Michel : Modifications finales

[LiCO.git] / LiCO_Journal.tex

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
index e9d10acce82a5cf96b29f801c3a1c87f8b3f2f83..8f1949b593bd4286643ec246cb8a1c267fcdb806 100644 (file)
--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -333,11 +333,11 @@ arcs.
 \begin{figure}[ht!]
   \centering
   \begin{tabular}{@{}cr@{}}
 \begin{figure}[ht!]
   \centering
   \begin{tabular}{@{}cr@{}}

-    \includegraphics[width=75mm]{pcm.jpg}        &        \raisebox{3.25cm}{(a)}
+    \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)}

     \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
   \end{tabular}
     \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
   \end{tabular}

-  \caption{Perimeter coverage of sensor node 0  (a) and finding the arc of $u$'s
-    perimeter covered by $v$.}
+  \caption{(a) Perimeter  coverage of sensor node  0 and (b) finding  the arc of
+    $u$'s perimeter covered by $v$.}

   \label{pcm2sensors}
 \end{figure} 
 
   \label{pcm2sensors}
 \end{figure} 
 


@@ -549,11 +549,8 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
       }  
   }
   \Else { Exclude $s_k$ from entering in the current sensing stage}
       }  
   }
   \Else { Exclude $s_k$ from entering in the current sensing stage}

-  
- 

 \caption{LiCO($s_k$)}
 \label{alg:LiCO}
 \caption{LiCO($s_k$)}
 \label{alg:LiCO}

-

 \end{algorithm}
 
 In this  algorithm, K.CurrentSize and  K.PreviousSize refer to the  current size
 \end{algorithm}
 
 In this  algorithm, K.CurrentSize and  K.PreviousSize refer to the  current size


@@ -757,110 +754,154 @@ approach.
   energy or if the network is not more connected. This last condition is crucial
   because without  network connectivity a  sensor may not be  able to send  to a
   base station an event it has sensed.
   energy or if the network is not more connected. This last condition is crucial
   because without  network connectivity a  sensor may not be  able to send  to a
   base station an event it has sensed.

-\item {{\bf  Coverage Ratio  (CR)}:} it  measures how  well the  WSN is  able to
+\item {\bf  Coverage Ratio (CR)} : it  measures how  well the  WSN is  able to

   observe the area of interest. In our  case, we discretized the sensor field as
   a regular grid, which yields the following equation:
   \begin{equation*}
     \scriptsize
   observe the area of interest. In our  case, we discretized the sensor field as
   a regular grid, which yields the following equation:
   \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 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 total  number of grid

-  points  in the  sensing field.  In our  simulations we  have set  a layout  of
+  points in  the sensing  field.  In  our simulations  we have  set a  layout of

   $N~=~51~\times~26~=~1326$~grid points.
   $N~=~51~\times~26~=~1326$~grid points.

-
-  % MICHEL TO BE CONTINUED FROM HERE
-
-\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
-in  order to  minimize  the communication  overhead  and maximize  the
-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{$S$}} \times 100 .
-\end{equation*}
-Where: $A_r^t$ is the number of active sensors in the subregion $r$ in the current sensing stage, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
-
- 
-
-\item {{\bf  Energy Consumption}:}  energy consumption (EC)  can be seen  as the
-  total   energy   consumed   by   the   sensors   during   $Lifetime_{95}$   or
-  $Lifetime_{50}$, divided  by the number of periods.  Formally, the computation
-  of EC can be expressed as follows:
+\item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to
+  activate nodes  as few  as possible,  in order  to minimize  the communication
+  overhead and maximize the WSN lifetime. The active sensors ratio is defined as
+  follows:

   \begin{equation*}
     \scriptsize
   \begin{equation*}
     \scriptsize

-    \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m  
-      + E^{a}_m+E^{s}_m \right)}{M},
+    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r|$}}{\mbox{$|S|$}} \times 100

