Update on fig. 2

[LiCO.git] / LiCO_Journal.tex

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
index c8e2eb501a2fd70c6b02f1cc4d7fb92315b95289..a71497461d5dfa53350c56917929e6b77a28af37 100644 (file)
--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -36,8 +36,10 @@
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 \begin{document}
 
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 \begin{document}
 

-\title{Lifetime Coverage Optimization Protocol \\
-  in Wireless Sensor Networks}  %LiCO Protocol 
+%\title{Lifetime Coverage Optimization Protocol \\
+%  in Wireless Sensor Networks}
+\title{Perimeter-based Coverage Optimization Protocol \\
+  to Improve Lifetime in Wireless Sensor Networks}

 
 \author{Ali Kadhum Idrees,~\IEEEmembership{}
         Karine Deschinkel,~\IEEEmembership{}
 
 \author{Ali Kadhum Idrees,~\IEEEmembership{}
         Karine Deschinkel,~\IEEEmembership{}


@@ -53,12 +55,12 @@
 \maketitle
 
 \begin{abstract}
 \maketitle
 
 \begin{abstract}

-The most important problem in Wireless Sensor Networks (WSNs) is to optimize the
+The most important problem in a Wireless Sensor Network (WSN) is to optimize the

 use of its limited energy provision, so  that it can fulfill its monitoring task
 as  long as  possible. Among  known  available approaches  that can  be used  to
 improve  power  management,  lifetime coverage  optimization  provides  activity
 scheduling which ensures  sensing coverage while minimizing the  energy cost. In
 use of its limited energy provision, so  that it can fulfill its monitoring task
 as  long as  possible. Among  known  available approaches  that can  be used  to
 improve  power  management,  lifetime coverage  optimization  provides  activity
 scheduling which ensures  sensing coverage while minimizing the  energy cost. In

-this paper,  we propose  a such approach  called Lifetime  Coverage Optimization
+this paper,  we propose such an approach  called Lifetime  Coverage Optimization

 protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
 region of interest is first subdivided  into subregions and our protocol is then
 distributed among sensor nodes in each  subregion. A sensor node which runs LiCO
 protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
 region of interest is first subdivided  into subregions and our protocol is then
 distributed among sensor nodes in each  subregion. A sensor node which runs LiCO


@@ -66,11 +68,11 @@ protocol  repeats   periodically  four  stages:  information   exchange,  leader
 election, optimization decision, and sensing.  More precisely, the scheduling of
 nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
 leader selected after  cooperation between nodes within the  same subregion. The
 election, optimization decision, and sensing.  More precisely, the scheduling of
 nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
 leader selected after  cooperation between nodes within the  same subregion. The

-novelty of  approach lies essentially in  the formulation of a  new mathematical
-optimization  model  based on  perimeter  coverage  level to  schedule  sensors'
-activities.  Extensive simulation experiments have been performed using OMNeT++,
-the  discrete event  simulator, to  demonstrate that  LiCO is  capable to  offer
-longer lifetime coverage for WSNs in comparison with some other protocols.
+novelty  of  our  approach  lies  essentially   in  the  formulation  of  a  new
+mathematical optimization  model based on  perimeter coverage level  to schedule
+sensors' activities.  Extensive simulation experiments have been performed using
+OMNeT++, the  discrete event simulator, to  demonstrate that LiCO is  capable to
+offer longer lifetime coverage for WSNs in comparison with some other protocols.

 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.
 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.


@@ -92,7 +94,7 @@ communicating with one another through multi-hop radio communications. Each node
 can send the data  it collects in its environment, thanks to  its sensor, to the
 user by means of  sink nodes. The features of a WSN made  it suitable for a wide
 range of application  in areas such as business,  environment, health, industry,
 can send the data  it collects in its environment, thanks to  its sensor, to the
 user by means of  sink nodes. The features of a WSN made  it suitable for a wide
 range of application  in areas such as business,  environment, health, industry,

-military, and  son~\cite{yick2008wireless}.  Typically,  a sensor  node contains
+military, and so on~\cite{yick2008wireless}.   Typically, a sensor node contains

 three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 processing unit which will process and store the collected measurements; a radio
 three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 processing unit which will process and store the collected measurements; a radio


