Update by Ali

[ThesisAli.git] / CHAPITRE_04.tex

diff --git a/CHAPITRE_04.tex b/CHAPITRE_04.tex
index ac6a480911152917f7f499aea3b06127f677f216..b715471594b22a1e36eec99fd960206df1299d55 100755 (executable)
--- a/CHAPITRE_04.tex
+++ b/CHAPITRE_04.tex
@@ -30,21 +30,15 @@ prolong the network lifetime and improve the coverage performance effectively.
 \section{Description of the DiLCO Protocol}
 \label{ch4:sec:02}
 
 \section{Description of the DiLCO Protocol}
 \label{ch4:sec:02}
 

-\noindent In this section, we introduce the DiLCO protocol which is distributed on  each subregion  in  the area  of interest.   It  is based  on two  efficient
-techniques: network leader election and sensor activity scheduling for coverage preservation  and  energy  conservation,  applied  periodically  to  efficiently
-maximize the lifetime in the network.
+\noindent In this section, we introduce the DiLCO protocol which is distributed on  each subregion in the area of interest. It is based  on two  efficient
+techniques: network leader election and sensor activity scheduling for coverage preservation and  energy conservation, applied periodically to efficiently maximize the lifetime in the network.

 
 \subsection{Assumptions and Network Model}
 \label{ch4:sec:02:01}
 
 \subsection{Assumptions and Network Model}
 \label{ch4:sec:02:01}

-\noindent  We consider  a sensor  network composed  of static  nodes distributed independently and uniformly at random.  A high density deployment ensures a high
-coverage ratio of the interested area at the start. The nodes are supposed to have homogeneous characteristics from a communication and a processing point of
-view, whereas they  have heterogeneous energy provisions.  Each  node has access to its location thanks,  either to a hardware component (like a  GPS unit), or a
-location discovery algorithm. Furthermore, we assume that sensor nodes are time synchronized in order to properly coordinate their operations to achieve complex sensing tasks~\cite{ref157}. The two sensor nodes have been supposed a neighbors if the euclidean distance between them is at most equal to 2$R_s$. 
+\noindent  We consider a sensor  network composed  of static  nodes distributed independently and uniformly at random.  A high-density deployment ensures a high coverage ratio of the interested area at the start. The nodes are supposed to have homogeneous characteristics from a communication and a processing point of view, whereas they  have heterogeneous energy provisions.  Each  node has access to its location thanks,  either to a hardware component (like a  GPS unit) or a location discovery algorithm. Furthermore, we assume that sensor nodes are time synchronized in order to properly coordinate their operations to achieve complex sensing tasks~\cite{ref157}. The two sensor nodes have been supposed neighbors if the euclidean distance between them is at most equal to 2$R_s$. 

  
 
  
 

-\indent We consider a boolean disk coverage model which is the most widely used sensor coverage  model in the  literature. Thus, since  a sensor has  a constant
-sensing range $R_s$, every space points  within a disk centered at a sensor with the radius of  the sensing range is said  to be covered by this  sensor. We also
-assume  that  the communication  range $R_c$ is at least twice the sensing range $R_s$ (i.e., $R_c \geq  2R_s$). In  fact, Zhang and Hou~\cite{ref126} proved  that if the transmission range  fulfills the previous hypothesis, a complete coverage of  a convex area implies connectivity among the working nodes in the active mode. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) is flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station.
+\indent We consider a boolean disk coverage model which is the most widely used sensor coverage  model in the  literature. Thus, since  a sensor has a constant sensing range $R_s$, every space points within a disk centered at a sensor with the radius of the sensing range is said to be covered with this sensor. We also assume  that  the communication  range $R_c$ is at least twice the sensing range $R_s$ (i.e., $R_c \geq  2R_s$). In  fact, Zhang and Hou~\cite{ref126} proved  that if the transmission range  fulfills the previous hypothesis, a complete coverage of  a convex area implies connectivity among the working nodes in the active mode. We assume that each sensor node can directly transmit its measurements toward a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) is flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station.