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

-
-where $M$  corresponds to the number  of periods. The total energy consumed by
-the sensors (EC) comes through taking into consideration four main energy factors. The  first one, denoted $E^{\scriptsize  \mbox{com}}_m$, represent 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 (active and sleeping nodes).
-
-
+  where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
+  current sensing period~$p$, $|S|$ is the number of sensors in the network, and
+  $R$ is the number of subregions.
+\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
+  energy  consumed by  the  sensors during  $Lifetime_{95}$ or  $Lifetime_{50}$,
+  divided by  the number of  periods. The value of  EC is computed  according to
+  this formula:
+  \begin{equation*}
+    \scriptsize
+    \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p  
+      + E^{a}_p+E^{s}_p \right)}{P},
+  \end{equation*}
+  where $P$ corresponds  to the number of periods. The  total energy consumed by
+  the  sensors  comes  through  taking   into  consideration  four  main  energy
+  factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
+  energy consumption spent  by all the nodes for  wireless communications during
+  period $p$.  $E^{\scriptsize \mbox{list}}_p$,  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 $p$.  $E^{\scriptsize \mbox{comp}}_p$
+  refers to  the energy  needed by  all the  leader nodes  to solve  the integer
+  program during a period.  Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
+  consumed by the WSN during the sensing phase (active and sleeping nodes).

 \end{itemize}
 %\end{enumerate}
 
 \subsection{Simulation Results}
 \end{itemize}
 %\end{enumerate}
 
 \subsection{Simulation Results}

-In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely 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,  the original execution time on the laptop is multiplied by  2944.2 $\left(\frac{35330}{2} \times  \frac{1}{6} \right)$  so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. 
- 
-We compared LiCO protocol to three other approaches: the first, called DESK and proposed  by ~\cite{ChinhVu}  is a fully distributed  coverage  algorithm;  the second, called GAF  ~\cite{xu2001geography}, 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; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).

 
 

-\subsubsection{\textbf{Coverage Ratio}}
-Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
- 
+In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
+implemented LiCO protocol in  OMNeT++~\cite{varga} simulator.  Besides LiCO, two
+other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for
+comparison purposes.   The simulations were run  on a laptop DELL  with an Intel
+Core~i3~2370~M (2.4~GHz)  processor (2  cores) whose MIPS  (Million Instructions
+Per Second) rate  is equal to 35330. To  be consistent with the use  of a sensor
+node based on  Atmels AVR ATmega103L microcontroller (6~MHz) having  a MIPS rate
+equal to 6,  the original execution time  on the laptop is  multiplied by 2944.2
+$\left(\frac{35330}{2} \times  \frac{1}{6} \right)$.  The modeling  language for
+Mathematical Programming (AMPL)~\cite{AMPL} is  employed to generate the integer
+program instance  in a  standard format, which  is then read  and solved  by the
+optimization solver  GLPK (GNU  linear Programming Kit  available in  the public
+domain) \cite{glpk} through a Branch-and-Bound method.
+
+As said previously, the LiCO is  compared with three other approaches. The first
+one,  called  DESK,  is  a  fully distributed  coverage  algorithm  proposed  by
+\cite{ChinhVu}. The second one,  called GAF~\cite{xu2001geography}, consists in
+dividing  the monitoring  area into  fixed  squares. Then,  during the  decision
+phase, in each square, one sensor is  chosen to remain active during the sensing
+phase. The last  one, the DiLCO protocol~\cite{Idrees2}, is  an improved version
+of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
+LiCO and  DiLCO protocols are  based on the  same framework. In  particular, the
+choice for the simulations of a partitioning in 16~subregions was chosen because
+it corresponds to the configuration producing  the better results for DiLCO. The
+protocols are distinguished  from one another by the formulation  of the integer
+program providing the set of sensors which  have to be activated in each sensing
+phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
+whereas LICO protocol objectif is to reach a desired level of coverage for each
+sensor perimeter. In our experimentations, we chose a level of coverage equal to
+one ($l=1$).
+
+\subsubsection{\bf Coverage Ratio}
+
+Figure~\ref{fig333}  shows the  average coverage  ratio for  200 deployed  nodes
+obtained with the  four protocols. DESK, GAF, and DiLCO  provide a little better
+coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, against 98.76\%
+produced by  LiCO for the  first periods. This  is due to  the fact that  at the
+beginning  DiLCO protocol  puts in  sleep status  more redundant  sensors (which
+slightly decreases the coverage ratio), while the three other protocols activate
+more sensor  nodes. Later, when the  number of periods is  beyond~70, it clearly
+appears that  LiCO provides a better  coverage ratio and keeps  a coverage ratio
+greater  than 50\%  for  longer periods  (15  more compared  to  DiLCO, 40  more
+compared to DESK). The energy saved by  LiCO in the early periods allows later a
+substantial increase of the coverage performance.
+

