X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Sensornets15.git/blobdiff_plain/c9f589ebfb3152a538f0362a51412d6963b9963b..ad0f1593c3a19abcc1abeed173f08282b0067936:/Example.tex

diff --git a/Example.tex b/Example.tex
index 8ed81a6..94a8536 100644
--- a/Example.tex
+++ b/Example.tex
@@ -53,7 +53,7 @@ Optimization, Scheduling.}
   to ensure  coverage at  a low  energy cost, allowing  to optimize  the network
   lifetime. More  precisely, a period  consists of four  phases: (i)~Information
   Exchange,  (ii)~Leader   Election,  (iii)~Decision,  and   (iv)~Sensing.   The
-  decision process,  which result in  an activity scheduling vector,  is carried
+  decision process, which results in  an activity scheduling vector,  is carried
   out by a leader node through  the solving of an integer program. In comparison
   with  some other  protocols, the  simulations  done using  the discrete  event
   simulator OMNeT++ show that our approach  is able to increase the WSN lifetime
@@ -63,42 +63,39 @@ Optimization, Scheduling.}
 
 \section{\uppercase{Introduction}}
 \label{sec:introduction}
+
 \noindent 
 Energy efficiency is  a crucial issue in wireless  sensor networks since sensory
-consumption,  in order  to maximize  the network  lifetime, represent  the major
+consumption, in  order to  maximize the network  lifetime, represents  the major
 difficulty when designing WSNs. As a consequence, one of the scientific research
 challenges in  WSNs, which has  been addressed by  a large amount  of literature
 during the  last few  years, is  the design of  energy efficient  approaches for
 coverage and connectivity~\cite{conti2014mobile}.   Coverage reflects how well a
-sensor field is  monitored.  The most discussed coverage  problems in literature
-can  be classified into  three types  \cite{li2013survey}: area  coverage (where
-every point inside an area is  to be monitored), target coverage (where the main
-objective is to  cover only a finite number of  discrete points called targets),
-and  barrier coverage (to  prevent intruders  from entering  into the  region of
-interest). On the one  hand we want to monitor the area  of interest in the most
-efficient way~\cite{Nayak04}. On the other hand we want to use as less energy as
-possible.  Sensor nodes  are  battery-powered  with no  means  of recharging  or
-replacing, usually due to environmental (hostile or unpractical environments) or
-cost reasons.  Therefore, it  is desired  that the WSNs  are deployed  with high
-densities so as to exploit the  overlapping sensing regions of some sensor nodes
-to save energy by  turning off some of them during the  sensing phase to prolong
-the network lifetime.
+sensor  field is  monitored. On  the one  hand we  want to  monitor the  area of
+interest in the most efficient way~\cite{Nayak04}.  On the other hand we want to
+use as less energy as possible.   Sensor nodes are battery-powered with no means
+of recharging or replacing, usually due to environmental (hostile or unpractical
+environments)  or cost  reasons.  Therefore,  it is  desired that  the  WSNs are
+deployed with high densities so as to exploit the overlapping sensing regions of
+some sensor nodes to save energy by  turning off some of them during the sensing
+phase to prolong the network lifetime.
 
 In this  paper we design  a protocol that  focuses on the area  coverage problem
 with  the objective  of maximizing  the network  lifetime. Our  proposition, the
-DiLCO protocol,  maintains the coverage and  improves the lifetime  in WSNs. The
-area of  interest is  first divided into  subregions using  a divide-and-conquer
-algorithm and  an activity scheduling  for sensor nodes  is then planned  by the
-elected leader in each subregion. In fact,  the nodes in a subregion can be seen
-as a cluster where each node sends  sensing data to the cluster head or the sink
-node.  Furthermore, the  activities in a subregion/cluster can  continue even if
-another cluster  stops due to too  many node failures.  Our Distributed Lifetime
-Coverage Optimization (DILCO) protocol  considers periods, where a period starts
-with  a  discovery phase  to  exchange information  between  sensors  of a  same
+Distributed  Lifetime  Coverage  Optimization  (DILCO) protocol,  maintains  the
+coverage  and improves  the lifetime  in  WSNs. The  area of  interest is  first
+divided  into subregions using  a divide-and-conquer  algorithm and  an activity
+scheduling  for sensor  nodes is  then  planned by  the elected  leader in  each
+subregion. In fact, the nodes in a subregion can be seen as a cluster where each
+node sends sensing data to the  cluster head or the sink node.  Furthermore, the
+activities in a subregion/cluster can continue even if another cluster stops due
+to too many node failures.  Our DiLCO protocol considers periods, where a period
+starts with a discovery phase to  exchange information between sensors of a same
 subregion, in order to choose in a suitable manner a sensor node (the leader) to
 carry out the coverage strategy. In each subregion the activation of the sensors
 for the  sensing phase of the current  period is obtained by  solving an integer
-program.
+program. The  resulting activation  vector is broadcasted  by a leader  to every
+node of its subregion.
 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes
@@ -110,7 +107,117 @@ in Section~\ref{sec:Conclusion and Future Works}.
 