 
 During the execution of the DiLCO protocol, two kinds of packet will be used:
 
 
 During the execution of the DiLCO protocol, two kinds of packet will be used:
 


@@ -65,19 +59,12 @@ There are five possible status for each sensor node in the network:
 
 \subsection{Primary Point Coverage Model}
 \label{ch4:sec:02:02}
 
 \subsection{Primary Point Coverage Model}
 \label{ch4:sec:02:02}

-\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 its $R_s$,  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.
+\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. 

 
 \indent  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:\\
 
 \indent  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:\\

+

 $(p_x,p_y)$ = point center of wireless sensor node\\  
 $X_1=(p_x,p_y)$ \\ 
 $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\           
 $(p_x,p_y)$ = point center of wireless sensor node\\  
 $X_1=(p_x,p_y)$ \\ 
 $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\           


@@ -125,32 +112,19 @@ $X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $.
 
 \subsection{Main Idea}
 \label{ch4:sec:02:03}
 
 \subsection{Main Idea}
 \label{ch4:sec:02:03}

-\noindent We start  by applying a divide-and-conquer algorithm  to partition the
-area of interest  into smaller areas called subregions and  then our protocol is
-executed   simultaneously  in   each   subregion.
+\noindent We start by applying a divide-and-conquer algorithm  to partition the area of interest  into smaller areas called subregions and  then our protocol is executed simultaneously in each subregion.

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

-\includegraphics[scale=0.60]{Figures/ch4/FirstModel.pdf} % 70mm
+\includegraphics[scale=0.80]{Figures/ch4/FirstModel.pdf} % 70mm

 \caption{DiLCO protocol}
 \label{FirstModel}
 \end{figure} 
 
 \caption{DiLCO protocol}
 \label{FirstModel}
 \end{figure} 
 

-As shown in Figure~\ref{FirstModel}, the  proposed DiLCO protocol is a periodic
-protocol where  each period is  decomposed into 4~phases:  Information Exchange,
-Leader Election,  Decision, and Sensing. For  each period there  will be exactly
-one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
-interesting  because it  enhances the  robustness  of the  network against  node
-failures. First,  a node  that has not  enough energy  to complete a  period, or
-which fails before  the decision is taken, will be  excluded from the scheduling
-process. Second,  if a node  fails later, whereas  it was supposed to  sense the
-region of  interest, it will only affect  the quality of the  coverage until the
-definition of  a new  cover set  in the next  period.  Constraints,  like energy
-consumption, can be easily taken into consideration since the sensors can update
-and exchange their  information during the first phase.  Let  us notice that the
-phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
-Decision) are  energy consuming for all the  nodes, even nodes that  will not be
-retained by the leader to keep watch over the corresponding area.
+As shown in Figure~\ref{FirstModel}, the  proposed DiLCO protocol is a periodic protocol where  each period is  decomposed into 4~phases:  Information Exchange, Leader Election,  Decision, and Sensing. For  each period, there  will be exactly one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is interesting  because it  enhances the  robustness  of the  network against  node failures. First,  a node  that has not  enough energy  to complete a  period, or which fails before  the decision is taken, will be  excluded from the scheduling
+process. Second,  if a node  fails later, whereas  it was supposed to sense the region of  interest, it will only affect  the quality of the  coverage until the definition of  a new  cover set  in the next  period.  Constraints,  like energy consumption, can be easily taken into consideration since the sensors can update and exchange their  information during the first phase.  Let  us notice that the
+phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and Decision) are  energy consuming for all the  nodes, even nodes that  will not be retained by the leader to keep watch over the corresponding area.
+

 
 Below, we describe each phase in more details.
 
 
 Below, we describe each phase in more details.
 


@@ -166,7 +140,7 @@ corresponds to the time that a sensor can live in the active mode.
 