@@ -121,7 +123,7 @@ This paper makes the following contributions.
 \begin{enumerate}
 \item We devise a framework to schedule nodes to be activated alternatively such
   that the network lifetime is prolonged  while ensuring that a certain level of
 \begin{enumerate}
 \item We devise a framework to schedule nodes to be activated alternatively such
   that the network lifetime is prolonged  while ensuring that a certain level of

-  coverage is preserved.  A  key idea in our framework is  to exploit spatial an
+  coverage is preserved.  A key idea in  our framework is to exploit spatial and

   temporal subdivision.   On the one hand  the area of interest  if divided into
   several smaller subregions and on the other hand the time line is divided into
   periods of equal length. In each subregion the sensor nodes will cooperatively
   temporal subdivision.   On the one hand  the area of interest  if divided into
   several smaller subregions and on the other hand the time line is divided into
   periods of equal length. In each subregion the sensor nodes will cooperatively


@@ -203,13 +205,13 @@ each period.   {\it Motivated by  these works,  LiCO protocol works  in periods,
 
 Various centralized  and distributed approaches, or  even a mixing of  these two
 concepts, have  been proposed  to extend the  network lifetime.   In distributed
 
 Various centralized  and distributed approaches, or  even a mixing of  these two
 concepts, have  been proposed  to extend the  network lifetime.   In distributed

-algorithms~\cite{yangnovel,ChinhVu,qu2013distributed}  each  sensors decides  of
-its own  activity scheduling after  an information exchange with  its neighbors.
-The main interest of  a such approach is to avoid  long range communications and
-thus to reduce the energy dedicated to the communications.  Unfortunately, since
-each node has  only information on its immediate neighbors  (usually the one-hop
-ones)  it may  take a  bad  decision leading  to a  global suboptimal  solution.
-Conversely,                                                          centralized
+algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
+own activity scheduling  after an information exchange with  its neighbors.  The
+main interest of a such approach is  to avoid long range communications and thus
+to reduce the energy dedicated to the communications.  Unfortunately, since each
+node has only information on its  immediate neighbors (usually the one-hop ones)
+it may take a bad decision leading to a global suboptimal solution.  Conversely,
+centralized

 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}    always
 provide nearly  or close to  optimal solution since  the algorithm has  a global
 view of the whole network. The disadvantage of a centralized method is obviously
 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}    always
 provide nearly  or close to  optimal solution since  the algorithm has  a global
 view of the whole network. The disadvantage of a centralized method is obviously


@@ -293,6 +295,7 @@ executed by each node.
 %Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
 
 \subsection{Assumptions and Models}
 %Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
 
 \subsection{Assumptions and Models}

+\label{CI}

 
 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
 distributed in  a bounded sensor field  is considered. The wireless  sensors are
 
 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
 distributed in  a bounded sensor field  is considered. The wireless  sensors are


@@ -318,7 +321,7 @@ complete coverage of a convex area implies connectivity among active nodes.
 Tseng in~\cite{huang2005coverage}. It  can be expressed as follows:  a sensor is
 said to be perimeter  covered if all the points on its  perimeter are covered by
 at least  one sensor  other than  itself.  They  proved that  a network  area is
 Tseng in~\cite{huang2005coverage}. It  can be expressed as follows:  a sensor is
 said to be perimeter  covered if all the points on its  perimeter are covered by
 at least  one sensor  other than  itself.  They  proved that  a network  area is

-$k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
+$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).