 \section{\uppercase{Literature Review}}
 \label{sec:Literature Review}
-\noindent In this section, we summarize some related works regarding coverage lifetime maximization and scheduling, and distinguish our DiLCO protocol from the works presented in the literature. Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
+
+\noindent In  this section, we  summarize some related works  regarding coverage
+problem  and distinguish  our DiLCO  protocol from  the works  presented  in the
+literature.
+
+The most discussed coverage  problems in literature
+can  be classified into  three types  \cite{li2013survey}: area  coverage (where
+every point inside an area is  to be monitored), target coverage (where the main
+objective is to  cover only a finite number of  discrete points called targets),
+and  barrier coverage (to  prevent intruders  from entering  into the  region of
+interest). 
+{\it In DiLCO  protocol, the area coverage, i.e. the coverage  of every point in
+  the sensing  region, is transformed  to the coverage  of a fraction  of points
+  called primary points. }
+
+The major  approach to extend network  lifetime while preserving  coverage is to
+divide/organize the  sensors into a suitable  number of set  covers (disjoint or
+non-disjoint)  where each  set completely  covers a  region of  interest  and to
+activate these set  covers successively. The network activity  can be planned in
+advance and scheduled  for the entire network lifetime  or organized in periods,
+and the set of  active sensor nodes is decided at the  beginning of each period.
+Active node selection is determined based on the problem requirements (e.g. area
+monitoring,  connectivity,  power   efficiency).  Different  methods  have  been
+proposed in literature.
+{\it DiLCO protocol  works in periods, where each  period contains a preliminary
+  phase  for information  exchange and  decisions, followed  by a  sensing phase
+  where one cover set is in charge of the sensing task.}
+
+Various   approaches,   including   centralized,  distributed,   and   localized
+algorithms, have been proposed to extend the network lifetime.
+%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
+%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. 
+In       distributed      algorithms~\cite{yangnovel,ChinhVu,qu2013distributed},
+information  is   disseminated  throughout   the  network  and   sensors  decide
+cooperatively by communicating with their neighbors which of them will remain in
+sleep    mode   for    a   certain    period   of    time.     The   centralized
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always
+provide nearly or close to optimal  solution since the algorithm has global view
+of the whole  network, but such a method has the  disadvantage of requiring high
+communication costs,  since the  node (located at  the base station)  making the
+decision needs information from all the sensor nodes in the area.
+
+A large  variety of coverage scheduling  algorithms have been  proposed. Many of
+the existing  algorithms, dealing with the  maximization of the  number of cover
+sets, are heuristics.  These heuristics  involve the construction of a cover set
+by including in priority the sensor  nodes which cover critical targets, that is
+to  say targets  that  are covered  by  the smallest  number  of sensors.  Other
+approaches  are based  on  mathematical programming  formulations and  dedicated
+techniques (solving with a branch-and-bound algorithms available in optimization
+solver).  The problem is formulated  as an optimization problem (maximization of
+the  lifetime  or  number  of  cover  sets) under  target  coverage  and  energy
+constraints.   Column  generation techniques,  well-known  and widely  practiced
+techniques for solving  linear programs with too many  variables, have been also
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+
+Diongue  and  Thiare~\cite{diongue2013alarm}  proposed  an  energy  aware  sleep
+scheduling  algorithm  for lifetime  maximization  in  wireless sensor  networks
+(ALARM).  The proposed approach permits to schedule redundant nodes according to
+the weibull distribution.  This work did not analyze the  ALARM scheme under the
+coverage problem.
+
+Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be
+changed  into a  set coverage  problem. By  using this  model, they  proposed an
+Energy-Efficient central-Scheduling  greedy algorithm, which  can reduces energy
+consumption and increases network lifetime, by selecting a appropriate subset of
+sensor nodes to support the networks periodically.
+
+In ~\cite{chenait2013distributed},  the authors presented  a coverage-guaranteed
+distributed  sleep/wake scheduling  scheme so  ass to  prolong  network lifetime
+while guaranteeing network coverage. This scheme mitigates scheduling process to
+be more stable by avoiding  useless transitions between states without affecting
+the coverage level required by the application.
+
+The work  in~\cite{cheng2014achieving} presented a  unified sensing architecture
+for duty  cycled sensor  networks, called uSense,  which comprises  three ideas:
+Asymmetric Architecture, Generic Switching  and Global Scheduling. The objective
+is to provide a flexible and efficient coverage in sensor networks.
+
+In~\cite{ling2009energy},  the  lifetime  of  a  sensor  node  is  divided  into
+epochs. At  each epoch,  the base station  deduces the current  sensing coverage
+requirement  from application  or user  request. It  then applies  the heuristic
+algorithm in order to produce the set  of active nodes which take the mission of
+sensing during the current epoch.  After  that, the produced schedule is sent to
+the sensor nodes in the network.
+
+{\it  In DiLCO  protocol,  the area  coverage  is divided  into several  smaller
+  subregions, and in  each of which, a  node called the leader is  on charge for
+  selecting the active sensors for the current period.}
+
+Yang et al.~\cite{yang2014energy} investigated  full area coverage problem under
+the probabilistic  sensing model in the  sensor networks. They  have studied the
+relationship between the coverage of two adjacent points mathematically and then
+convert  the problem of  full area  coverage into  point coverage  problem. They
+proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select
+a subset of sensors to provide  probabilistic area coverage dynamically so as to
+extend the network lifetime.
+
+The work proposed by  \cite{qu2013distributed} considers the coverage problem in
+WSNs where  each sensor has variable  sensing radius. The final  objective is to
+maximize the network coverage lifetime in WSNs.
+
+{\it  In DiLCO  protocol,  each leader,  in  each subregion,  solves an  integer
+  program with a double objective  consisting in minimizing the overcoverage and
+  limiting  the  undercoverage.  This  program  is inspired  from  the  work  of
+  \cite{pedraza2006}  where the  objective is  to maximize  the number  of cover
+  sets.}
+ 
+
+\iffalse
+
+Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
 
