$J$}} \times 100,

 \end{equation*}
 \end{equation*}

-Where: $A_r$ is the number of active sensors in the subregion $r$ during current period, $J$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
+where $A_r$ is the number of active sensors in the subregion $r$ during current period, $J$ is the total number of sensors in the network, and $R$ is the total number of subregions in the network.

 
 \item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power, therefore it is important that the proposed algorithm has the shortest possible execution  time. The energy of  a sensor node  must be mainly used   for  the  sensing   phase,  not   for  the   pre-sensing  ones. In this dissertation, 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 Atmel's AVR ATmega103L  microcontroller (6 MHz) and  a MIPS rate  equal to 6 to  run the optimization   resolution,   this  time   is   multiplied   by  2944.2   $\left( \frac{35330}{2} \times  \frac{1}{6} \right)$.  
   
 
 \item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power, therefore it is important that the proposed algorithm has the shortest possible execution  time. The energy of  a sensor node  must be mainly used   for  the  sensing   phase,  not   for  the   pre-sensing  ones. In this dissertation, 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 Atmel's AVR ATmega103L  microcontroller (6 MHz) and  a MIPS rate  equal to 6 to  run the optimization   resolution,   this  time   is   multiplied   by  2944.2   $\left( \frac{35330}{2} \times  \frac{1}{6} \right)$.  
   

-\item {{\bf Stopped simulation runs}:} A simulation ends  when the  sensor network becomes disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.% ( in chapter 4, period consists of one round).
+\item {{\bf Stopped simulation runs}:} a simulation ends  when the  sensor network becomes disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.% ( in chapter 4, period consists of one round).

 
 \end{enumerate}
 
 
 \end{enumerate}
 


@@ -440,15 +440,15 @@ Where: $A_r$ is the number of active sensors in the subregion $r$ during current
 \subsection{Performance Analysis for Different Number of Subregions}
 \label{ch4:sec:04:05}
   
 \subsection{Performance Analysis for Different Number of Subregions}
 \label{ch4:sec:04:05}
   

-In this subsection, we are study the performance of our DiLCO protocol for a different number of subregions (Leaders).
-The DiLCO-1 protocol is a centralized approach to all the area of the interest, while  DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take the DiLCO-1 protocol in our simulation results because it needs a high execution time to give the decision leading to consume all its energy before producing the solution for the optimization problem.
+In this subsection, we study the performance of our DiLCO protocol for different numbers of subregions.
+The DiLCO-1 protocol is a centralized approach for the whole area of the interest, while  DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLCO-1 protocol in our simulation results because it needs a high execution time to give the decision, leading to consume all its energy before producing the solution for the optimization problem.

 
 \begin{enumerate}[i)]
 \item {{\bf Coverage Ratio}}
 %\subsubsection{Coverage Ratio} 
 %\label{ch4:sec:04:02:01}
 
 
 \begin{enumerate}[i)]
 \item {{\bf Coverage Ratio}}
 %\subsubsection{Coverage Ratio} 
 %\label{ch4:sec:04:02:01}
 

-In this experiment, Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ratio for 150 deployed nodes.  
+Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ratio for 150 deployed nodes.  

 \parskip 0pt    
 \begin{figure}[h!]
 \centering
 \parskip 0pt    
 \begin{figure}[h!]
 \centering


@@ -457,8 +457,8 @@ In this experiment, Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ra
 \label{Figures/ch4/R1/CR}
 \end{figure} 
 It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty rounds.  
 \label{Figures/ch4/R1/CR}
 \end{figure} 
 It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty rounds.  

-DiLCO-2 protocol gives near similar coverage ratio with other ones for first 10 rounds and then decreased until the died of the network in the round $18^{th}$. In case of only 2 subregions, the energy consumption is high and the network is rapidly disconnected. 
-As shown in the Figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases,  the coverage preservation for the area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to  DiLCO-8,  DiLCO-16, and  DiLCO-32 protocols,  other nodes are  preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the  coverage for a larger number of rounds. DiLCO-8,  DiLCO-16, and  DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
+DiLCO-2 protocol gives a coverage ratio very close to the other protocols for the first 10 periods, and then the coverage decreases until the died of the network in the period $18^{th}$. In case of only 2 subregions, the energy consumption is high and the network is rapidly disconnected. 
+As can be seen in Figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases,  the coverage preservation for the area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to  DiLCO-8,  DiLCO-16, and  DiLCO-32 protocols,  other nodes are  preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the  coverage for a larger number of rounds. DiLCO-8,  DiLCO-16, and  DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.

 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 
 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 


@@ -471,9 +471,9 @@ Figure~\ref{Figures/ch4/R1/ASR} shows the average active nodes ratio for 150 dep
 \label{Figures/ch4/R1/ASR}
 \end{figure} 
 
 \label{Figures/ch4/R1/ASR}
 \end{figure} 
 

-The results presented in Figure~\ref{Figures/ch4/R1/ASR} show the increase of the number of subregions lead to the increase of the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but it preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.
+The results presented in the figure show that increasing the number of subregions lead to the increase of the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but they both preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continue the optimization process, and this extends the lifetime of the network.