 \parskip 0pt    
 \begin{figure}[h!]
 \centering
  \includegraphics[scale=0.5] {R/CR.eps} 
 \parskip 0pt    
 \begin{figure}[h!]
 \centering
  \includegraphics[scale=0.5] {R/CR.eps} 

-\caption{The coverage ratio for 200 deployed nodes}
+\caption{Coverage ratio for 200 deployed nodes.}

 \label{fig333}
 \end{figure} 
 
 \label{fig333}
 \end{figure} 
 

-DESK,  GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
-

 %When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
 
 %because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches. 
 
 
 %When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
 
 %because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches. 
 
 

-\subsubsection{\textbf{Active Sensors Ratio}} 
-Having active nodes as few as possible in each period is essential in order to minimize the energy consumption and so maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 200 deployed nodes. 
+\subsubsection{\bf Active Sensors Ratio}
+
+Having the less active sensor nodes in  each period is essential to minimize the
+energy consumption  and so  maximize the network  lifetime.  Figure~\ref{fig444}
+shows the  average active nodes ratio  for 200 deployed nodes.   We observe that
+DESK and  GAF have 30.36  \% and  34.96 \% active  nodes for the  first fourteen
+rounds and  DiLCO and LiCO  protocols compete perfectly  with only 17.92  \% and
+20.16 \% active  nodes during the same  time interval. As the  number of periods
+increases, LiCO protocol  has a lower number of active  nodes in comparison with
+the three other approaches, while keeping a greater coverage ratio as shown in
+figure \ref{fig333}.

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R/ASR.eps}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R/ASR.eps}  

-\caption{The active sensors ratio for 200 deployed nodes }
+\caption{Active sensors ratio for 200 deployed nodes.}

 \label{fig444}
 \end{figure} 
 
 \label{fig444}
 \end{figure} 
 

-We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, LiCO protocol has a lower number of active nodes in comparison with the three other approaches, while keeping of greater coverage ratio as shown in figure \ref{fig333}.
-
-\subsubsection{\textbf{The Energy Consumption}}
-We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it for the four approaches. Figures~\ref{fig3EC95} and \ref{fig3EC50} illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$. 
+\subsubsection{\bf Energy Consumption}
+
+We study the effect of the energy  consumed by the WSN during the communication,
+computation, listening, active, and sleep status for different network densities
+and  compare  it for  the  fours  approaches.  Figures~\ref{fig3EC}(a)  and  (b)
+illustrate  the  energy   consumption  for  different  network   sizes  and  for
+$Lifetime95$ and  $Lifetime50$. The results show  that our LiCO protocol  is the
+most competitive  from the energy  consumption point of  view. As shown  in both
+figures, LiCO consumes much less energy than the three other methods.  One might
+think that the  resolution of the integer  program is too costly  in energy, but
+the  results show  that it  is very  beneficial to  lose a  bit of  time in  the
+selection of  sensors to  activate.  Indeed the  optimization program  allows to
+reduce significantly the number of active  sensors and so the energy consumption
+while keeping a good coverage level.

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

-\centering
-\includegraphics[scale=0.5]{R/EC95.eps} 
-\caption{The Energy Consumption per period with $Lifetime_{95}$}
-\label{fig3EC95}
-\end{figure} 
-                                           
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/EC50.eps} 
-\caption{The Energy Consumption per period with $Lifetime_{50}$}
-\label{fig3EC50}
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[scale=0.475]{R/EC95.eps} & \raisebox{2.75cm}{(a)} \\
+    \includegraphics[scale=0.475]{R/EC50.eps} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+  \label{fig3EC}

 \end{figure} 
 
 \end{figure} 
 

-The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures~\ref{fig3EC95} and \ref{fig3EC50}, LiCO consumes much less energy  than the three other methods. One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed this optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.

