version R4 pour soumission

[LiCO.git] / PeCO-EO / articleeo.tex~

diff --git a/PeCO-EO/articleeo.tex~ b/PeCO-EO/articleeo.tex~
index ab832aedbe67d137e48e078c8e6a97ee23054613..ea3bddf43b9e66044e2aabf27e7a6e9d4f5cab67 100644 (file)
--- a/PeCO-EO/articleeo.tex~
+++ b/PeCO-EO/articleeo.tex~
@@ -2,17 +2,12 @@
 % v4.0 released April 2013
 
 \documentclass{gENO2e}
 % v4.0 released April 2013
 
 \documentclass{gENO2e}

-%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
-%\renewcommand{\algorithmcfname}{ALGORITHM}
+

 \usepackage{indentfirst}
 \usepackage{color}
 \usepackage[algo2e,ruled,vlined]{algorithm2e}
 \begin{document}
 
 \usepackage{indentfirst}
 \usepackage{color}
 \usepackage[algo2e,ruled,vlined]{algorithm2e}
 \begin{document}
 

-%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}
-
-%\articletype{GUIDE}
-

 \title{{\itshape Perimeter-based Coverage Optimization \\
   to Improve Lifetime in Wireless Sensor Networks}}
 
 \title{{\itshape Perimeter-based Coverage Optimization \\
   to Improve Lifetime in Wireless Sensor Networks}}
 


@@ -29,11 +24,11 @@ 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
 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. We
-propose such  an approach called Perimeter-based  Coverage Optimization protocol
-(PeCO). It  is a hybrid  of centralized and  distributed methods: the  region of
-interest  is  first  subdivided  into   subregions  and  the  protocol  is  then
-distributed among sensor  nodes in each subregion.  The novelty  of our approach
+scheduling which ensures  sensing coverage while minimizing the  energy cost. In
+this  paper an  approach called  Perimeter-based Coverage  Optimization protocol
+(PeCO) is proposed.  It is a hybrid of centralized  and distributed methods: the
+region of interest is first subdivided  into subregions and the protocol is then
+distributed among sensor  nodes in each subregion.  The novelty  of the approach

 lies essentially  in the  formulation of a  new mathematical  optimization model
 based  on  the  perimeter  coverage   level  to  schedule  sensors'  activities.
 Extensive simulation experiments demonstrate that PeCO can offer longer lifetime
 lies essentially  in the  formulation of a  new mathematical  optimization model
 based  on  the  perimeter  coverage   level  to  schedule  sensors'  activities.
 Extensive simulation experiments demonstrate that PeCO can offer longer lifetime


@@ -89,17 +84,17 @@ This paper makes the following contributions :
   architecture.
 \item A new  mathematical optimization model is proposed.  Instead  of trying to
   cover a set of specified points/targets as  in most of the methods proposed in
   architecture.
 \item A new  mathematical optimization model is proposed.  Instead  of trying to
   cover a set of specified points/targets as  in most of the methods proposed in

-  the literature,  we formulate a  mixed-integer program based on  the perimeter
-  coverage of each sensor.  The model  involves integer variables to capture the
-  deviations  between the  actual  level  of coverage  and  the required  level.
+  the literature,  a mixed-integer  program based on  the perimeter  coverage of
+  each sensor  is formulated.  The  model involves integer variables  to capture
+  the deviations  between the actual level  of coverage and the  required level.

   Hence, an  optimal schedule will be  obtained by minimizing a  weighted sum of
   these deviations.
 \item Extensive  simulation experiments are  conducted using the  discrete event
   Hence, an  optimal schedule will be  obtained by minimizing a  weighted sum of
   these deviations.
 \item Extensive  simulation experiments are  conducted using the  discrete event

-  simulator OMNeT++,  to demonstrate  the efficiency of  our protocol.   We have
-  compared  the  PeCO  protocol  to  two approaches  found  in  the  literature:
-  DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
-  protocol DiLCO published in~\citep{Idrees2}. DiLCO  uses the same framework as
-  PeCO but is based on another optimization model for sensor scheduling.
+  simulator OMNeT++,  to demonstrate the  efficiency of the PeCO  protocol.  The
+  PeCO protocol  has been compared  to two  approaches found in  the literature:
+  DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to the protocol
+  DiLCO published in~\citep{Idrees2}. DiLCO uses  the same framework as PeCO but
+  is based on another optimization model for sensor scheduling.

 \end{enumerate}
 
 The rest of the paper is organized as follows.  In the next section some related
 \end{enumerate}
 
 The rest of the paper is organized as follows.  In the next section some related


@@ -134,7 +129,7 @@ algorithm  in  $O(nd~log~d)$ time  to  compute  the perimeter-coverage  of  each
 sensor.  $d$ denotes  the maximum  number  of sensors  that are  neighbors to  a
 sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
   protocol, instead  of determining the level  of coverage of a  set of discrete
 sensor.  $d$ denotes  the maximum  number  of sensors  that are  neighbors to  a
 sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
   protocol, instead  of determining the level  of coverage of a  set of discrete

-  points, our optimization model is  based on checking the perimeter-coverage of
+  points, the optimization model is  based on checking the perimeter-coverage of

   each sensor to activate a minimal number of sensors.}
 
 The major  approach to extend network  lifetime while preserving coverage  is to
   each sensor to activate a minimal number of sensors.}
 