 
 

-\item {{\bf The percentage of stopped simulation runs}}
+\item {{\bf Stopped simulation runs}}

 %\subsubsection{The percentage of stopped simulation runs}
 
 Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 
 %\subsubsection{The percentage of stopped simulation runs}
 
 Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 


@@ -485,36 +485,37 @@ Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation
 \end{figure} 
 
 DiLCO-2 is the approach which stops first because it applies the optimization on only two subregions and the high energy consumption accelerate the network disconnection.
 \end{figure} 
 
 DiLCO-2 is the approach which stops first because it applies the optimization on only two subregions and the high energy consumption accelerate the network disconnection.

-Thus, as explained previously, in case of the DiLCO-16 and DiLCO-32 with several subregions, the optimization effectively continues as long as a network in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime. 
+Thus, as explained previously, in case of DiLCO-16 and DiLCO-32 which have many subregions, the optimization effectively continues as long as a subnetwork in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime. 

 
 

-\item {{\bf The Energy Consumption}}
+\item {{\bf Energy Consumption}}

 %\subsubsection{The 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 $Lifetime95$ and $Lifetime50$. 
+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 $Lifetime_{50}$. 

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf} 
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf} 

-\caption{Energy Consumption for Lifetime95}
+\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.\\
  
 \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 time computation to solve the optimization problem, as well as the higher energy consumed during the communication.  
+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!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf} 

-\caption{Energy Consumption for Lifetime50}
+\caption{Energy Consumption for $Lifetime_{50}$}

 \label{Figures/ch4/R1/EC50}
 \end{figure} 
 \label{Figures/ch4/R1/EC50}
 \end{figure} 

-In fact,  the distribution of the computation over many subregions greatly reduces the number of communications, the time of listening and computation so thanks to the partitioning of the initial network in several independent subnetworks. 
+In fact,  the distribution of the computation over many subregions greatly reduces the number of communications, the time of listening and computation. 

 
 \item {{\bf Execution Time}}
 %\subsubsection{Execution Time}
 
 In this experiment, the execution time of the our distributed optimization approach has been studied. Figure~\ref{Figures/ch4/R1/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. They are given for the different approaches and various numbers of sensors. The original execution time is computed as described in section \ref{ch4:sec:04:04}. 
 
 \item {{\bf Execution Time}}
 %\subsubsection{Execution Time}
 
 In this experiment, the execution time of the our distributed optimization approach has been studied. Figure~\ref{Figures/ch4/R1/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. They are given for the different approaches and various numbers of sensors. The original execution time is computed as described in section \ref{ch4:sec:04:04}. 

-%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 AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times 6\right)$ and reported on Figure~\ref{fig8} for different network sizes.
+
+We can see from Figure~\ref{Figures/ch4/R1/T} that DiLCO-32 has very low execution times in comparison with other DiLCO versions because it is distributed on larger number of small subregions.  Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion and thus presents high execution times. Overall, to be able to deal with very large networks,  a distributed method is clearly required.

 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering


@@ -523,31 +524,30 @@ In this experiment, the execution time of the our distributed optimization appro
 \label{Figures/ch4/R1/T}
 \end{figure} 
 
 \label{Figures/ch4/R1/T}
 \end{figure} 
 

-We can see from Figure~\ref{Figures/ch4/R1/T}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions because it is distributed on larger number of small subregions.  Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.

 
 

-We think that in distributed fashion the solving of the  optimization problem 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.

 
 

-\item {{\bf The Network Lifetime}}
+\item {{\bf Network Lifetime}}

 %\subsubsection{The Network Lifetime}
 
 %\subsubsection{The Network Lifetime}
 

-In Figure~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes. 
+In Figure~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, network lifetime, $Lifetime_{95}$ and $Lifetime_{50}$ respectively, are illustrated for different network sizes. 

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}  

-\caption{Network Lifetime for $Lifetime95$}
+\caption{Network Lifetime for $Lifetime_{95}$}

 \label{Figures/ch4/R1/LT95}
 \end{figure} 
 \label{Figures/ch4/R1/LT95}
 \end{figure} 

-For DiLCO-2 protocol results, 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.
+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. DiLCO-16 protocol leads to the larger lifetime improvement. DiLCO-16 protocol efficiently extends the network lifetime because the benefit from the optimization with 16 subregions is better than DiLCO-32 protocol with 32 subregions. in fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.
+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 also 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.
+%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.