 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 
 Figure~\ref{pcm2sensors}(a)  shows  the coverage  of  sensor  node~$0$. On  this
 figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on
 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 
 Figure~\ref{pcm2sensors}(a)  shows  the coverage  of  sensor  node~$0$. On  this
 figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on


@@ -332,17 +335,17 @@ 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} 
 
 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
 locations of the  left and right points of  an arc on the perimeter  of a sensor
   \label{pcm2sensors}
 \end{figure} 
 
 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
 locations of the  left and right points of  an arc on the perimeter  of a sensor

-node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the
+node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the

 west  side of  sensor~$u$,  with  the following  respective  coordinates in  the
 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
 compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
 west  side of  sensor~$u$,  with  the following  respective  coordinates in  the
 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
 compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert


@@ -362,7 +365,8 @@ positions. The intersection points are  then visited one after another, starting
 from  first  intersection point  after  point~zero,  and  the maximum  level  of
 coverage is determined  for each interval defined by two  successive points. The
 maximum  level of  coverage is  equal to  the number  of overlapping  arcs.  For
 from  first  intersection point  after  point~zero,  and  the maximum  level  of
 coverage is determined  for each interval defined by two  successive points. The
 maximum  level of  coverage is  equal to  the number  of overlapping  arcs.  For

-example, between~$5L$  and~$6L$ the maximum  level of  coverage is equal  to $3$
+example, 
+between~$5L$  and~$6L$ the maximum  level of  coverage is equal  to $3$

 (the value is highlighted in yellow  at the bottom of figure~\ref{expcm}), which
 means that at most 2~neighbors can cover  the perimeter in addition to node $0$.
 Table~\ref{my-label} summarizes for each coverage  interval the maximum level of
 (the value is highlighted in yellow  at the bottom of figure~\ref{expcm}), which
 means that at most 2~neighbors can cover  the perimeter in addition to node $0$.
 Table~\ref{my-label} summarizes for each coverage  interval the maximum level of


@@ -374,7 +378,7 @@ above is thus given by the sixth line of the table.
 
 \begin{figure*}[ht!]
 \centering
 
 \begin{figure*}[ht!]
 \centering

-\includegraphics[width=137.5mm]{expcm.pdf}  
+\includegraphics[width=137.5mm]{expcm2.jpg}  

 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
 \label{expcm}
 \end{figure*} 
 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
 \label{expcm}
 \end{figure*} 


@@ -396,7 +400,7 @@ above is thus given by the sixth line of the table.
  \caption{Coverage intervals and contributing sensors for sensor node 0.}
 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
 \hline
  \caption{Coverage intervals and contributing sensors for sensor node 0.}
 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
 \hline

-\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\  level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in interval coverage\end{tabular}} \\ \hline
+\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\  level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline

 0.0291    & 1L                                                                        & 2L                                                        & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
 0.104     & 2L                                                                        & 3R                                                        & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
 0.3168    & 3R                                                                        & 4R                                                        & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
 0.0291    & 1L                                                                        & 2L                                                        & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
 0.104     & 2L                                                                        & 3R                                                        & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
 0.3168    & 3R                                                                        & 4R                                                        & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline


@@ -452,7 +456,7 @@ homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
 our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion
 simultaneously to schedule nodes' activities for one sensing period.
 
 our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion
 simultaneously to schedule nodes' activities for one sensing period.
 

-As shown  in figure~\label{fig2},  node activity scheduling  is produced  by our
+As  shown in  figure~\ref{fig2}, node  activity  scheduling is  produced by  our

 protocol in a periodic manner. Each period is divided into 4 stages: Information
 (INFO)  Exchange,  Leader Election,  Decision  (the  result of  an  optimization
 problem),  and  Sensing.   For  each  period there  is  exactly  one  set  cover
 protocol in a periodic manner. Each period is divided into 4 stages: Information
 (INFO)  Exchange,  Leader Election,  Decision  (the  result of  an  optimization
 problem),  and  Sensing.   For  each  period there  is  exactly  one  set  cover


@@ -473,7 +477,7 @@ the area.
 \begin{figure}[t!]
 \centering
 \includegraphics[width=80mm]{Model.pdf}  
 \begin{figure}[t!]
 \centering
 \includegraphics[width=80mm]{Model.pdf}  

-\caption{LiCO protocol}
+\caption{LiCO protocol.}

 \label{fig2}
 \end{figure} 
 
 \label{fig2}
 \end{figure} 
 


@@ -496,16 +500,16 @@ Five status are possible for a sensor node in the network:
   determine the activities scheduling;
 \item ACTIVE: node is sensing;
 \item SLEEP: node is turned off;
   determine the activities scheduling;
 \item ACTIVE: node is sensing;
 \item SLEEP: node is turned off;

-\item COMMUNICATION: transmits or recevives packets.
+\item COMMUNICATION: transmits or receives packets.