 The major  approach to extend network  lifetime while preserving coverage  is to


@@ -212,8 +207,8 @@ decomposed into 4  phases: information exchange, leader  election, decision, and
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set

-  of specified points/targets as in the  DiLCO protocol, we formulate an integer
-  program based  on the perimeter  coverage of  each sensor. The  model involves
+  of specified points/targets as in the DiLCO protocol, an integer program based
+  on the  perimeter coverage of  each sensor  is formulated. The  model involves

   integer  variables to  capture  the  deviations between  the  actual level  of
   coverage and the  required level. The idea is that  an optimal scheduling will
   be obtained by minimizing a weighted sum of these deviations.}
   integer  variables to  capture  the  deviations between  the  actual level  of
   coverage and the  required level. The idea is that  an optimal scheduling will
   be obtained by minimizing a weighted sum of these deviations.}


@@ -221,13 +216,6 @@ and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 

-%In  this  section,  the Perimeter-based  Coverage
-%Optimization protocol is decribed in details.  First we present the  assumptions we made and the models
-%we considered (in particular the perimeter coverage one), second we describe the
-%background idea of our protocol, and third  we give the outline of the algorithm
-%executed by each node.
-
-

 \subsection{Assumptions and Models}
 \label{CI}
 
 \subsection{Assumptions and Models}
 \label{CI}
 


@@ -242,7 +230,7 @@ algorithms. A Boolean disk coverage model,  which is the most widely used sensor
 coverage model  in the  literature, is  considered and all  sensor nodes  have a
 constant sensing range $R_s$.  Thus, all the space points within a disk centered
 at a sensor with  a radius equal to the sensing range are  said to be covered by
 coverage model  in the  literature, is  considered and all  sensor nodes  have a
 constant sensing range $R_s$.  Thus, all the space points within a disk centered
 at a sensor with  a radius equal to the sensing range are  said to be covered by

-this sensor.  We  also assume that the communication range  $R_c$ satisfies $R_c
+this sensor.  The communication range  $R_c$ is assumed to satisfy : $R_c

 \geq 2  \cdot R_s$.  In  fact, \citet{Zhang05}  proved that if  the transmission
 range fulfills the  previous hypothesis, the complete coverage of  a convex area
 implies connectivity among active nodes.
 \geq 2  \cdot R_s$.  In  fact, \citet{Zhang05}  proved that if  the transmission
 range fulfills the  previous hypothesis, the complete coverage of  a convex area
 implies connectivity among active nodes.


@@ -256,11 +244,11 @@ $k$~sensors) if and only if each  sensor in the network is $k$-perimeter-covered
 (perimeter covered by at least $k$ sensors).
  
 Figure~\ref{figure1}(a) shows the coverage of  sensor node~$0$.  On this figure,
 (perimeter covered by at least $k$ sensors).
  
 Figure~\ref{figure1}(a) shows the coverage of  sensor node~$0$.  On this figure,

-sensor~$0$  has nine  neighbors  and  we have  reported  on  its perimeter  (the
-perimeter of the  disk covered by the  sensor) for each neighbor  the two points
-resulting from  the intersection  of the  two sensing  areas.  These  points are
-denoted for neighbor~$i$ by $iL$ and  $iR$, respectively for left and right from
-a  neighboring point  of view.   The  resulting couples  of intersection  points
+sensor~$0$ has nine  neighbors. For each neighbor the two  points resulting from
+the intersection  of the two sensing  areas have been reported  on its perimeter
+(the perimeter of the disk covered by the sensor~$0$).  These points are denoted
+for  neighbor~$i$ by  $iL$ and  $iR$,  respectively for  left and  right from  a
+neighboring  point  of  view.   The resulting  couples  of  intersection  points

 subdivide the perimeter of sensor~$0$ into portions called arcs.
 
 \begin{figure}[ht!]
 subdivide the perimeter of sensor~$0$ into portions called arcs.
 
 \begin{figure}[ht!]


@@ -301,7 +289,7 @@ from the first  intersection point  after  point~zero,  and  the maximum  level
 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 $3$
 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 $3$

-(the value is highlighted in yellow  at the bottom of Figure~\ref{figure2}), which
+(the value is given at the bottom of Figure~\ref{figure2}), 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
 coverage and  the sensor  nodes covering the  perimeter.  The  example discussed
 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
 coverage and  the sensor  nodes covering the  perimeter.  The  example discussed


@@ -364,7 +352,7 @@ optimization algorithm.
 \subsection{Main Idea}
 
 The WSN area of  interest is, in a first step,  divided into regular homogeneous
 \subsection{Main Idea}
 
 The WSN area of  interest is, in a first step,  divided into regular homogeneous

-subregions using a  divide-and-conquer algorithm. In a second  step our protocol
+subregions using a  divide-and-conquer algorithm. In a second  step the protocol

 will  be executed  in  a distributed  way in  each  subregion simultaneously  to
 schedule nodes' activities  for one sensing period. Sensor nodes  are assumed to
 be deployed  almost uniformly over the  region. The regular subdivision  is made
 will  be executed  in  a distributed  way in  each  subregion simultaneously  to
 schedule nodes' activities  for one sensing period. Sensor nodes  are assumed to
 be deployed  almost uniformly over the  region. The regular subdivision  is made


@@ -397,7 +385,7 @@ of the application.
 \label{figure4}
 \end{figure} 
 
 \label{figure4}
 \end{figure} 
 

-We define two types of packets to be used by the PeCO protocol:
+Two types of packets used by the PeCO protocol are defined:

 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.