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}  

-\caption{Network Lifetime for $Lifetime50$}
+\caption{Network Lifetime for $Lifetime_{50}$}

 \label{Figures/ch4/R1/LT50}
 \end{figure} 
 
 \label{Figures/ch4/R1/LT50}
 \end{figure} 
 


@@ -556,7 +556,7 @@ Comparison shows that DiLCO-16 protocol, which uses 16 leaders, is the best one
 \subsection{Performance Analysis for Different Number of Primary Points}
 \label{ch4:sec:04:06}
 
 \subsection{Performance Analysis for Different Number of Primary Points}
 \label{ch4:sec:04:06}
 

-In this section, we study the performance of DiLCO~16 approach for a different number of primary points. The objective of this comparison is to select the suitable primary point model to be used by DiLCO protocol. In this comparison, DiLCO-16 protocol is used with five models which are called Model-5( With 5 Primary Points), Model-9 ( With 9 Primary Points), Model-13 ( With 13 Primary Points), Model-17 ( With 17 Primary Points), and Model-21 ( With 21 Primary Points). 
+In this section, we study the performance of DiLCO~16 approach for different numbers of primary points. The objective of this comparison is to select the suitable primary point model to be used by a DiLCO protocol. In this comparison, DiLCO-16 protocol is used with five models, which are called Model-5(it uses 5 primary points), Model-9 (it uses 9 primary points), Model-13 (it uses 13 primary points), Model-17 (it uses 17 primary points), and Model-21 (it uses 21 primary points). 

 
 
 \begin{enumerate}[i)]
 
 
 \begin{enumerate}[i)]


@@ -572,14 +572,13 @@ Figure~\ref{Figures/ch4/R2/CR} shows the average coverage ratio for 150 deployed
 \caption{Coverage ratio for 150 deployed nodes}
 \label{Figures/ch4/R2/CR}
 \end{figure} 
 \caption{Coverage ratio for 150 deployed nodes}
 \label{Figures/ch4/R2/CR}
 \end{figure} 

-
-It is shown that all models provide a very near coverage ratios during the network lifetime, with a very small superiority for the models with higher number of primary points. Moreover, when the number of rounds increases, coverage ratio produced by Model-13, Model-17, and Model-21 decreases in comparison with Model-5 and Model-9 due to a larger time computation for the decision process for larger number of primary points. 
-As shown in Figure ~\ref{Figures/ch4/R2/CR}, Coverage ratio decreases when the number of rounds increases due to dead nodes. Model-9 is slightly more efficient than other models, because it is balanced between the number of rounds and the better coverage ratio in comparison with other Models.
+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. 
+As shown in Figure ~\ref{Figures/ch4/R2/CR}, coverage ratio decreases when the number of rounds 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}}
 %\subsubsection{Active Sensors Ratio} 
 
 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 
 

- Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes.
+Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes.

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/ASR.pdf}  
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/ASR.pdf}  


@@ -587,10 +586,11 @@ As shown in Figure ~\ref{Figures/ch4/R2/CR}, Coverage ratio decreases when the n
 \label{Figures/ch4/R2/ASR}
 \end{figure} 
 
 \label{Figures/ch4/R2/ASR}
 \end{figure} 
 

-The results presented in Figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed  Model-5, in comparison with the other models. The model with fewer number of primary points uses fewer active nodes than the other models. According to the results presented in Figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model-5 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model-9 approach is to use fewer number of active nodes for each round compared with Model-13,  Model-17, and Model-21. This led to continuing for a larger number of rounds with extending the network lifetime. Model-9 has a better coverage ratio compared to Model-5 and acceptable number of rounds.
+The results presented in Figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed  Model-5, in comparison with the other models. The model with fewer number of primary points uses fewer active nodes than the other models. 
+According to the results presented in Figure~\ref{Figures/ch4/R2/CR}, we observe that Model-5 continue to a larger number of periods with a better coverage ratio compared with other models. The advantage of the Model-5 approach is to use fewer number of active nodes for each period compared with Model-9, Model-13,  Model-17, and Model-21. This led to continuing for a larger number of periods with extending the network lifetime.

 
 
 
 

-\item {{\bf The percentage of stopped simulation runs}}
+\item {{\bf Stopped simulation runs}}

 %\subsubsection{The percentage of stopped simulation runs}
 
 Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 
 %\subsubsection{The percentage of stopped simulation runs}
 
 Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 


@@ -602,33 +602,33 @@ Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation
 \label{Figures/ch4/R2/SR}
 \end{figure} 
 
 \label{Figures/ch4/R2/SR}
 \end{figure} 
 

-When the number of primary points is increased, the percentage of the stopped simulation runs per round is increased. The reason behind the increase is the increase in the sensors dead when the primary points increase. Model-5 is better than other models because it conserve more energy by turn on less number of sensors during the sensing phase, but in the same time it preserve the coverage with a less coverage ratio in comparison with other models. Model~2 seems to be more suitable to be used in wireless sensor networks. \\
+When the number of primary points is increased, the percentage of the stopped simulation runs per period is increased. The reason behind the increase is the increasing number of dead sensors when the primary points increase. Model-5 is better than other models because it conserve more energy by turning on less sensors during the sensing phase and in the same time it preserves a good coverage for a larger number of periods in comparison with other models. Model~5 seems to be more suitable to be used in wireless sensor networks. \\