 \subsubsection{Leader Election Phase}
 \label{ch4:sec:02:03:02}
 
 \subsubsection{Leader Election Phase}
 \label{ch4:sec:02:03:02}

-This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL), which  will  be  responsible  for executing  the coverage  algorithm. Each subregion in the area of interest  will select its  own  WSNL independently  for each  round.  All the  sensor  nodes cooperate  to select WSNL. The nodes in the  same subregion will  select the leader based on  the received  information from all  other nodes in  the same subregion.  The selection  criteria are,  in order  of importance: larger  number  of neighbors,  larger  remaining energy,  and  then  in case  of equality, larger index. Observations on  previous simulations suggest to use the number  of  one-hop  neighbors  as   the  primary  criterion  to  reduce  energy consumption due to the communications.  
+This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL), which  will  be  responsible  for executing  the coverage  algorithm. Each subregion in the area of interest  will select its  own  WSNL independently  for each  round.  All the  sensor  nodes cooperate  to select WSNL. The nodes in the  same subregion will  select the leader based on  the received  information from all  other nodes in  the same subregion.  The selection  criteria are,  in order  of importance: larger  number  of neighbors,  larger  remaining energy,  and  then  in case  of equality, larger index. Observations on  previous simulations suggest using the number  of  one-hop  neighbors  as   the  primary  criterion  to  reduce  energy consumption due to the communications.  

 
 
 \subsubsection{Decision phase}
 
 
 \subsubsection{Decision phase}


@@ -184,23 +158,8 @@ will receive  an Active-Sleep  packet from WSNL  informing it  to stay
 awake or to go to sleep  for a time  equal to  the period of  sensing until
 starting a new round.
 
 awake or to go to sleep  for a time  equal to  the period of  sensing until
 starting a new round.
 

-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  $j$). At  the beginning  a node  checks whether  it has
-enough energy to stay active during the next sensing phase. 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.
-
+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. 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!]                
 
 
 \begin{algorithm}[h!]                
 


@@ -388,9 +347,9 @@ The modeling  language for Mathematical Programming (AMPL)~\cite{AMPL} is  emplo
 \subsection{Energy Consumption Model}
 \label{ch4:sec:04:03}
 
 \subsection{Energy Consumption Model}
 \label{ch4:sec:04:03}
 

-\indent In this dissertation, we used an energy consumption model proposed by~\cite{ref111} and based on \cite{ref112} with slight  modifications.  The energy consumption for  sending/receiving the packets is added, whereas the  part related to the sensing range is removed because we consider a fixed sensing range.
+\indent In this dissertation, we used an energy consumption model proposed by~\cite{DESK} and based on \cite{ref112} with slight  modifications.  The energy consumption for  sending/receiving the packets is added, whereas the  part related to the sensing range is removed because we consider a fixed sensing range.

 
 

-\indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmels  AVR ATmega103L microcontroller~\cite{ref112}. The typical architecture  of a  sensor  is composed  of four  subsystems: the  MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible  for transmitting/receiving messages, the  sensing subsystem that collects  data, and  the  power supply  which  powers the  complete sensor  node \cite{ref112}. Each  of the first three subsystems  can be turned on or  off depending on  the current status  of the sensor.   Energy consumption (expressed in  milliWatt per second) for  the different status of  the sensor is summarized in Table~\ref{table1}.
+\indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmel's  AVR ATmega103L microcontroller~\cite{ref112}. The typical architecture  of a  sensor  is composed  of four  subsystems: the  MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible  for transmitting/receiving messages, the  sensing subsystem that collects  data, and  the  power supply  which  powers the  complete sensor  node \cite{ref112}. Each  of the first three subsystems  can be turned on or  off depending on  the current status  of the sensor.   Energy consumption (expressed in  milliWatt per second) for  the different status of  the sensor is summarized in Table~\ref{table1}.

 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}
 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}


@@ -426,7 +385,7 @@ COMPUTATION & on & on & on & 26.83 \\
 
 %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}. 
 