 %The optimization algorithm, which used by LiCO protocol,  was improved the lifetime coverage efficiently based on the perimeter coverage model.
 
  %The other approaches have a high energy consumption due to activating a larger number of sensors. 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. 
 %The optimization algorithm, which used by LiCO protocol,  was improved the lifetime coverage efficiently based on the perimeter coverage model.
 
  %The other approaches have a high energy consumption due to activating a larger number of sensors. 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. 


@@ -868,48 +909,68 @@ The results show that our LiCO protocol is the most competitive from the energy
 
 %\subsubsection{Execution Time}
 
 
 %\subsubsection{Execution Time}
 

-\subsubsection{\textbf{The Network Lifetime}}
-We observe the superiority of LiCO and DiLCO protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.  
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/LT95.eps}  
-\caption{The Network Lifetime for $Lifetime_{95}$}
-\label{fig3LT95}
-\end{figure}
+\subsubsection{\bf Network Lifetime}

 
 

+We observe the superiority of LiCO and DiLCO protocols in comparison against the
+two other approaches  in prolonging the network  WSN. In figures~\ref{fig3LT}(a)
+and (b),  $Lifetime95$ and $Lifetime50$  are shown for different  network sizes.
+As highlighted  by these figures,  the lifetime increases  with the size  of the
+network,  and it  is  clearly the  larger  for DiLCO  and  LiCO protocols.   For
+instance, for a network of 300 sensors  and coverage ratio greater than 50\%, we
+can see  on figure~\ref{fig3LT}(b) that the  lifetime is about two  times longer
+with LiCO compared to DESK protocol.  The performance difference is more obvious
+in  figure~\ref{fig3LT}(b)  than  in  figure~\ref{fig3LT}(a)  because  the  gain
+induced  by our  protocols increases  with  the time,  and the  lifetime with  a
+coverage of 50\% is far more longer than with 95\%.

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

-\centering
-\includegraphics[scale=0.5]{R/LT50.eps}  
-\caption{The Network Lifetime for $Lifetime_{50}$}
-\label{fig3LT50}
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[scale=0.475]{R/LT95.eps} & \raisebox{2.75cm}{(a)} \\  
+    \includegraphics[scale=0.475]{R/LT50.eps} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
+    and (b)~$Lifetime_{50}$.}
+  \label{fig3LT}

 \end{figure} 
 
 \end{figure} 
 

-As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously increases when the size of the network increases, and it is clearly larger with DiLCO and LiCO protocols compared with the two other methods. For instance, for a network of 300 sensors, the coverage ratio is greater than 50\% about two times longer with LiCO compared to DESK method.
+%By choosing the best suited nodes, for each period, 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 rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to  DiLCO-16 protocol for $95 \%$.

 
 

-%By choosing the best suited nodes, for each period, 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 rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to  DiLCO-16 protocol for $95 \%$.  
-Figure~\ref{figLTALL} introduces the comparisons of the lifetime coverage for different coverage ratios for LiCO and DiLCO protocols. 
-We denote by Protocol/50, Protocol/80, Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ respectively. Indeed there are applications that do not require a 100\% coverage of the surveillance region. LiCO might be an interesting  method  since it achieves a good balance between a high level coverage ratio and network lifetime.
+Figure~\ref{figLTALL}  compares  the  lifetime  coverage of  our  protocols  for
+different coverage  ratios. We denote by  Protocol/50, Protocol/80, Protocol/85,
+Protocol/90, and  Protocol/95 the amount  of time  during which the  network can
+satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
+respectively, where  Protocol is DiLCO  or LiCO.  Indeed there  are applications
+that do not require a 100\% coverage of  the area to be monitored. LiCO might be
+an interesting  method since  it achieves  a good balance  between a  high level
+coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three
+lower  coverage  ratios,  moreover  the   improvements  grow  with  the  network
+size. DiLCO is better for coverage ratios near 100\%, but LiCO is not so bad for
+the smallest network sizes.