 
 
 
 

-\item {{\bf The Energy Consumption}}
+\item {{\bf Energy Consumption}}

 %\subsubsection{The Energy Consumption}
 
 %\subsubsection{The Energy Consumption}
 

-In this experiment, we study the effect of increasing the primary points to represent the area of the sensor on the energy consumed by the wireless sensor network for different network densities.  Figures~\ref{Figures/ch4/R2/EC95} and ~\ref{Figures/ch4/R2/EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$.
+In this experiment, we study the effect of increasing the primary points to represent the area of the sensor on the energy consumed by the wireless sensor network for different network densities.  Figures~\ref{Figures/ch4/R2/EC95} and ~\ref{Figures/ch4/R2/EC50} illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$.

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf} 

-\caption{Energy Consumption with $95\%-Lifetime$}
+\caption{Energy Consumption with $Lifetime_{95}$}

 \label{Figures/ch4/R2/EC95}
 \end{figure} 
  
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf} 
 \label{Figures/ch4/R2/EC95}
 \end{figure} 
  
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf} 

-\caption{Energy Consumption with $Lifetime50$}
+\caption{Energy Consumption with $Lifetime_{50}$}

 \label{Figures/ch4/R2/EC50}
 \end{figure} 
 
 \label{Figures/ch4/R2/EC50}
 \end{figure} 
 

-We see from the results presented in Figures~\ref{Figures/ch4/R2/EC95} and \ref{Figures/ch4/R2/EC50}, The energy consumed by the network for each round increases when the primary points increases, because the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model-5 is the most competitive from the energy consumption point of view, but the worst one from coverage ratio point of view. The other models have a high energy consumption  due to the increase in the primary points, which are led to increase the energy consumption during the listening mode before producing the solution by solving the optimization process. In fact, Model-9 is a good candidate to be used by wireless sensor network because it preserves a good coverage ratio with a suitable energy consumption in comparison with other models. 
+We see from the results presented in both figures that the energy consumed by the network for each period increases when the number of primary points increases. Indeed, the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model-5 is the most competitive from the energy consumption point of view and the coverage ratio point of view. The other models have a high energy consumption  due to the increase in the primary points. In fact, Model-5 is a good candidate to be used by wireless sensor network because it preserves a good coverage ratio with a suitable energy consumption in comparison with other models. 

 
 \item {{\bf Execution Time}}
 %\subsubsection{Execution Time}
 
 
 \item {{\bf Execution Time}}
 %\subsubsection{Execution Time}
 

-In this experiment, we study the impact of the increase in primary points on the execution time of DiLCO protocol. Figure~\ref{Figures/ch4/R2/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. The original execution time is computed as described in section \ref{ch4:sec:04:04}. 
+In this experiment, we study the impact of the increase in primary points on the execution time of DiLCO protocol. Figure~\ref{Figures/ch4/R2/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one period. The original execution time is computed as described in section \ref{ch4:sec:04:04}. 

 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering


@@ -637,18 +637,17 @@ In this experiment, we study the impact of the increase in primary points on the
 \label{Figures/ch4/R2/T}
 \end{figure} 
 
 \label{Figures/ch4/R2/T}
 \end{figure} 
 

-They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model-5 has lower execution time in comparison with other models because it used smaller number of primary points to represent the area of the sensor.  Conversely, the other primary point models  have been presented  a higher execution times.
-Moreover, Model-9 has more suitable times and coverage ratio that lead to continue for a larger number of rounds extending the network lifetime. We  think that a good primary point model, this one that balances between the coverage ratio and the number of rounds during the lifetime of the network.
+They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model-5 has the lower execution time in comparison with other models because it used the smaller number of primary points to represent the area of the sensor.  Conversely, the other primary point models have presented  higher execution times.
+Moreover, Model-5 has more suitable execution times and coverage ratio that lead to continue for a larger number of period extending the network lifetime. We think that a good primary point model, is one that balances between the coverage ratio and the number of periods during the lifetime of the network.

 
 

-\item {{\bf The Network Lifetime}}
+\item {{\bf Network Lifetime}}

 %\subsubsection{The Network Lifetime}
 
 %\subsubsection{The Network Lifetime}
 

-Finally, we study the effect of increasing the primary points on the lifetime of the network. In Figure~\ref{Figures/ch4/R2/LT95} and in Figure~\ref{Figures/ch4/R2/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes. 
-
+Finally, we study the effect of increasing the primary points on the lifetime of the network. %In Figure~\ref{Figures/ch4/R2/LT95} and in Figure~\ref{Figures/ch4/R2/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes. 