@@ -422,12 +410,7 @@ The  pseudocode implementing  the  protocol  on a  node  is  given below.   More
 precisely, Algorithm~\ref{alg:PeCO}  gives a  brief description of  the protocol
 applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 
 precisely, Algorithm~\ref{alg:PeCO}  gives a  brief description of  the protocol
 applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 

-

 \begin{algorithm2e}      
 \begin{algorithm2e}      

- % \KwIn{all the parameters related to information exchange}
-%  \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
-%  \BlankLine
-  %\emph{Initialize the sensor node and determine it's position and subregion} \;

   \label{alg:PeCO}
   \caption{PeCO pseudocode}
   \eIf{$RE_k \geq E_{th}$}{
   \label{alg:PeCO}
   \caption{PeCO pseudocode}
   \eIf{$RE_k \geq E_{th}$}{


@@ -462,42 +445,6 @@ applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
   }
 \end{algorithm2e}
 
   }
 \end{algorithm2e}
 

-%\begin{algorithm}
-%\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
-%\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
-%\hspace*{0.6cm}  \emph{Send $INFO()$ packet to other nodes in subregion;}\\
-%\hspace*{0.6cm}  \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
-%\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
-%\hspace*{0.6cm}  \emph{LeaderID = Leader election;}\\
-%\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
-%\hspace*{1.2cm}   \emph{$s_k.status$ = COMPUTATION;}\\
-%\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
-%\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
-%\hspace*{1.2cm} {\bf end}\\
-%\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
-%\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
-%\hspace*{1.2cm}  {\bf end}\\
-%\hspace*{1.2cm}  {\bf else}\\
-%\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
-%\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
-%\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
-%\hspace*{1.2cm}  {\bf end}\\
-%\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
-%\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
-%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-%\hspace*{0.6cm}  {\bf end}\\
-%\hspace*{0.6cm}  {\bf else}\\
-%\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
-%\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
-%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-%\hspace*{0.6cm}  {\bf end}\\
-%{\bf end}\\
-%{\bf else}\\
-%\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
-%{\bf end}\\
-%\label{alg:PeCO}
-%\end{algorithm}
-

 In this  algorithm, $K.CurrentSize$ and $K.PreviousSize$  respectively represent
 the current number and the previous number  of living nodes in the subnetwork of
 the  subregion.   At the  beginning  of  the  first period  $K.PreviousSize$  is
 In this  algorithm, $K.CurrentSize$ and $K.PreviousSize$  respectively represent
 the current number and the previous number  of living nodes in the subnetwork of
 the  subregion.   At the  beginning  of  the  first period  $K.PreviousSize$  is


@@ -506,17 +453,22 @@ $RE_k$, 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,
 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. \textcolor{blue}{We suppose that both INFO packet and ActiveSleep packet contain two parts: header and data payload. The sensor id is included in the header, where the header size is 8 bits. The data part includes position coordinates (64 bits), remaining energy (32 bits), and the number of their one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112 bits. The ActiveSleep packet is 16 bits size, 8 bits for the header and 8 bits for data part that includes only sensor status (0 or 1)}
-The sensors  inside a same  region cooperate to  elect a leader.   The selection
-criteria for the leader are (in order  of priority):
+and the number of their one-hop  live neighbors during the information exchange.
+Both  INFO packet  and ActiveSleep  packet contain  two parts:  header and  data
+payload. The  sensor ID is included  in the header,  where the header size  is 8
+bits. The  data part includes  position coordinates (64 bits),  remaining energy
+(32 bits), and the number of one-hop live neighbors (8 bits). Therefore the size
+of the INFO packet  is 112 bits. The ActiveSleep packet is 16  bits size, 8 bits
+for the header and  8 bits for data part that includes only  sensor status (0 or
+1).   The  sensors inside  a  same  region cooperate  to  elect  a leader.   The
+selection criteria for the leader are (in order of priority):

 \begin{enumerate}
 \item larger number of neighbors;
 \item larger  remaining energy;
 \item and then,  in case  of equality,  larger indexes.
 \end{enumerate}
 Once chosen, the leader collects information  to formulate and solve the integer
 \begin{enumerate}
 \item larger number of neighbors;
 \item larger  remaining energy;
 \item and then,  in case  of equality,  larger indexes.
 \end{enumerate}
 Once chosen, the leader collects information  to formulate and solve the integer

-program  which allows  to build  the set  of active  sensors in  the sensing
-stage.
+program which allows to build the set of active sensors in the sensing stage.

 
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}
 
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}


@@ -568,7 +520,7 @@ coverage level. As the number of  alive sensors decreases, it becomes impossible
 to reach  the desired level  of coverage  for all coverage  intervals. Therefore
 variables  $M^j_i$ and  $V^j_i$ are  introduced as  a measure  of the  deviation
 between the  desired number  of active  sensors in a  coverage interval  and the
 to reach  the desired level  of coverage  for all coverage  intervals. Therefore
 variables  $M^j_i$ and  $V^j_i$ are  introduced 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
+effective number.  And these deviations are minimized, 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.
 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.