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

-\centering
-\includegraphics[scale=0.5]{R/LTa.eps}  
-\caption{The Network Lifetime for different coverage ratios}
+\centering \includegraphics[scale=0.5]{R/LTa.eps}
+\caption{Network lifetime for different coverage ratios.}

 \label{figLTALL}
 \end{figure} 
 
 \label{figLTALL}
 \end{figure} 
 

-

 %Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. 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.
 
 
 %Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. 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.
 
 

-\section{\uppercase{Conclusion and Future Works}}
+\section{Conclusion and Future Works}

 \label{sec:Conclusion and Future Works}
 \label{sec:Conclusion and Future Works}

-In this paper we have studied the problem of lifetime coverage optimization in
-WSNs. We designed a protocol LiCO that schedules node' activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.
-
- 

 
 

+In this paper  we have studied the problem of  lifetime coverage optimization in
+WSNs. We designed  a new protocol, called Lifetime  Coverage Optimization, which
+schedules  node' activities  (wake up and  sleep  stages) with  the objective  of
+maintaining a  good coverage ratio  while maximizing the network  lifetime. This
+protocol is  applied in a distributed  way in regular subregions  obtained after
+partitioning the area of interest in a preliminary step. It works in periods and
+is based on the resolution of an integer program to select the subset of sensors
+operating in active status for each period. Our work is original in so far as it
+proposes for  the first  time an  integer program  scheduling the  activation of
+sensors  based on  their perimeter  coverage level,  instead of  using a  set of
+targets/points to be covered.

 
 %To cope with this problem, the area of interest is divided into a smaller subregions using  divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques:  network
 %leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the  most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
 
 %To cope with this problem, the area of interest is divided into a smaller subregions using  divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques:  network
 %leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the  most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage


@@ -918,21 +979,26 @@ WSNs. We designed a protocol LiCO that schedules node' activities (wakeup and sl
 %periods, each period consists  of four stages: (i) Information Exchange,
 %(ii) Leader Election, (iii) a Decision based new optimization model in order to
 %select the  nodes remaining  active for the last stage,  and  (iv) Sensing.
 %periods, each period consists  of four stages: (i) Information Exchange,
 %(ii) Leader Election, (iii) a Decision based new optimization model in order to
 %select the  nodes remaining  active for the last stage,  and  (iv) Sensing.

-We carried out severals simulations to evaluate the proposed protocol.  The  simulation results show that LiCO is  is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption. 
-%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily.
-
-We have identified different research directions that arise out of the work presented here. 
-We plan to extend our framework such that the schedules are planned for multiple periods in advance.
+We  carried out  several simulations  to  evaluate the  proposed protocol.   The
+simulation  results  show   that  LiCO  is  more   energy-efficient  than  other
+approaches, with respect to lifetime,  coverage ratio, active sensors ratio, and
+energy consumption.
+%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have  identified different  research directions  that arise  out of  the work presented here.
+We plan to extend our framework such that the schedules are planned for multiple
+sensing periods.

 %in order to compute all active sensor schedules in only one step for many periods;
 %in order to compute all active sensor schedules in only one step for many periods;

-We also want to improve our integer program to take into account the heterogeneous sensors, which do not have the same energy, processing,  sensing and communication capabilities;
+We also want  to improve our integer program to  take into account heterogeneous
+sensors  from both  energy  and node  characteristics point of views.

 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;

-Finally, our final goal is to implement our protocol using a sensor-testbed to evaluate their performance in real world applications.
+Finally,  it   would  be   interesting  to  implement   our  protocol   using  a
+sensor-testbed to evaluate it in real world applications.

 
 

-\section*{\uppercase{Acknowledgements}}
-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
-
- 
+\section*{Acknowledgments}

 
 

+\noindent  As a  Ph.D.   student, Ali  Kadhum IDREES  would  like to  gratefully
+acknowledge the  University of Babylon -  IRAQ for financial support  and Campus
+France for the  received support. This work has also been supported by the Labex
+ACTION.

 
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