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf}  
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf}  

-\caption{Network Lifetime for $Lifetime95$}
+\caption{Network Lifetime for $Lifetime_{95}$}

 \label{Figures/ch4/R2/LT95}
 \end{figure} 
 
 \label{Figures/ch4/R2/LT95}
 \end{figure} 
 


@@ -656,20 +655,19 @@ Finally, we study the effect of increasing the primary points on the lifetime of
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf}  
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf}  

-\caption{Network Lifetime for $Lifetime50$}
+\caption{Network Lifetime for $Lifetime_{50}$}

 \label{Figures/ch4/R2/LT50}
 \end{figure} 
 
 \label{Figures/ch4/R2/LT50}
 \end{figure} 
 

-

 As highlighted by figures~\ref{Figures/ch4/R2/LT95} and \ref{Figures/ch4/R2/LT50}, the network lifetime obviously increases when the size of the network increases, with  Model-5 that leads to the larger lifetime improvement.
 As highlighted by figures~\ref{Figures/ch4/R2/LT95} and \ref{Figures/ch4/R2/LT50}, the network lifetime obviously increases when the size of the network increases, with  Model-5 that leads to the larger lifetime improvement.

-Comparison shows that the Model-5, which uses less number of primary points, is the best one because it is less energy consumption during the network lifetime. It is also the worst one from the point of view of coverage ratio. Our proposed Model-9 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models.
+Comparison shows that Model-5, which uses less number of primary points, is the best one because it is less energy consuming during the network lifetime. It is also the better one from the point of view of coverage ratio. Our proposed Model-5 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models.

  
 \end{enumerate}
 
 \subsection{Performance Comparison with other Approaches}
 \label{ch4:sec:04:07}
 
  
 \end{enumerate}
 
 \subsection{Performance Comparison with other Approaches}
 \label{ch4:sec:04:07}
 

-Based on the results, conducted in the previous subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, DiLCO-16 protocol and DiLCO-32 protocol with Model-9 seems to be the best candidates to be compared with other two approaches. The first approach is called DESK~\cite{DESK}, which is a fully distributed coverage algorithm. The second approach called GAF~\cite{GAF}, consists in dividing the region into fixed squares.   During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time. \\ \\
+Based on the results, conducted in the previous subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, DiLCO-16 and DiLCO-32 protocols, both with Model-5, seem to be the best candidates to be compared with other approaches. The first approach is called DESK~\cite{DESK}, which is a fully distributed coverage algorithm. The second approach called GAF~\cite{GAF}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain active during the sensing phase time. \\ \\

 
 \begin{enumerate}[i)]
 \item {{\bf Coverage Ratio}}
 
 \begin{enumerate}[i)]
 \item {{\bf Coverage Ratio}}


@@ -680,14 +678,17 @@ The average coverage ratio for 150 deployed nodes is demonstrated in Figure~\ref
 \parskip 0pt    
 \begin{figure}[h!]
 \centering
 \parskip 0pt    
 \begin{figure}[h!]
 \centering

- \includegraphics[scale=0.8] {Figures/ch4/R3/CR.pdf} 
+ \includegraphics[scale=0.8] {Figures/ch4/R3/CR.eps} 

 \caption{Coverage ratio for 150 deployed nodes}
 \label{Figures/ch4/R3/CR}
 \end{figure} 
 
 \caption{Coverage ratio for 150 deployed nodes}
 \label{Figures/ch4/R3/CR}
 \end{figure} 
 

-DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 99.1\% and 99.2\% produced by DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of DESK and GAF.
+DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 98.4\% and 98.9\% produced by DiLCO-16 and DiLCO-32 for the lowest number of periods. This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors thanks to the optimization (which lightly decreases the coverage ratio), while there are more active nodes in the case of DESK and GAF.

 
 

-Moreover, when the number of rounds increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO-16 protocol and DiLCO-32 protocol maintain almost a good coverage. This is because they optimize the coverage and the lifetime in wireless sensor network by selecting the best representative sensor nodes to take the responsibility of coverage during the sensing phase.
+Moreover, when the number of rounds increases, coverage ratio produced by DESK and GAF protocols decreases. 
+%This is due to dead nodes. However, DiLCO-16 protocol and DiLCO-32 protocol maintain almost a good coverage. 
+GAF exhibits in particular a fast decrease. Our protocols also provide decreasing coverage ratio, but far more better than those of DESK and GAF. DiLCO-16 and DiLCO-32 clearly outperform DESK and GAF for number of periods between 32 and 103.
+This is because they optimize the coverage and the lifetime in wireless sensor network by selecting the best representative sensor nodes to take the responsibility of coverage during the sensing phase.

 %, and this will lead to continuing for a larger number of rounds and prolonging the network lifetime. Furthermore, although some nodes are dead, sensor activity scheduling of our protocol chooses other nodes to ensure the coverage of the area of interest. 
 