@@ -585,18 +537,6 @@ The coverage optimization problem can then be mathematically expressed as follow
   \end{aligned}
 \end{equation}
 
   \end{aligned}
 \end{equation}
 

-%\begin{equation} 
-%\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 ) & \\
-%\textrm{subject to :} &\\
-%\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
-%\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\
-%X_{k} \in \{0,1\}, \forall k \in A \\
-%M^j_i, V^j_i \in \mathbb{R}^{+} 
-%\end{array}
-%\right.
-%\end{equation}

 
 If a given level of coverage $l$ is  required for one sensor, the sensor is said
 to be undercovered (respectively overcovered) if the level of coverage of one of
 
 If a given level of coverage $l$ is  required for one sensor, the sensor is said
 to be undercovered (respectively overcovered) if the level of coverage of one of


@@ -633,7 +573,7 @@ be alive during one sensing phase) are considered in the model.
 \subsection{Simulation Settings}
 
 The WSN  area of interest is  supposed to be divided  into 16~regular subregions
 \subsection{Simulation Settings}
 
 The WSN  area of interest is  supposed to be divided  into 16~regular subregions

-and   we  use   the  same   energy  consumption   model  as   in  our   previous
+and the  energy  consumption   model  used is described in previous

 work~\citep{Idrees2}.  Table~\ref{table3} gives the chosen parameters settings.
 
 \begin{table}[ht]
 work~\citep{Idrees2}.  Table~\ref{table3} gives the chosen parameters settings.
 
 \begin{table}[ht]


@@ -668,12 +608,12 @@ coverage task. This value corresponds to the energy needed by the sensing phase,
 obtained by multiplying  the energy consumed in the 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
 obtained by multiplying  the energy consumed in the 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 information exchange to update the coverage
-is executed every  hour, but the length  of the sensing period  could be reduced
-and adapted dynamically. On  the one hand a small sensing  period would allow the network to
-be more  reliable but would  have resulted in  higher communication costs.  On the
-other hand  the choice of a  long duration may  cause problems in case  of nodes
-failure during the sensing period.
+be active  during at  most 20  periods. the information  exchange to  update the
+coverage is executed every  hour, but the length of the  sensing period could be
+reduced and  adapted dynamically. On the  one hand a small  sensing period would
+allow  the  network to  be  more  reliable but  would  have  resulted in  higher
+communication costs.  On the other hand the  choice of a long duration may cause
+problems in case of nodes failure during the sensing period.

 
 The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
 network coverage  and a longer  WSN lifetime.  Higher  priority is given  to the
 
 The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
 network coverage  and a longer  WSN lifetime.  Higher  priority is given  to the


@@ -696,7 +636,7 @@ approach.
   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
   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, the sensor field is discretized as
+  observe the area of interest. Here the sensor field is discretized as

   a regular grid, which yields the following equation:
   \begin{equation*}
     \scriptsize
   a regular grid, which yields the following equation:
   \begin{equation*}
     \scriptsize


@@ -706,26 +646,25 @@ approach.
   subregions during  the current sensing phase  and $N$ is total  number of grid
   points in the sensing field. A layout of $N~=~51~\times~26~=~1326$~grid points
   is considered in the simulations.
   subregions during  the current sensing phase  and $N$ is total  number of grid
   points in the sensing field. A layout of $N~=~51~\times~26~=~1326$~grid points
   is considered in the simulations.

-\item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to
-  activate as  few nodes  as possible,  in order  to minimize  the communication
-  overhead and maximize the WSN lifetime. The active sensors ratio is defined as
-  follows:
+\item  {\bf Active  Sensors  Ratio (ASR)}:  a major  objective  of the  proposed
+  protocol is  to activate as  few nodes 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{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
+   \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
   sensing period~$p$, $R$  is the number of subregions, and  $|J|$ is the number
   of sensors in the network.
   
   \end{equation*}
   where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
   sensing period~$p$, $R$  is the number of subregions, and  $|J|$ is the number
   of sensors in the network.
   

-\item {\bf \textcolor{blue}{Energy Saving Ratio (ESR)}}:  
-\textcolor{blue}{we consider a performance metric linked to energy. This metric, called Energy Saving Ratio (ESR), is defined by:
+\item {\bf Energy Saving Ratio (ESR)}: this metric, which shows the ability of a
+  protocol to save energy, is defined by:

 \begin{equation*}
 \scriptsize
 \mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
 {\mbox{Total number of sensors in the network}} \times 100.
 \end{equation*}  
 \begin{equation*}
 \scriptsize
 \mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
 {\mbox{Total number of sensors in the network}} \times 100.
 \end{equation*}  

-  }

 \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
 \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


@@ -750,16 +689,16 @@ approach.
 
