X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/blobdiff_plain/900859cd09dd04b3dd6cbd7b932ad46d844a8cc6..32bb9d99dab11650563d89a201f193aca31a93c4:/PeCO-EO/articleeo.tex?ds=sidebyside

diff --git a/PeCO-EO/articleeo.tex b/PeCO-EO/articleeo.tex
index 9968b77..f9a5f6d 100644
--- a/PeCO-EO/articleeo.tex
+++ b/PeCO-EO/articleeo.tex
@@ -2,17 +2,12 @@
 % 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}
 
-%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}
-
-%\articletype{GUIDE}
-
 \title{{\itshape Perimeter-based Coverage Optimization \\
   to Improve Lifetime in Wireless Sensor Networks}}
 
@@ -29,11 +24,10 @@ 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. We
-propose such  an approach called Perimeter-based  Coverage Optimization protocol
-(PeCO). It  is a hybrid  of centralized and  distributed methods: the  region of
+scheduling which ensures  sensing coverage while minimizing the  energy cost. 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 our approach
+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
@@ -89,15 +83,14 @@ 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
-  the literature,  we formulate a  mixed-integer program based on  the perimeter
-  coverage of each sensor.  The model  involves integer variables to capture the
+  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
-  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
+  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}
@@ -134,7 +127,7 @@ 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
-  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
@@ -212,8 +205,8 @@ 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
-  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.}
@@ -221,12 +214,6 @@ 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}
 
-%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}
@@ -242,7 +229,7 @@ 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
-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.
@@ -256,9 +243,9 @@ $k$~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,
-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
+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.
@@ -364,7 +351,7 @@ optimization algorithm.
 \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
@@ -397,7 +384,7 @@ of the application.
 \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.
@@ -424,10 +411,6 @@ applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 
 
 \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{$RE_k \geq E_{th}$}{
@@ -462,42 +445,6 @@ applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
   }
 \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
@@ -506,7 +453,8 @@ $RE_k$, 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. \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)}
+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}
@@ -568,7 +516,7 @@ 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
-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.
@@ -585,18 +533,6 @@ The coverage optimization problem can then be mathematically expressed as follow
   \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
@@ -633,7 +569,7 @@ 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
-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]
@@ -696,7 +632,7 @@ 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
-  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
@@ -706,7 +642,7 @@ 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.
-\item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to
+\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:
@@ -718,14 +654,12 @@ approach.
   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*}  
-  }
 \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
@@ -750,9 +684,9 @@ approach.
 
 \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)
+
+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
@@ -784,9 +718,9 @@ 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)  \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
-consuming and more efficient, or implement a lightweight heuristic. For example,
+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,
@@ -798,8 +732,8 @@ 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
-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
@@ -808,8 +742,9 @@ 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
-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}
 
@@ -838,7 +773,7 @@ allows later a substantial increase of the coverage performance.
 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
-nodes.  We observe that DESK and GAF have 30.36~\% and 34.96~\% active nodes for
+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
@@ -852,29 +787,35 @@ keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 \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
-\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
-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
 $Lifetime_{95}$ 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,
@@ -883,60 +824,58 @@ 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
+coverage level. The energy overhead  when increasing network
 size is the lowest with PeCO.
 
 \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)~$Lifetime_{50}$.}
-  \label{figure7}
+  \label{figure8}
 \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
+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\%, we can see  on Figure~\ref{figure8}(b) that the  lifetime is
+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{figure8}(b)   than    in
-Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
+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@{}}
-    \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)~$Lifetime_{50}$.}
-  \label{figure8}
+  \label{figure9}
 \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
-PeCO.  \textcolor{blue}{Indeed there are applications that do not require a 100\% coverage of the
+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 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.
+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!]
-\centering \includegraphics[scale=0.55]{figure9.eps}
+\centering \includegraphics[scale=0.55]{figure10.eps}
 \caption{Network lifetime for different coverage ratios.}
-\label{figure9}
+\label{figure10}
 \end{figure} 
 
 \subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}
@@ -948,15 +887,15 @@ 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
-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
+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
-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.
 
-%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
@@ -983,14 +922,14 @@ $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
 \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
+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.  Our  work is
+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
@@ -998,8 +937,8 @@ 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
+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.
@@ -1013,6 +952,6 @@ received support. This work is also partially funded by the Labex ACTION program
 (contract ANR-11-LABX-01-01).  
  
 \bibliographystyle{gENO}
-\bibliography{biblio} %articleeo
+\bibliography{biblio} 
 
 \end{document}