 \item {{\bf Active Sensors Ratio}}
 %, and this will lead to continuing for a larger number of rounds and prolonging the network lifetime. Furthermore, although some nodes are dead, sensor activity scheduling of our protocol chooses other nodes to ensure the coverage of the area of interest. 
 
 \item {{\bf Active Sensors Ratio}}


@@ -697,76 +698,76 @@ It is important to have as few active nodes as possible in each round, in  order
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.8]{Figures/ch4/R3/ASR.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R3/ASR.eps}  

 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R3/ASR}
 \end{figure} 
 
 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R3/ASR}
 \end{figure} 
 

-The results presented in Figure~\ref{Figures/ch4/R3/ASR} show the superiority of the proposed DiLCO-16 protocol and DiLCO-32 protocol, in comparison with the other approaches.  DESK and GAF have 37.5 \% and 44.5 \% active nodes and DiLCO-16 protocol and DiLCO-32 protocol compete perfectly with only 17.4 \%, 24.8 \% and 26.8 \%  active nodes for the first 14 rounds. Then as the number of rounds increases DiLCO-16 protocol and DiLCO-32 protocol have larger number of active nodes in comparison with DESK and GAF, especially from round $35^{th}$ because they give a better coverage ratio than other approaches. We see that DESK and GAF have less number of active nodes beginning at the rounds $35^{th}$ and $32^{th}$ because there are many nodes are died due to the high energy consumption by the redundant nodes during the sensing phase. \\
+The results presented in Figure~\ref{Figures/ch4/R3/ASR} show the superiority of the proposed DiLCO-16 protocol and DiLCO-32 protocol, in comparison with the other approaches.  DESK and GAF have, respectively, 37.5 \% and 44.5 \% active nodes, whereas DiLCO-16 and DiLCO-32 protocols compete perfectly with only 23.7 \% and 25.8 \%  active nodes for the first 14 periods. Then as the number of periods increases DiLCO-16 and DiLCO-32 protocols have larger number of active nodes in comparison with DESK and GAF, especially from period $35^{th}$ because they give a better coverage ratio than other approaches. We see that DESK and GAF have less number of active nodes beginning at the rounds $35^{th}$ and $32^{th}$ because there are many died nodes due to the high energy consumption by the redundant nodes during the previous sensing phases. \\

 
 
 
 

-\item {{\bf The percentage of stopped simulation runs}}
+\item {{\bf Stopped simulation runs}}

 %\subsubsection{The percentage of stopped simulation runs}
 %The results presented in this experiment, are to show the comparison of DiLCO-16 protocol and DiLCO-32 protocol with other two approaches from the point of view of stopped simulation runs per round.
 
 Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 
 \begin{figure}[h!]
 \centering
 %\subsubsection{The percentage of stopped simulation runs}
 %The results presented in this experiment, are to show the comparison of DiLCO-16 protocol and DiLCO-32 protocol with other two approaches from the point of view of stopped simulation runs per round.
 
 Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.8]{Figures/ch4/R3/SR.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R3/SR.eps} 

 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R3/SR}
 \end{figure} 
 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R3/SR}
 \end{figure} 

-DESK is the approach, which stops first because it consumes more energy for communication as well as it turns on a large number of redundant nodes during the sensing phase. On the other  hand DiLCO-16 protocol and DiLCO-32 protocol have less stopped simulation runs in comparison with DESK and GAF because they distribute the optimization on several subregions.
+On the one hand, DESK is the approach which stops first because it consumes more energy for communication as well as it turns on a large number of redundant nodes during the sensing phase. On the other hand, DiLCO-16 protocol and DiLCO-32 protocol have less stopped simulation runs in comparison with DESK and GAF because they distribute the optimization on several subregions.

 % in order to optimize the coverage and the lifetime of the network by activating a less number of nodes during the sensing phase leading to extending the network lifetime and coverage preservation. The optimization effectively continues as long as a network in a subregion is still connected.
 
 
 % in order to optimize the coverage and the lifetime of the network by activating a less number of nodes during the sensing phase leading to extending the network lifetime and coverage preservation. The optimization effectively continues as long as a network in a subregion is still connected.
 
 

-\item {{\bf The Energy Consumption}}
+\item {{\bf Energy Consumption}}

 %\subsubsection{The Energy Consumption}
 %In this experiment, we have studied the effect of the energy consumed by the wireless sensor network during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches.
 
 %\subsubsection{The Energy Consumption}
 %In this experiment, we have studied the effect of the energy consumed by the wireless sensor network during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches.
 

-Figures~\ref{Figures/ch4/R3/EC95} and ~\ref{Figures/ch4/R3/EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$. 
+Figures~\ref{Figures/ch4/R3/EC95} and ~\ref{Figures/ch4/R3/EC50} illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. 