 \subsection{Simulation Results}
 
 
 \subsection{Simulation Results}
 

-In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
-implemented  the   PeCO  protocol   in  OMNeT++~\citep{varga}   simulator.   The
-simulations were  run on a  DELL laptop  with an Intel  Core~i3~2370~M (1.8~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  $\left(\frac{35330}{2}
-\times \frac{1}{6} \right)$.  Energy consumption  is calculated according to the
-power consumption values, in milliWatt  per second, given in Table~\ref{tab:EC},
-based on the energy model proposed in \citep{ChinhVu}.
+The PeCO  protocol has  been implemented  in OMNeT++~\citep{varga}  simulator in
+order to assess and analyze its performance.  The simulations were run on a DELL
+laptop with  an Intel  Core~i3~2370~M (1.8~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 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$.  Energy
+consumption  is  calculated  according  to  the  power  consumption  values,  in
+milliWatt per  second, given  in Table~\ref{tab:EC}, based  on the  energy model
+proposed in \citep{ChinhVu}.

 
 \begin{table}[h]
 \centering
 
 \begin{table}[h]
 \centering


@@ -781,16 +720,16 @@ based on the energy model proposed in \citep{ChinhVu}.
 
 The modeling  language for Mathematical Programming  (AMPL)~\citep{AMPL} is used
 to generate  the integer program  instance in a  standard format, which  is then
 
 The modeling  language for Mathematical Programming  (AMPL)~\citep{AMPL} is used
 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
+read and  solved by  the optimization  solver GLPK  (GNU Linear  Programming Kit

 available in the public domain)  \citep{glpk} through a Branch-and-Bound method.
 In practice, executing GLPK on a sensor node is obviously intractable due to the
 available in the public domain)  \citep{glpk} through a Branch-and-Bound method.
 In practice, executing GLPK on a sensor node is obviously intractable due to the

-huge memory  use. Fortunately, to  solve the  optimization problem we  could use
+huge memory  use. Fortunately,  to solve  the optimization  problem, the  use of

 commercial  solvers  like  CPLEX  \citep{iamigo:cplex}  which  are  less  memory
 commercial  solvers  like  CPLEX  \citep{iamigo:cplex}  which  are  less  memory

-consuming and more efficient, or implement a lightweight heuristic. For example,
-for  a WSN  of 200  sensor nodes,  a leader  node has  to deal  with constraints
-induced  by about  12 sensor  nodes.  In  that case,  to solve  the optimization
-problem  a memory  consumption of  more  than 1~MB  can be  observed with  GLPK,
-whereas less than 300~KB would be needed with CPLEX.
+consuming and  more efficient  is possible,  or a  lightweight heuristic  may be
+implemented. For example,  for a WSN of  200 sensor nodes, a leader  node has to
+deal with constraints induced by about 12  sensor nodes.  In that case, to solve
+the optimization problem a memory consumption  of more than 1~MB can be observed
+with GLPK, whereas less than 300~KB would be needed with CPLEX.

 
 Besides  PeCO,   three  other  protocols   will  be  evaluated   for  comparison
 purposes. The first one, called DESK,  is a fully distributed coverage algorithm
 
 Besides  PeCO,   three  other  protocols   will  be  evaluated   for  comparison
 purposes. The first one, called DESK,  is a fully distributed coverage algorithm


@@ -798,8 +737,8 @@ proposed      by     \citep{ChinhVu}.       The      second     one,      called
 GAF~\citep{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
 GAF~\citep{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~\citep{Idrees2}, is an improved version of a research work we presented
-in~\citep{idrees2014coverage}. Let us  notice that the PeCO  and DiLCO protocols
+protocol~\citep{Idrees2}, is an improved version of a research work presented
+in~\citep{idrees2014coverage}. PeCO  and DiLCO protocols

 are based on  the same framework. In particular, the  choice for the simulations
 of  a partitioning  in  16~subregions was  made because  it  corresponds to  the
 configuration producing  the best results for  DiLCO. Of course, this  number of
 are based on  the same framework. In particular, the  choice for the simulations
 of  a partitioning  in  16~subregions was  made because  it  corresponds to  the
 configuration producing  the best results for  DiLCO. Of course, this  number of


@@ -808,8 +747,9 @@ the number of sensors.  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.  The DiLCO  protocol  tries  to satisfy  the
 coverage of a set of primary points,  whereas the objective of the PeCO protocol
 formulation of the integer program providing the set of sensors which have to be
 activated  in each  sensing  phase.  The DiLCO  protocol  tries  to satisfy  the
 coverage of a set of primary points,  whereas the objective of the PeCO protocol

-is  to reach  a desired  level of  coverage for  each sensor  perimeter. In  our
-experimentations, we chose a level of coverage equal to one ($l=1$).
+is  to reach  a desired  level of  coverage for  each sensor  perimeter. In the
+experimentations, a level of coverage equal to one ($l=1$) is chosen
+.

 
 \subsubsection{Coverage Ratio}
 
 
 \subsubsection{Coverage Ratio}
 


@@ -835,13 +775,13 @@ allows later a substantial increase of the coverage performance.
 
 \subsubsection{Active Sensors Ratio}
 
 
 \subsubsection{Active Sensors Ratio}
 

-Minimizing the number of active sensor nodes in  each period is essential to minimize the
-energy   consumption    and   thus    to   maximize   the    network   lifetime.
+Minimizing the  number of  active sensor  nodes in each  period is  essential to
+minimize  the energy  consumption and  thus  to maximize  the network  lifetime.