 \end{itemize}
 %\end{enumerate}
 %Below, we describe each phase in more details.
 
 \subsection{LiCO Protocol Algorithm}
 
 \end{itemize}
 %\end{enumerate}
 %Below, we describe each phase in more details.
 
 \subsection{LiCO Protocol Algorithm}
 

-The  pseudocode  implementing the  protocol  on  a  node  is given  below.  More
-precisely, Algorithm~\label{alg:LiCO} gives a  brief description of the protocol
-applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
+\noindent The  pseudocode implementing the  protocol on  a node is  given below.
+More  precisely,  Algorithm~\ref{alg:LiCO}  gives  a brief  description  of  the
+protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.

 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}
 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}


@@ -548,62 +552,81 @@ 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}
 
 \end{algorithm}
 

-\noindent  In this  algorithm,  K.CurrentSize and  K.PreviousSize  refer to  the
-current  size  and  the  previous  size  of  the  subnetwork  in  the  subregion
-respectively.   That  means   the  number  of  sensor  nodes   which  are  still
-alive. Initially, the sensor node checks its remaining energy $RE_k$, which must
-be greater  than a  threshold $E_{th}$  in order to  participate in  the current
-period. Each  sensor node  determines its  position and  its subregion  using an
-embedded GPS  or a  location discovery  algorithm. After  that, all  the sensors
-collect position coordinates,  remaining energy, sensor node ID,  and the number
-of  its one-hop  live neighbors  during  the information  exchange. The  sensors
-inside a same region cooperate to elect a leader. The selection criteria for the
-leader, in order of priority, are:  larger number of neighbors, larger remaining
-energy, and  then in case  of equality, larger  index.  Once chosen,  the leader
-collects information to formulate and solve  the integer program which allows to
-construct the set of active sensors in the sensing stage.
+In this  algorithm, K.CurrentSize and  K.PreviousSize refer to the  current size
+and the  previous size of  the subnetwork  in the subregion  respectively.  That
+means the number  of sensor nodes which are still  alive.  Initially, the sensor
+node checks its remaining energy $RE_k$,  which must be greater than a threshold
+$E_{th}$  in order  to  participate in  the current  period.   Each sensor  node
+determines its  position and its subregion  using an embedded GPS  or a location
+discovery algorithm. After  that, all the sensors  collect position coordinates,
+remaining energy, sensor node ID, and the number of their one-hop live neighbors
+during the information  exchange. The sensors inside a same  region cooperate to
+elect a  leader. The selection  criteria for the  leader, in order  of priority,
+are: larger  number of neighbors, larger  remaining energy, and then  in case of
+equality,  larger  index.   Once  chosen, the  leader  collects  information  to
+formulate and  solve the integer  program which allows  to construct the  set of
+active sensors in the sensing stage.

 
 %After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter,  if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
 
 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
 
 
 %After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter,  if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
 
 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
 

-% MICHEL TO BE CONTINUED
-

 \section{Lifetime Coverage problem formulation}
 \section{Lifetime Coverage problem formulation}

-

 \label{cp}
 \label{cp}

-In this section, the coverage model is mathematically formulated.
-For convenience, the notations are described first. 
-%Then the lifetime problem of sensor network is formulated. 
-\noindent $S :$ the set of all sensors in the network.\\
-\noindent $A :$ the set of alive sensors within $S$.\\
-%\noindent $I :$ the set of segment points.\\
-\noindent $I_j :$ the set of coverage intervals (CI)  for sensor $j$.\\
-\noindent $I_j$ refers to the set of intervals which have been defined for each sensor $j$ in section~\ref{sec:The LiCO Protocol Description}.
-\noindent For a coverage interval  $i$,  let  $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:
+
+\noindent In this  section, the coverage model is  mathematically formulated. We
+start  with a  description of  the notations  that will  be used  throughout the
+section.
+
+First, we have the following sets:
+\begin{itemize}
+\item $S$ represents the set of WSN sensor nodes;
+\item $A \subseteq S $ is the subset of alive sensors;
+\item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
+  sensor~$j$.
+\end{itemize}
+$I_j$ refers to the set of  coverage intervals which have been defined according
+to the  method introduced in  subsection~\ref{CI}. For a coverage  interval $i$,
+let $a^j_{ik}$ denote  the indicator function of whether  sensor~$k$ is involved
+in coverage interval~$i$ of sensor~$j$, that is:

 \begin{equation}
 a^j_{ik} = \left \{ 
 \begin{array}{lll}
 \begin{equation}
 a^j_{ik} = \left \{ 
 \begin{array}{lll}

-  1 & \mbox{if the sensor $k$ is involved in the } \\
+  1 & \mbox{if sensor $k$ is involved in the } \\

        &       \mbox{coverage interval $i$ of sensor $j$}, \\
        &       \mbox{coverage interval $i$ of sensor $j$}, \\

-  0 & \mbox{Otherwise.}\\
+  0 & \mbox{otherwise.}\\

 \end{array} \right.
 %\label{eq12} 
 \notag
 \end{equation}
 \end{array} \right.
 %\label{eq12} 
 \notag
 \end{equation}

-Note that $a^k_{ik}=1$ by definition of the interval.\\
+Note that $a^k_{ik}=1$ by definition of the interval.

 %, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.
 %, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.

-%We defined some parameters, which are related to our optimization model. In our model,  we  consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .   
-\noindent We  consider binary variables $X_{k}$ ($X_k=1$ if the sensor $k$ is active or 0 otherwise), which determine the activation of sensor $k$ in the sensing phase. We define the integer variable $M^j_i$ which measures the undercoverage for the coverage interval $i$ for sensor $j$. In the same way, we define the integer variable $V^j_i$, which measures the overcoverage for the coverage interval $i$ for sensor $j$. If we decide to sustain a level of coverage equal to $l$ all along the perimeter of the sensor $j$, we have to ensure that at least $l$ sensors involved in each coverage interval $i$ ($i \in I_j$) of sensor $j$ are active. According to the previous notations, the number of active sensors in the coverage interval $i$ of sensor $j$ is given by $\sum_{k \in K} a^j_{ik} X_k$. To extend the network lifetime, the objective is to active a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to satisfy the level of coverage for all covergae intervals. We uses variables $M^j_i$ and $V^j_i$ as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number of active sensors. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the desired coverage level, and if the desired level can not be completely  satisfied, to reach a coverage level as close as possible that the desired one.
-
-
+%We defined some parameters, which are related to our optimization model. In our model,  we  consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .
+Second,  we define  several binary  and integer  variables.  Hence,  each binary
+variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase
+($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  an integer
+variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
+corresponding to  sensor~$j$. In  the same  way, the  overcoverage for  the same
+coverage interval is given by the variable $V^j_i$.
+
+If we decide to sustain a level of coverage equal to $l$ all along the perimeter
+of sensor  $j$, we have  to ensure  that at least  $l$ sensors involved  in each
+coverage  interval $i  \in I_j$  of  sensor $j$  are active.   According to  the
+previous notations, the number of active sensors in the coverage interval $i$ of
+sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
+lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
+period to  ensure the  desired coverage  level. As the  number of  alive sensors
+decreases, it becomes impossible to reach  the desired level of coverage for all
+coverage intervals. Therefore we use variables  $M^j_i$ and $V^j_i$ as a measure
+of the  deviation between  the desired  number of active  sensors in  a coverage
+interval and  the effective  number. And  we try  to minimize  these deviations,
+first to  force the  activation of  a minimal  number of  sensors to  ensure the
+desired coverage level, and if the desired level cannot be completely satisfied,
+to reach a coverage level as close as possible to the desired one.

 
 %A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized. 
 
 
 %A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized. 
 


@@ -625,13 +648,9 @@ Note that $a^k_{ik}=1$ by definition of the interval.\\
 
 %\noindent $V^j_i (overcoverage): $ integer value $\in  \mathbb{N}$ for segment point $i$ of sensor $j$.
 