 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.8]{Figures/ch4/R3/EC95.pdf} 
-\caption{Energy Consumption with $95\%-Lifetime$}
+\includegraphics[scale=0.8]{Figures/ch4/R3/EC95.eps} 
+\caption{Energy Consumption with $Lifetime_{95}$}

 \label{Figures/ch4/R3/EC95}
 \end{figure} 
 
 \begin{figure}[h!]
 \centering
 \label{Figures/ch4/R3/EC95}
 \end{figure} 
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.8]{Figures/ch4/R3/EC50.pdf} 
-\caption{Energy Consumption with $Lifetime50$}
+\includegraphics[scale=0.8]{Figures/ch4/R3/EC50.eps} 
+\caption{Energy Consumption with $Lifetime_{50}$}

 \label{Figures/ch4/R3/EC50}
 \end{figure} 
 
 DiLCO-16 protocol and DiLCO-32 protocol are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes.
 %as well as the energy consumed during the different modes of sensor nodes. 
 \label{Figures/ch4/R3/EC50}
 \end{figure} 
 
 DiLCO-16 protocol and DiLCO-32 protocol are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes.
 %as well as the energy consumed during the different modes of sensor nodes. 

-In fact,  The distribution of computation over the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 
+In fact,  the distribution of computation over the subregions greatly reduces the number of communications and the time of listening, thanks to the partitioning of the initial network into several independent subnetworks. 

 
 
 
 

-\item {{\bf The Network Lifetime}}
+\item {{\bf Network Lifetime}}

 %\subsubsection{The Network Lifetime}
 %In this experiment, we have observed the superiority of DiLCO-16 protocol and DiLCO-32 protocol against other two approaches in prolonging the network lifetime. 
 
 %\subsubsection{The Network Lifetime}
 %In this experiment, we have observed the superiority of DiLCO-16 protocol and DiLCO-32 protocol against other two approaches in prolonging the network lifetime. 
 

-In figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.  
+%In figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.  

 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.8]{Figures/ch4/R3/LT95.pdf}  
-\caption{Network Lifetime for $Lifetime95$}
+\includegraphics[scale=0.8]{Figures/ch4/R3/LT95.eps}  
+\caption{Network Lifetime for $Lifetime_{95}$}

 \label{Figures/ch4/R3/LT95}
 \end{figure}
 
 
 \begin{figure}[h!]
 \centering
 \label{Figures/ch4/R3/LT95}
 \end{figure}
 
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.8]{Figures/ch4/R3/LT50.pdf}  
-\caption{Network Lifetime for $Lifetime50$}
+\includegraphics[scale=0.8]{Figures/ch4/R3/LT50.eps}  
+\caption{Network Lifetime for $Lifetime_{50}$}

 \label{Figures/ch4/R3/LT50}
 \end{figure} 
 
 \label{Figures/ch4/R3/LT50}
 \end{figure} 
 

-As highlighted by figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol and DiLCO-32 protocol that leads to maximize the lifetime of the network compared with other approaches. 
+As highlighted by figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol and DiLCO-32 protocol which lead to maximize the lifetime of the network compared with other approaches. 

 By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next periods, DiLCO-16 protocol and DiLCO-32 protocol efficiently prolong the network lifetime. 
 Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which use distributed optimization over the subregions, are the best ones because they are robust to network disconnection during the network lifetime as well as they consume less energy in comparison with other approaches. 
 %It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
 By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next periods, DiLCO-16 protocol and DiLCO-32 protocol efficiently prolong the network lifetime. 
 Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which use distributed optimization over the subregions, are the best ones because they are robust to network disconnection during the network lifetime as well as they consume less energy in comparison with other approaches. 
 %It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.


@@ -776,7 +777,7 @@ Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which use distrib
 
 \section{Conclusion}
 \label{ch4:sec:05}
 
 \section{Conclusion}
 \label{ch4:sec:05}

-A crucial problem in WSN is to schedule the sensing activities of the different nodes  in order to ensure both of  coverage of  the area  of interest  and longer network lifetime. The inherent limitations of sensor nodes, in energy provision, communication and computing capacities,  require protocols that optimize the use of the  available resources  to  fulfill the sensing  task. To address  this problem, this chapter proposes a  two-step approach. Firstly, the field of sensing
+A crucial problem in WSN is to schedule the sensing activities of the different nodes  in order to ensure both coverage of  the area  of interest  and longer network lifetime. The inherent limitations of sensor nodes, in energy provision, communication, and computing capacities,  require protocols that optimize the use of the  available resources  to  fulfill the sensing  task. To address  this problem, this chapter proposes a  two-step approach. Firstly, the field of sensing

 is  divided into  smaller  subregions using  the  concept of  divide-and-conquer method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage Optimization is applied in each  subregion to optimize the coverage and lifetime performances. In a subregion,  our protocol  consists in  electing a  leader node, which will then perform a sensor activity scheduling. The challenges include how to  select the most efficient leader in each  subregion and  the  best representative set of active nodes to ensure a high level of coverage. To assess the performance of our approach, we  compared it with two other approaches using many performance metrics  like coverage ratio or network  lifetime. We have also studied the  impact of the  number of subregions  chosen to subdivide the  area of interest, considering  different  network  sizes. The  experiments  show  that increasing the  number of subregions improves  the lifetime. The  more subregions there are, the  more robust the network is against random disconnection resulting from dead nodes.  However, for  a given sensing field and network size there is an optimal number of  subregions. Therefore, in case of our simulation context  a subdivision in  $16$~subregions seems to be the most relevant.
 
