X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/ThesisAli.git/blobdiff_plain/00e1a4c411c07d09489772c40f87682af1425f48..9b7796a5f0b1031f41f762d6d46eb69475bb764c:/CHAPITRE_04.tex?ds=sidebyside

diff --git a/CHAPITRE_04.tex b/CHAPITRE_04.tex
index ce90fb0..52d2916 100644
--- a/CHAPITRE_04.tex
+++ b/CHAPITRE_04.tex
@@ -60,7 +60,7 @@ There are five possible status for each sensor node in the network:
 \indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points. We also assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered. By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless sensor node  and it's $R_s$,  we calculate the primary  points directly based on the proposed model. We  use these primary points (that can be increased or decreased if necessary)  as references to ensure that the monitored  region  of interest  is  covered by the selected  set  of sensors, instead of using all the points in the area. 
 We can  calculate  the positions of the selected primary
 points in the circle disk of the sensing range of a wireless sensor
-node (see figure~\ref{fig1}) as follows:\\
+node (see Figure~\ref{fig1}) as follows:\\
 
 $(p_x,p_y)$ = point center of wireless sensor node\\  
 $X_1=(p_x,p_y)$ \\ 
@@ -458,6 +458,7 @@ The DiLCO-1 protocol is a centralized approach to all the area of the interest,
 \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.  
 \parskip 0pt    
 \begin{figure}[h!]
@@ -468,11 +469,12 @@ In this experiment, Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ra
 \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.
+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.
 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 
- Figure~\ref{Figures/ch4/R1/ASR} shows the average active nodes ratio for 150 deployed nodes.
+
+Figure~\ref{Figures/ch4/R1/ASR} shows the average active nodes ratio for 150 deployed nodes.
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/ASR.pdf}  
@@ -480,10 +482,11 @@ As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions inc
 \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 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.
 
 \item {{\bf The percentage of 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. 
 \begin{figure}[h!]
 \centering
@@ -497,6 +500,7 @@ Thus, as explained previously, in case of the DiLCO-16 and DiLCO-32 with several
 
 \item {{\bf 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 $Lifetime50$. 
 
 \begin{figure}[h!]
@@ -519,6 +523,7 @@ In fact,  the distribution of the computation over many subregions greatly reduc
 
 \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.
 
@@ -529,13 +534,14 @@ In this experiment, the execution time of the our distributed optimization appro
 \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 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}}
 %\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, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes. 
 
 \begin{figure}[h!]
 \centering
@@ -561,15 +567,14 @@ 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}
 
-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 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). 
 
 
 \begin{enumerate}[i)]
 
 \item {{\bf Coverage Ratio}}
 %\subsubsection{Coverage Ratio} 
+
 Figure~\ref{Figures/ch4/R2/CR} shows the average coverage ratio for 150 deployed nodes.  
 \parskip 0pt    
 \begin{figure}[h!]
@@ -580,10 +585,11 @@ Figure~\ref{Figures/ch4/R2/CR} shows the average coverage ratio for 150 deployed
 \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 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.
 
 \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.
 \begin{figure}[h!]
 \centering
@@ -592,11 +598,12 @@ As shown in figure ~\ref{Figures/ch4/R2/CR}, Coverage ratio decreases when the n
 \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 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.
 
 
 \item {{\bf The percentage of 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. 
 
 \begin{figure}[h!]
@@ -606,11 +613,12 @@ Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation
 \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 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. \\
 
 
 \item {{\bf 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 $Lifetime50$.
 \begin{figure}[h!]
 \centering
@@ -626,11 +634,12 @@ In this experiment, we study the effect of increasing the primary points to repr
 \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 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. 
 
 \item {{\bf Execution Time}}
 %\subsubsection{Execution Time}
-In this experiment, we have studied 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:04:02}. 
+
+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}. 
 
 \begin{figure}[h!]
 \centering
@@ -644,6 +653,7 @@ Moreover, Model-9 has more suitable times and coverage ratio that lead to contin
 
 \item {{\bf 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. 
 
 \begin{figure}[h!]
@@ -669,12 +679,13 @@ Comparison shows that the Model-5, which uses less number of primary points, is
 
 \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. 
 
-\begin{enumerate}[i)]
+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. \\ \\
 
+\begin{enumerate}[i)]
 \item {{\bf Coverage Ratio}}
 %\subsubsection{Coverage Ratio} 
+
 The average coverage ratio for 150 deployed nodes is demonstrated in Figure~\ref{Figures/ch4/R3/CR}. 
  
 \parskip 0pt    
@@ -685,12 +696,14 @@ The average coverage ratio for 150 deployed nodes is demonstrated in Figure~\ref
 \label{Figures/ch4/R3/CR}
 \end{figure} 
 
-It has been shown that 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 nodes are active in the case of DESK and GAF.
+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.
 
-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 optimized 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. 
+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.
+%, 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}}
 %\subsubsection{Active Sensors Ratio} 
+
 It is important to have as few active nodes as possible in each round, in  order to  minimize the energy consumption and maximize the network lifetime. Figure~\ref{Figures/ch4/R3/ASR} shows the average active nodes ratio for 150 deployed nodes. 
 
 \begin{figure}[h!]
@@ -700,12 +713,13 @@ It is important to have as few active nodes as possible in each round, in  order
 \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.  We have observed that 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 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. \\
 
 
 \item {{\bf The percentage of 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.
+%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
@@ -713,12 +727,15 @@ Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation
 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R3/SR}
 \end{figure} 
-It has been observed that 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 it distributed 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.
+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.
 
 
 \item {{\bf The 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. Figures~\ref{Figures/ch4/R3/EC95} and ~\ref{Figures/ch4/R3/EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$. 
+%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 $Lifetime50$. 
 
 \begin{figure}[h!]
 \centering
@@ -734,12 +751,16 @@ In this experiment, we have studied the effect of the energy consumed by the wir
 \label{Figures/ch4/R3/EC50}
 \end{figure} 
 
-The results show that 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,  a distributed method on 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. 
+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. 
 
 
 \item {{\bf 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 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.  
 
 \begin{figure}[h!]
 \centering
@@ -757,8 +778,9 @@ In this experiment, we have observed the superiority of DiLCO-16 protocol and Di
 \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. 
-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 prolonged the network lifetime. 
-Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which are used distributed optimization over the subregions, is the best one because it is robust to network disconnection during the network lifetime as well as it consumes 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.
 
 
 \end{enumerate}