 
 %\noindent $V^j_i (overcoverage): $ integer value $\in  \mathbb{N}$ for segment point $i$ of sensor $j$.
 

-
-
-
-
-\noindent Our coverage optimization problem can be mathematically formulated as follows: 
+Our coverage optimization problem can then be mathematically expressed as follows: 

 %Objective:
 %Objective:

-\begin{equation} \label{eq:ip2r}
+\begin{equation} %\label{eq:ip2r}

 \left \{
 \begin{array}{ll}
 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
 \left \{
 \begin{array}{ll}
 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\


@@ -645,27 +664,35 @@ Note that $a^k_{ik}=1$ by definition of the interval.\\
 X_{k} \in \{0,1\}, \forall k \in A
 \end{array}
 \right.
 X_{k} \in \{0,1\}, \forall k \in A
 \end{array}
 \right.

+\notag

 \end{equation}
 \end{equation}

-
-
-\noindent $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
-relative importance of satisfying the associated
-level of coverage. For example, weights associated with coverage intervals of a specified part of a region
-may be given a relatively
-larger magnitude than weights associated
-with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model. 
-
-
-\section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}  
+$\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
+relative importance of satisfying the associated level of coverage. For example,
+weights associated with  coverage intervals of a specified part  of a region may
+be  given a  relatively larger  magnitude than  weights associated  with another
+region. This  kind of integer program  is inspired from the  model developed for
+brachytherapy    treatment   planning    for   optimizing    dose   distribution
+\cite{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
+each subregion at the beginning of  each sensing phase, whenever the environment
+has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
+constraints in the model is constant  (constraints of coverage expressed for all
+sensors), whereas the number of variables $X_k$ decreases over periods, since we
+consider only alive  sensors (sensors with enough energy to  be alive during one
+sensing phase) in the model.
+
+\section{Performance Evaluation and Analysis}  

 \label{sec:Simulation Results and Analysis}
 %\noindent \subsection{Simulation Framework}
 
 \subsection{Simulation Settings}
 %\label{sub1}
 \label{sec:Simulation Results and Analysis}
 %\noindent \subsection{Simulation Framework}
 
 \subsection{Simulation Settings}
 %\label{sub1}

-In this section, we focus on the performance of LiCO protocol, which is distributed in each sensor node in the sixteen subregions of WSN. We use the same energy consumption model which is used in~\cite{Idrees2}. Table~\ref{table3} gives the chosen parameters setting.
+
+The WSN  area of interest is  supposed to be divided  into 16~regular subregions
+and we use the same energy consumption than in our previous work~\cite{Idrees2}.
+Table~\ref{table3} gives the chosen parameters settings.

 
 \begin{table}[ht]
 
 \begin{table}[ht]

-\caption{Relevant parameters for network initializing.}
+\caption{Relevant parameters for network initialization.}

 % title of Table
 \centering
 % used for centering table
 % title of Table
 \centering
 % used for centering table


@@ -676,14 +703,14 @@ Parameter & Value  \\ [0.5ex]
    
 \hline
 % inserts single horizontal line
    
 \hline
 % inserts single horizontal line

-Sensing  Field  & $(50 \times 25)~m^2 $   \\
+Sensing field & $(50 \times 25)~m^2 $   \\

 
 

-Nodes Number &  100, 150, 200, 250 and 300~nodes   \\
+WSN size &  100, 150, 200, 250, and 300~nodes   \\

 %\hline
 %\hline

-Initial Energy  & 500-700~joules  \\  
+Initial energy  & in range 500-700~Joules  \\  

 %\hline
 %\hline

-Sensing Period & 60 Minutes \\
-$E_{th}$ & 36 Joules\\
+Sensing period & duration of 60 minutes \\
+$E_{th}$ & 36~Joules\\

 $R_s$ & 5~m   \\     
 %\hline
 $\alpha^j_i$ & 0.6   \\
 $R_s$ & 5~m   \\     
 %\hline
 $\alpha^j_i$ & 0.6   \\


@@ -695,142 +722,189 @@ $\beta^j_i$ & 0.4
 \label{table3}
 % is used to refer this table in the text
 \end{table}
 \label{table3}
 % is used to refer this table in the text
 \end{table}