 Figure~\ref{figure6}  shows the  average  active nodes  ratio  for 200  deployed
 Figure~\ref{figure6}  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 the DiLCO and PeCO protocols  compete perfectly with
-only 17.92~\%  and 20.16~\% active nodes  during the same time  interval. As the
-number of periods increases, the PeCO protocol has a lower number of active nodes in
+nodes.  DESK and  GAF have  30.36~\%  and 34.96~\%  active nodes  for the  first
+fourteen rounds,  and the DiLCO and  PeCO protocols compete perfectly  with only
+17.92~\% and 20.16~\% active nodes during  the same time interval. As the number
+of periods increases,  the PeCO protocol has  a lower number of  active nodes in

 comparison with the  three other approaches and exhibits a  slow decrease, while
 keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 
 comparison with the  three other approaches and exhibits a  slow decrease, while
 keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 


@@ -852,91 +792,99 @@ keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 \label{figure6}
 \end{figure} 
 
 \label{figure6}
 \end{figure} 
 

-\subsubsection{\textcolor{blue}{Energy Saving Ratio (ESR)}} 
+\subsubsection{Energy Saving Ratio} 

 
 

-\textcolor{blue}{In this experiment, we consider an Energy Saving Ratio (see Figure~\ref{fig5}) for 200 deployed nodes. 
-The  longer the ratio  is,  the more  redundant sensor  nodes are switched off, and consequently  the longer the  network may  live. }
+The simulation results  show that the protocol PeCO saves  efficiently energy by
+turning   off  some   sensors   during   the  sensing   phase.    As  shown   in
+Figure~\ref{figure7}, GAF provides better energy  saving than PeCO for the first
+fifty  rounds. Indeed  GAF balances  the energy  consumption among  sensor nodes
+inside each small fixed  grid and thus permits to extend the  life of sensors in
+each  grid fairly.  However, at  the same  time it  turns on  a large  number of
+sensors  and that  leads  later  to quickly  deplete  sensor's batteries.   DESK
+algorithm  shows  less  energy  saving   compared  with  other  approaches.   In
+comparison  with  PeCO, DiLCO  protocol  usually  provides lower  energy  saving
+ratios.  Moreover, it  can  be noticed  that after  round  fifty, PeCO  protocol
+exhibits the slowest decrease among all the considered protocols.

 
 \begin{figure}[h!]
 %\centering
 % \begin{multicols}{6}
 \centering
 
 \begin{figure}[h!]
 %\centering
 % \begin{multicols}{6}
 \centering

-\includegraphics[scale=0.5]{ESR.eps} %\\~ ~ ~(a)
-\caption{Energy Saving Ratio for 200 deployed nodes}
-\label{fig5}
-\end{figure} 
-
-\textcolor{blue}{The simulation results show that our protocol PeCO allows to efficiently save energy by turning off some sensors during the sensing phase. 
-As shown in Figure~\ref{fig5}, GAF provides better energy saving than PeCO for the first fifty rounds, because GAF balance the energy consumption among sensor nodes inside each small fixed grid that permits to extend the life of sensors in each grid fairly but in the same time turn on large number of sensors during sensing that lead later to quickly deplete sensor's batteries togehter. After that GAF provide less energy saving compared with other approches because of the large number of dead nodes. DESK algorithm shows less energy saving compared with other approaches due to activate a larg number of sensors during the sensing. DiLCO protocol provides less energy saving ratio commpared with PeCO because it generally activate a larger number of sensor nodes during sensing. Note that again as the number of  rounds increases PeCO becomes  the most performing one, since it consumes less energy compared with other approaches.}
-
+\includegraphics[scale=0.5]{figure7.eps} %\\~ ~ ~(a)
+\caption{Energy Saving Ratio for 200 deployed nodes.}
+\label{figure7}
+\end{figure}

 
 \subsubsection{Energy Consumption}
 
 The  effect  of  the  energy  consumed by  the  WSN  during  the  communication,
 computation,  listening,  active, and  sleep  status  is studied  for  different
 
 \subsubsection{Energy Consumption}
 
 The  effect  of  the  energy  consumed by  the  WSN  during  the  communication,
 computation,  listening,  active, and  sleep  status  is studied  for  different

-network densities  and the  four approaches  compared.  Figures~\ref{figure7}(a)
+network densities  and the  four approaches  compared.  Figures~\ref{figure8}(a)

 and (b)  illustrate the energy consumption  for different network sizes  and for
 and (b)  illustrate the energy consumption  for different network sizes  and for

-$Lifetime_{95}$ and $Lifetime_{50}$.  The results show  that the PeCO protocol is the most
-competitive from the energy consumption point of view. As shown by both figures,
-PeCO consumes much less energy than the  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 also  the energy consumption  while keeping  a good
-coverage level. Let  us notice that the energy overhead  when increasing network
-size is the lowest with PeCO.
+$Lifetime_{95}$ and $Lifetime_{50}$.  The results show that the PeCO protocol is
+the most competitive from the energy consumption point of view. As shown by both
+figures, PeCO consumes much less energy  than the 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 also the energy consumption while
+keeping a good coverage level. The  energy overhead when increasing network size
+is the lowest with PeCO.