-The initial energy of each node  is randomly set in the interval $[500;700]$.  A sensor node  will not participate in the  next round if its  remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  active state (9.72 mW) by the time in second  for one round (3600 seconds), and  adding  the energy  for  the pre-sensing  phases. According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.
+The initial energy of each node  is randomly set in the interval $[500;700]$.  A sensor node  will not participate in the  next round if its  remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  the active state (9.72 mW) by the time in second  for one round (3600 seconds), and  adding  the energy  for  the pre-sensing  phases. According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.

 
 
 \subsection{Performance Metrics}
 
 
 \subsection{Performance Metrics}


@@ -469,16 +428,8 @@ points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
       + E^{a}_m+E^{s}_m \right)}{M},
   \end{equation*}
 
       + E^{a}_m+E^{s}_m \right)}{M},
   \end{equation*}
 

-where $M$  corresponds to  the number  of periods.  The  total amount  of energy
-consumed by the  sensors (EC) comes through taking  into consideration four main
-energy   factors.  The  first   one,  denoted   $E^{\scriptsize  \mbox{com}}_m$,
-represents  the  energy  consumption  spent   by  all  the  nodes  for  wireless
-communications  during period  $m$.  $E^{\scriptsize  \mbox{list}}_m$,  the next
-factor, corresponds  to the energy consumed  by the sensors  in LISTENING status
-before  receiving   the  decision  to  go   active  or  sleep   in  period  $m$.
-$E^{\scriptsize \mbox{comp}}_m$  refers to the  energy needed by all  the leader
-nodes  to solve the  integer program  during a  period.  Finally,  $E^a_{m}$ and
-$E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase
+where $M$  corresponds to  the number  of periods.  The  total amount  of energy consumed by the  sensors (EC) comes through taking  into consideration four main energy   factors.  The  first   one,  denoted   $E^{\scriptsize  \mbox{com}}_m$, represents  the  energy consumption  spent   by  all  the  nodes  for  wireless communications  during the period  $m$.  $E^{\scriptsize  \mbox{list}}_m$,  the next
+factor, corresponds  to the energy consumed  by the sensors  in LISTENING status before  receiving the  decision  to  go   active  or  sleep   in  the period  $m$. $E^{\scriptsize \mbox{comp}}_m$  refers to the  energy needed for all  the leader nodes  to solve the  integer program  during a  period.  Finally,  $E^a_{m}$ and $E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase

 (active and sleeping nodes).
 
 \item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
 (active and sleeping nodes).
 
 \item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,


@@ -490,7 +441,7 @@ network lifetime. The Active Sensors Ratio is defined as follows:
 \end{equation*}
 Where: $A_r$ is the number of active sensors in the subregion $r$ during current period, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
 
 \end{equation*}
 Where: $A_r$ is the number of active sensors in the subregion $r$ during current period, $S$ is the total number of sensors in the network, and $R$ is the total number of the 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 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   $\left( \frac{35330}{2} \times  \frac{1}{6} \right)$.  
+\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 3, 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 3, period consists of one round).
 


@@ -502,7 +453,7 @@ Where: $A_r$ is the number of active sensors in the subregion $r$ during current
 \label{ch4:sec:04:05}
   
 In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).
 \label{ch4:sec:04:05}
   
 In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).

-The DiLCO-1 protocol is a centralized approach on 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 did not take the DiLCO-1 protocol in our simulation results because it need high execution time to give the decision leading to consume all it's energy before producing the solution for optimization problem.
+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 did 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.

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


@@ -512,31 +463,32 @@ In this experiment, Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ra
 \parskip 0pt    
 \begin{figure}[h!]
 \centering
 \parskip 0pt    
 \begin{figure}[h!]
 \centering

- \includegraphics[scale=0.6] {Figures/ch4/R1/CR.pdf} 
+ \includegraphics[scale=0.8] {Figures/ch4/R1/CR.pdf} 

 \caption{Coverage ratio for 150 deployed nodes}
 \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 $18^{th}$ because it consumes more energy with the effect of the network disconnection. 
 \caption{Coverage ratio for 150 deployed nodes}
 \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 $18^{th}$ because it consumes more energy with the effect of the network disconnection. 