 
 is  divided into  smaller  subregions using  the  concept of  divide-and-conquer method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage Optimization is applied in each  subregion to optimize the coverage and lifetime performances. In a subregion,  our protocol  consists in  electing a  leader node, which will then perform a sensor activity scheduling. The challenges include how to  select the most efficient leader in each  subregion and  the  best representative set of active nodes to ensure a high level of coverage. To assess the performance of our approach, we  compared it with two other approaches using many performance metrics  like coverage ratio or network  lifetime. We have also studied the  impact of the  number of subregions  chosen to subdivide the  area of interest, considering  different  network  sizes. The  experiments  show  that increasing the  number of subregions improves  the lifetime. The  more subregions there are, the  more robust the network is against random disconnection resulting from dead nodes.  However, for  a given sensing field and network size there is an optimal number of  subregions. Therefore, in case of our simulation context  a subdivision in  $16$~subregions seems to be the most relevant.
 
 

diff --git a/CHAPITRE_05.tex b/CHAPITRE_05.tex
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@@ -246,7 +246,7 @@ range.
 
 Our protocol  is declined into four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5, and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of rounds in one sensing period).  In  the following, we will make comparisons with two other methods. DESK \cite{DESK} and GAF~\cite{GAF}.
 %Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions  which subdivides  the  sensing field,  considering different  network sizes. They show that as the number of subregions increases, so does the network lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random network  disconnection due  to node  failures.  However,  too  many subdivisions reduce the advantage  of the optimization. In fact, there  is a balance between the  benefit  from the  optimization  and the  execution  time  needed to  solve it. Therefore, 
 
 Our protocol  is declined into four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5, and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of rounds in one sensing period).  In  the following, we will make comparisons with two other methods. DESK \cite{DESK} and GAF~\cite{GAF}.
 %Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions  which subdivides  the  sensing field,  considering different  network sizes. They show that as the number of subregions increases, so does the network lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random network  disconnection due  to node  failures.  However,  too  many subdivisions reduce the advantage  of the optimization. In fact, there  is a balance between the  benefit  from the  optimization  and the  execution  time  needed to  solve it. Therefore, 

-we set the number of subregions to 16 rather than 32 as explained in chapter 4, section ref{ch4:sec:04:05}. We use the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, the energy consumption model is presented in chapter 4, section \ref{ch4:sec:04:03}. 
+We set the number of subregions to 16 rather than 32 as explained in chapter 4, section \ref{ch4:sec:04:05}. We use the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, the energy consumption model is presented in chapter 4, section \ref{ch4:sec:04:03}. 

 
 \subsection{Metrics}
 \label{ch5:sec:04:02}
 
 \subsection{Metrics}
 \label{ch5:sec:04:02}

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diff --git a/INTRODUCTION.tex b/INTRODUCTION.tex
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diff --git a/Resume.tex b/Resume.tex
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diff --git a/Thesis.toc b/Thesis.toc
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@@ -69,10 +69,10 @@
 \contentsline {subsection}{\numberline {4.4.1}Simulation Framework}{80}{subsection.4.4.1}
 \contentsline {subsection}{\numberline {4.4.2}Modeling Language and Optimization Solver}{80}{subsection.4.4.2}
 \contentsline {subsection}{\numberline {4.4.3}Energy Consumption Model}{81}{subsection.4.4.3}
 \contentsline {subsection}{\numberline {4.4.1}Simulation Framework}{80}{subsection.4.4.1}
 \contentsline {subsection}{\numberline {4.4.2}Modeling Language and Optimization Solver}{80}{subsection.4.4.2}
 \contentsline {subsection}{\numberline {4.4.3}Energy Consumption Model}{81}{subsection.4.4.3}

-\contentsline {subsection}{\numberline {4.4.4}Performance Metrics}{82}{subsection.4.4.4}
+\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 {4.4.5}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}{88}{subsection.4.4.6}
-\contentsline {subsection}{\numberline {4.4.7}Performance Comparison with other Approaches}{95}{subsection.4.4.7}
+\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 {chapter}{\numberline {5}Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}{101}{chapter.5}
 \contentsline {section}{\numberline {5.1}Introduction}{101}{section.5.1}
 \contentsline {section}{\numberline {4.5}Conclusion}{100}{section.4.5}
 \contentsline {chapter}{\numberline {5}Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}{101}{chapter.5}
 \contentsline {section}{\numberline {5.1}Introduction}{101}{section.5.1}

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