 
 \begin{figure}[h!]
   \centering
   \begin{tabular}{@{}cr@{}}
 
 \begin{figure}[h!]
   \centering
   \begin{tabular}{@{}cr@{}}

-    \includegraphics[scale=0.5]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
-    \includegraphics[scale=0.5]{figure7b.eps} & \raisebox{2.75cm}{(b)}
+    \includegraphics[scale=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
+    \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)}

   \end{tabular}
   \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
   \end{tabular}
   \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}

-  \label{figure7}
+  \label{figure8}

 \end{figure} 
 
 \subsubsection{Network Lifetime}
 
 \end{figure} 
 
 \subsubsection{Network Lifetime}
 

-We observe the  superiority of both the PeCO and DiLCO  protocols in comparison with
-the   two   other  approaches   in   prolonging   the  network   lifetime.    In
-Figures~\ref{figure8}(a) and  (b), $Lifetime_{95}$  and $Lifetime_{50}$ are  shown for
-different  network  sizes.  As  can  be  seen  in  these figures,  the  lifetime
-increases with the size of the network,  and it is clearly larger for the DiLCO and
-PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio
-greater than  50\%, we can see  on Figure~\ref{figure8}(b) that the  lifetime is
-about  twice  longer with  PeCO  compared  to  the DESK protocol.   The  performance
-difference    is   more    obvious    in    Figure~\ref{figure8}(b)   than    in
-Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
-time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
+In comparison with the two other approaches, PeCO and DiLCO protocols are better
+for  prolonging  the network  lifetime.   In  Figures~\ref{figure9}(a) and  (b),
+$Lifetime_{95}$ and $Lifetime_{50}$  are shown for different  network sizes.  As
+can  be seen  in these  figures, the  lifetime increases  with the  size of  the
+network,  and it  is  clearly larger  for  the DiLCO  and  PeCO protocols.   For
+instance, for a network of 300~sensors  and coverage ratio greater than 50\%, it
+can  be observed  on Figure~\ref{figure9}(b)  that the  lifetime is  about twice
+longer with PeCO  compared to the DESK protocol.  The  performance difference is
+more obvious in Figure~\ref{figure9}(b)  than in Figure~\ref{figure9}(a) because
+the gain  induced by  protocols (PeCO  and DiLCO) increases  with time,  and the
+lifetime with a coverage over 50\% is far longer than with 95\%.

 
 \begin{figure}[h!]
   \centering
   \begin{tabular}{@{}cr@{}}
 
 \begin{figure}[h!]
   \centering
   \begin{tabular}{@{}cr@{}}

-    \includegraphics[scale=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\  
-    \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)}
+    \includegraphics[scale=0.5]{figure9a.eps} & \raisebox{2.75cm}{(a)} \\  
+    \includegraphics[scale=0.5]{figure9b.eps} & \raisebox{2.75cm}{(b)}

   \end{tabular}
   \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
   \end{tabular}
   \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}

-  \label{figure8}
+  \label{figure9}

 \end{figure} 
 
 \end{figure} 
 

-Figure~\ref{figure9} compares the lifetime coverage  of the DiLCO and PeCO 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  $50\%$, $80\%$,  $85\%$,
+Figure~\ref{figure10}  compares the  lifetime  coverage of  the  DiLCO and  PeCO
+protocols for different coverage ratios.  Protocol/70, Protocol/80, Protocol/85,
+Protocol/90, and Protocol/95  correspond to the amount of time  during which the
+network  can satisfy  an  area  coverage greater  than  $70\%$, $80\%$,  $85\%$,

 $90\%$, and  $95\%$ respectively,  where the  term Protocol  refers to  DiLCO or
 $90\%$, and  $95\%$ respectively,  where the  term Protocol  refers to  DiLCO or

-PeCO.  \textcolor{blue}{Indeed there are applications that do not require a 100\% coverage of the
-area to be  monitored. For example, forest
-fire application might require complete coverage
-in summer seasons while only requires 80$\%$ of the area to be covered in rainy seasons \cite{li2011transforming}. As another example, birds habit study requires only 70$\%$-coverage at nighttime when the birds are sleeping while requires 100$\%$-coverage at daytime when the birds are active \cite{vu2009universal}. Mudflows monitoring applications may require part of the area to be covered in sunny days. Thus, to extend network lifetime, the coverage quality can be decreased if it is acceptable\cite{wang2014keeping}}. PeCO might be  an interesting method since  it achieves a good balance  between a high level  coverage ratio  and network  lifetime. PeCO
-always  outperforms DiLCO  for the  three  lower coverage  ratios, moreover  the
-improvements grow  with the network  size. \textcolor{blue}{DiLCO outperforms PeCO when the coverage ratio is required to be $>90\%$, but PeCo extends the network lifetime significantly when coverage ratio can be relaxed.}
-%DiLCO  is better for  coverage ratios near 100\%, but  in that case PeCO  is not ineffective for  the smallest network sizes.
+PeCO. Indeed there are applications that do  not require a 100\% coverage of the
+area  to  be monitored.  For  example,  forest  fire application  might  require
+complete coverage in summer seasons while only  require 80$\%$ of the area to be
+covered in  rainy seasons~\citep{li2011transforming}. As another  example, birds
+habit  study requires  only  70$\%$-coverage  at nighttime  when  the birds  are
+sleeping  while  requires  100$\%$-coverage  at   daytime  when  the  birds  are
+active~\citep{1279193}.   PeCO  always outperforms  DiLCO  for  the three  lower
+coverage ratios,  moreover the  improvements grow with  the network  size. DiLCO
+outperforms PeCO  when the coverage  ratio is required  to be $>90\%$,  but PeCO
+extends the network lifetime significantly when coverage ratio can be relaxed.