-Simulations with five  different node densities going from  100 to 250~nodes were
-performed  considering  each  time  25~randomly generated  networks,  to  obtain
-experimental results  which are relevant. All simulations are repeated 25 times and the results are averaged. The  nodes are deployed on a field of interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a high coverage ratio.
-
-Each node has an initial energy level, in Joules, which is randomly drawn in the
-interval  $[500-700]$.  If  it's  energy  provision reaches  a  value below  the
-threshold  $E_{th}=36$~Joules, the  minimum energy  needed  for a  node to  stay
-active during one period, it will no more participate in the coverage task. This
-value  corresponds  to the  energy  needed by  the  sensing  phase, obtained  by
-multiplying the energy consumed in active  state (9.72 mW) by the time in seconds
-for one period (3600 seconds), and  adding the energy for the pre-sensing phases.
-According to  the interval of initial energy,  a sensor may be  active during at
-most 20 rounds.
-
-The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen in a way that ensuring a good network coverage and for a longer time during the lifetime of the WSN.  We have given a higher priority for the undercoverage ( by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so as to minimize the number of active sensor nodes that contribute in covering the interval i in sensor j.
-
-In the simulations,  we introduce the following performance  metrics to evaluate
-the efficiency of our approach:
+To  obtain  experimental  results  which are  relevant,  simulations  with  five
+different node densities going from  100 to 300~nodes were performed considering
+each time 25~randomly  generated networks. The nodes are deployed  on a field of
+interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
+high coverage ratio. Each node has an  initial energy level, in Joules, which is
+randomly drawn in the interval $[500-700]$.   If it's energy provision reaches a
+value below  the threshold $E_{th}=36$~Joules,  the minimum energy needed  for a
+node  to stay  active during  one period,  it will  no more  participate in  the
+coverage task. This value corresponds to the energy needed by the sensing phase,
+obtained by multiplying  the energy consumed in active state  (9.72 mW) with the
+time in  seconds for one  period (3600 seconds), and  adding the energy  for the
+pre-sensing phases.  According  to the interval of initial energy,  a sensor may
+be active during at most 20 periods.
+
+The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
+network coverage and a longer WSN lifetime.  We have given a higher priority for
+the  undercoverage  (by  setting  the  $\alpha^j_i$ with  a  larger  value  than
+$\beta^j_i$)  so as  to prevent  the non-coverage  for the  interval~$i$ of  the
+sensor~$j$.  On the  other hand,  we have  given a  little bit  lower value  for
+$\beta^j_i$ so as to minimize the number of active sensor nodes which contribute
+in covering the interval.
+
+We introduce the following performance metrics to evaluate the efficiency of our
+approach.

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

-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
-  the  coverage  ratio  drops  below  a  predefined  threshold.   We  denote  by
-  $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
-  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
-  $50\%$). We assume that the sensor  network can fulfill its task until all its
-  nodes have  been drained of their  energy or it  becomes disconnected. Network
-  connectivity  is crucial because  an active  sensor node  without connectivity
-  towards a base  station cannot transmit any information  regarding an observed
-  event in the area that it monitors.
-  
-    
-\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 to compute the
-  coverage ratio: 
-\begin{equation*}
-\scriptsize
-\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
-points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
-\times 26 = 1326$ grid points.
-
-
-\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 Network Lifetime}: the lifetime  is defined as the time elapsed until
+  the  coverage  ratio  falls  below a  fixed  threshold.   $Lifetime_{95}$  and
+  $Lifetime_{50}$  denote, respectively,  the  amount of  time  during which  is
+  guaranteed a  level of coverage  greater than $95\%$  and $50\%$. The  WSN can
+  fulfill the expected  monitoring task until all its nodes  have depleted their
+  energy or if the network is no  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
+  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
   \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{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \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 $n$  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
+  $N~=~51~\times~26~=~1326$~grid points.
+\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
+    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
+  \end{equation*}
+  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 objective 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  four  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. 


@@ -838,48 +912,69 @@ 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   lifetime.    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 in  that case 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 nodes'  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


@@ -888,21 +983,26 @@ 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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