-As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases,  the coverage preservation for 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.
 \begin{figure}[h!]
 \centering
 
 \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.
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R1/ASR.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R1/ASR.pdf}  

 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R1/ASR}
 \end{figure} 
 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R1/ASR}
 \end{figure} 

-The results presented in figure~\ref{Figures/ch4/R1/ASR} show the increase in the number of subregions led to increase in 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 in the number of subregions led to increasing in 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
 
 \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

-\includegraphics[scale=0.6]{Figures/ch4/R1/SR.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R1/SR.pdf} 

 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R1/SR}
 \end{figure} 
 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R1/SR}
 \end{figure} 


@@ -550,17 +502,17 @@ We measure the energy consumed by the sensors during the communication, listenin
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R1/EC95.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf} 

 \caption{Energy Consumption for Lifetime95}
 \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 but as the network size increase the energy consumption increase compared with DiLCO-2,  DiLCO-4, and DiLCO-8. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.\\
  
 \caption{Energy Consumption for Lifetime95}
 \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 but as the network size increase the energy consumption increase compared with DiLCO-2,  DiLCO-4, and DiLCO-8. 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 time computation to solve the optimization problem, as well as the higher energy consumed during the communication.  

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

-\includegraphics[scale=0.6]{Figures/ch4/R1/EC50.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf} 

 \caption{Energy Consumption for Lifetime50}
 \label{Figures/ch4/R1/EC50}
 \end{figure} 
 \caption{Energy Consumption for Lifetime50}
 \label{Figures/ch4/R1/EC50}
 \end{figure} 


@@ -573,14 +525,14 @@ In this experiment, the execution time of the our distributed optimization appro
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R1/T.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R1/T.pdf}  

 \caption{Execution Time (in seconds)}
 \label{Figures/ch4/R1/T}
 \end{figure} 
 
 \caption{Execution Time (in seconds)}
 \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 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 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.

 
 

-The DiLCO-32 protocol has more suitable times at the same time it turn on redundant nodes more.  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.
+The DiLCO-32 protocol has more suitable times at the same time it turns on redundant nodes more.  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}
 
 \item {{\bf The Network Lifetime}}
 %\subsubsection{The Network Lifetime}


@@ -588,19 +540,20 @@ In figure~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, network lifet
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R1/LT95.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}  

 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R1/LT95}
 \end{figure} 
 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R1/LT95}
 \end{figure} 

-We see that DiLCO-2 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumed during the communication seems to be huge because it is distributed over only two subregions.
+We see that DiLCO-2 protocol results in execution times that quickly become unsuitable for a sensor network, as well as 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, with DiLCO-16 protocol that leads to the larger lifetime improvement. By choosing the best suited nodes, for each round, to cover the area of interest and by
-letting the other ones sleep in order to be used later in next rounds, 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 subregion. 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, with DiLCO-16 protocol that leads to the larger lifetime improvement. By choosing the best-suited nodes, for each round, to cover the area of interest and by
+letting the other ones sleep in order to be used later in next rounds, 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. 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 is used 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 the most 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 is used 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 the most relevant way to maximize the lifetime of a network.

+

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

-\includegraphics[scale=0.6]{Figures/ch4/R1/LT50.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}  

 \caption{Network Lifetime for $Lifetime50$}
 \label{Figures/ch4/R1/LT50}
 \end{figure} 
 \caption{Network Lifetime for $Lifetime50$}
 \label{Figures/ch4/R1/LT50}
 \end{figure} 


@@ -623,10 +576,11 @@ In this experiment, we Figure~\ref{Figures/ch4/R2/CR} shows the average coverage
 \parskip 0pt    
 \begin{figure}[h!]
 \centering
 \parskip 0pt    
 \begin{figure}[h!]
 \centering

- \includegraphics[scale=0.6] {Figures/ch4/R2/CR.pdf} 
+ \includegraphics[scale=0.8] {Figures/ch4/R2/CR.pdf} 

 \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 very small superiority for the models with higher number of primary points. Moreover, when the number of rounds increases, coverage ratio produced by Model~3, Model~4, and Model~5 decreases in comparison with Model~1 and Model~2 due to the high energy consumption during the listening to take the decision after finishing optimization 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. Although  some nodes are dead,
 thanks to  Model~2, which 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.
 