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

-\centering \includegraphics[scale=0.55]{figure9.eps}
+\centering \includegraphics[scale=0.55]{figure10.eps}

 \caption{Network lifetime for different coverage ratios.}
 \caption{Network lifetime for different coverage ratios.}

-\label{figure9}
+\label{figure10}

 \end{figure} 
 
 \subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}
 \end{figure} 
 
 \subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}


@@ -948,16 +896,14 @@ hand,  the choice  of $\beta  \gg \alpha$  prevents the  overcoverage, and  also
 limits the activation of a large number of sensors, but as $\alpha$ is low, some
 areas  may  be   poorly  covered.   This  explains  the   results  obtained  for
 $Lifetime_{50}$ with  $\beta \gg  \alpha$: a  large number  of periods  with low
 limits the activation of a large number of sensors, but as $\alpha$ is low, some
 areas  may  be   poorly  covered.   This  explains  the   results  obtained  for
 $Lifetime_{50}$ with  $\beta \gg  \alpha$: a  large number  of periods  with low

-coverage ratio.  On the other hand, when  we choose $\alpha \gg \beta$, we favor
-the coverage even if some areas may  be overcovered, so a high coverage ratio is
-reached,  but a  large number  of sensors  are activated  to achieve  this goal.
-Therefore  the  network  lifetime  is  reduced.   The  choice  $\alpha=0.6$  and
+coverage  ratio.  On  the other  hand, when  $\alpha \gg  \beta$ is  chosen, the
+coverage is favored  even if some areas  may be overcovered, so  a high coverage
+ratio is reached,  but a large number  of sensors are activated  to achieve this
+goal.  Therefore the  network lifetime is reduced.  The  choice $\alpha=0.6$ and

 $\beta=0.4$ seems to  achieve the best compromise between  lifetime and coverage
 $\beta=0.4$ seems to  achieve the best compromise between  lifetime and coverage

-ratio.   That explains  why  we have  chosen this  setting  for the  experiments
+ratio.   That explains  why this  setting has  been chosen  for the  experiments

 presented in the previous subsections.
 
 presented in the previous subsections.
 

-%As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
-

 \begin{table}[h]
 \centering
 \caption{The impact of $\alpha$ and $\beta$ on PeCO's performance}
 \begin{table}[h]
 \centering
 \caption{The impact of $\alpha$ and $\beta$ on PeCO's performance}


@@ -983,36 +929,34 @@ $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
 \section{Conclusion and Future Works}
 \label{sec:Conclusion and Future Works}
 
 \section{Conclusion and Future Works}
 \label{sec:Conclusion and Future Works}
 

-In this paper we have studied  the problem of perimeter coverage optimization in
-WSNs.   We  have  designed  a  new  protocol,  called  Perimeter-based  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. Several simulations have
-been carried out to evaluate the  proposed protocol. The simulation results show
-that  PeCO is  more  energy-efficient  than other  approaches,  with respect  to
-lifetime, coverage ratio, active sensors ratio, and energy consumption.
-
-We plan to extend  our framework so that the schedules  are planned for multiple
-sensing  periods. We  also want  to  improve the  integer program  to take  into
-account heterogeneous sensors from both energy and node characteristics point of
-views.  Finally, it would be interesting  to implement the PeCO protocol using a
+In this  paper the problem of  perimeter coverage optimization in  WSNs has been
+studied.   A  new  protocol  called  Perimeter-based  Coverage  Optimization  is
+designed. This protocol  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.
+This 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.  Several
+simulations  have  been carried  out  to  evaluate  the proposed  protocol.  The
+simulation  results  show   that  PeCO  is  more   energy-efficient  than  other
+approaches, with respect to lifetime,  coverage ratio, active sensors ratio, and
+energy consumption.
+
+This framework will  be extented so that the schedules  are planned for multiple
+sensing periods.  The integer  program would  be improved  to take  into account
+heterogeneous sensors from both energy  and node characteristics point of views.
+Finally,  it  would be  interesting  to  implement  the  PeCO protocol  using  a

 sensor-testbed to evaluate it in real world applications.
 
 \subsection*{Acknowledgments}
 sensor-testbed to evaluate it in real world applications.
 
 \subsection*{Acknowledgments}

-The  authors  are   deeply  grateful  to  the  anonymous   reviewers  for  their
-constructive advice,  which improved the  technical quality  of the paper.  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 is also partially funded by the Labex ACTION program
+Ali  Kadhum Idrees is supported in part by University of  Babylon (Iraq). 
+This work is also partially funded by the Labex ACTION program

 (contract ANR-11-LABX-01-01).  
  
 \bibliographystyle{gENO}
 (contract ANR-11-LABX-01-01).  
  
 \bibliographystyle{gENO}

-\bibliography{biblio} % biblio
+\bibliography{biblio} 

 
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