 It is shown that all models provide a very near coverage ratios during the network lifetime, with very small superiority for the models with higher number of primary points. Moreover, when the number of rounds increases, coverage ratio produced by Model~3, Model~4, and Model~5 decreases in comparison with Model~1 and Model~2 due to the high energy consumption during the listening to take the decision after finishing optimization 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. Although  some nodes are dead,
 thanks to  Model~2, which 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.
 


@@ -635,13 +589,12 @@ thanks to  Model~2, which is slightly more efficient than other Models, because
  Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes.
 \begin{figure}[h!]
 \centering
  Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes.
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R2/ASR.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R2/ASR.pdf}  

 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R2/ASR}
 \end{figure} 
 
 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R2/ASR}
 \end{figure} 
 

-The results presented in figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed  Model 1, in comparison with the other Models. The
-model with less number of primary points uses less active nodes than the other models, which uses a more number of primary points to represent the area of the sensor. According to the results that presented in figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model~1 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model~2 approach is to use less number of active nodes for each round compared with Model~3,  Model~4, and Model~5; and this led to continue for a larger number of rounds with extending the network lifetime. Model~2 has a better coverage ratio compared to Model~1 and acceptable number of rounds.
+The results presented in figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed  Model 1, in comparison with the other Models. The model with fewer number of primary points uses fewer active nodes than the other models, which uses larger number of primary points to represent the area of the sensor. According to the results that presented in figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model~1 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model~2 approach is to use fewer number of active nodes for each round compared with Model~3,  Model~4, and Model~5. This led to continuing for a larger number of rounds with extending the network lifetime. Model~2 has a better coverage ratio compared to Model~1 and acceptable number of rounds.

 
 
 \item {{\bf he percentage of stopped simulation runs}}
 
 
 \item {{\bf he percentage of stopped simulation runs}}


@@ -650,12 +603,12 @@ In this study, we want to show the effect of increasing the primary points on th
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R2/SR.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R2/SR.pdf} 

 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R2/SR}
 \end{figure} 
 
 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R2/SR}
 \end{figure} 
 

-As shown in Figure~\ref{Figures/ch4/R2/SR}, when the number of primary points are 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 increases. We are observed that the Model~1 is a 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.
+As shown in Figure~\ref{Figures/ch4/R2/SR}, 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. We are observed that the Model~1 is a 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}}
 
 
 \item {{\bf The Energy Consumption}}


@@ -663,19 +616,19 @@ As shown in Figure~\ref{Figures/ch4/R2/SR}, when the number of primary points ar
 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
 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

-\includegraphics[scale=0.6]{Figures/ch4/R2/EC95.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf} 

 \caption{Energy Consumption with $95\%-Lifetime$}
 \label{Figures/ch4/R2/EC95}
 \end{figure} 
  
 \begin{figure}[h!]
 \centering
 \caption{Energy Consumption with $95\%-Lifetime$}
 \label{Figures/ch4/R2/EC95}
 \end{figure} 
  
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R2/EC50.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf} 

 \caption{Energy Consumption with $Lifetime50$}
 \label{Figures/ch4/R2/EC50}
 \end{figure} 
 
 \caption{Energy Consumption with $Lifetime50$}
 \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 optimization process will takes more time leads to consume more energy during the listening mode. The results show that Model~1 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, we see that Model~2 is a good candidate to be used by wireless sensor network because it preserve a good coverage ratio and 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~1 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, we see that Model~2 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}


@@ -683,12 +636,12 @@ In this experiment, we have studied the impact of the increase in primary points
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R2/T.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R2/T.pdf}  

 \caption{Execution Time(s) vs The Number of Sensors }
 \label{Figures/ch4/R2/T}
 \end{figure} 
 
 \caption{Execution Time(s) vs The Number of Sensors }
 \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~1 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.
+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~1 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~2 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.
 
 \item {{\bf The Network Lifetime}}
 Moreover, Model~2 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.
 
 \item {{\bf The Network Lifetime}}


@@ -697,7 +650,7 @@ Finally, we will study the effect of increasing the primary points on the lifeti
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R2/LT95.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf}  

 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R2/LT95}
 \end{figure} 
 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R2/LT95}
 \end{figure} 


@@ -705,7 +658,7 @@ Finally, we will study the effect of increasing the primary points on the lifeti
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R2/LT50.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf}  

 \caption{Network Lifetime for $Lifetime50$}
 \label{Figures/ch4/R2/LT50}
 \end{figure} 
 \caption{Network Lifetime for $Lifetime50$}
 \label{Figures/ch4/R2/LT50}
 \end{figure} 


@@ -718,7 +671,7 @@ Comparison shows that the Model~1, which uses less number of primary points, is
 
 \subsection{Performance Comparison with other Approaches}
 \label{ch4:sec:04:07}
 
 \subsection{Performance Comparison with other Approaches}
 \label{ch4:sec:04:07}

-Based on the results, which are conducted from previous two subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are the best candidates to be compared with other two approaches. The first approach, called DESK that proposed by ~\cite{DESK}, which is a full 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, which are conducted from previous two subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are 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 is 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)]
 
 
 \begin{enumerate}[i)]
 


@@ -729,7 +682,7 @@ In this experiment, the average coverage ratio for 150 deployed nodes has been d
 \parskip 0pt    
 \begin{figure}[h!]
 \centering
 \parskip 0pt    
 \begin{figure}[h!]
 \centering

- \includegraphics[scale=0.6] {Figures/ch4/R3/CR.pdf} 
+ \includegraphics[scale=0.8] {Figures/ch4/R3/CR.pdf} 

 \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} 


@@ -744,7 +697,7 @@ 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=0.6]{Figures/ch4/R3/ASR.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R3/ASR.pdf}  

 \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} 


@@ -759,7 +712,7 @@ Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation
 runs per round for 150 deployed nodes. 
 \begin{figure}[h!]
 \centering
 runs per round for 150 deployed nodes. 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R3/SR.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R3/SR.pdf} 

 \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} 


@@ -772,14 +725,14 @@ In this experiment, we have studied the effect of the energy consumed by the wir
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R3/EC95.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R3/EC95.pdf} 

 \caption{Energy Consumption with $95\%-Lifetime$}
 \label{Figures/ch4/R3/EC95}
 \end{figure} 
 
 \begin{figure}[h!]
 \centering
 \caption{Energy Consumption with $95\%-Lifetime$}
 \label{Figures/ch4/R3/EC95}
 \end{figure} 
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R3/EC50.pdf} 
+\includegraphics[scale=0.8]{Figures/ch4/R3/EC50.pdf} 

 \caption{Energy Consumption with $Lifetime50$}
 \label{Figures/ch4/R3/EC50}
 \end{figure} 
 \caption{Energy Consumption with $Lifetime50$}
 \label{Figures/ch4/R3/EC50}
 \end{figure} 


@@ -793,7 +746,7 @@ In this experiment, we have observed the superiority of DiLCO-16 protocol and Di
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R3/LT95.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R3/LT95.pdf}  

 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R3/LT95}
 \end{figure}
 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R3/LT95}
 \end{figure}


@@ -801,7 +754,7 @@ In this experiment, we have observed the superiority of DiLCO-16 protocol and Di
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch4/R3/LT50.pdf}  
+\includegraphics[scale=0.8]{Figures/ch4/R3/LT50.pdf}  

 \caption{Network Lifetime for $Lifetime50$}
 \label{Figures/ch4/R3/LT50}
 \end{figure} 
 \caption{Network Lifetime for $Lifetime50$}
 \label{Figures/ch4/R3/LT50}
 \end{figure}