 
 Yang et al.~\cite{yang2014energy} investigated full area coverage problem
@@ -137,7 +244,7 @@ The work in~\cite{cheng2014achieving} presented a unified sensing architecture f
 a sensor node is divided into epochs. At each epoch, the
 base station deduces the current sensing coverage requirement
 from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch.  After that, the produced schedule is sent to the sensor nodes in the network. 
-
+\fi
 
 \iffalse
 
@@ -155,7 +262,7 @@ coverage. They are proposed a low-complexity heuristic algorithm to obtain full
 achieve increased sensing lifetime of the network. 
 
 
-\fi
+
   
 
 
@@ -163,10 +270,10 @@ In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (
 
 The main contributions of our DiLCO Protocol can be summarized as follows:
 (1) The distributed optimization over the subregions in the area of interest, 
-(2) The distributed dynamic leader election at each round by each sensor node in the subregion, 
+(2) The distributed dynamic leader election at each period by each sensor node in the subregion, 
 (3) The primary point coverage model to represent each sensor node in the network, 
 (4) The activity scheduling based optimization on the subregion, which are based on  the primary point coverage model to activate as less number as possible of sensor nodes  to take the mission of the coverage in each subregion, and (5) The improved energy consumption model.
-
+\fi
 \iffalse
 The work presented in~\cite{luo2014parameterized,tian2014distributed} tries to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
 %Je ne comprends pas la phrase ci-dessus
@@ -178,9 +285,9 @@ Our Work in~\cite{idrees2014coverage} proposes a coverage optimization protocol
 The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
 
 The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
-\fi
 
-\iffalse
+
+
 Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to  extend the network lifetime with connectivity and coverage constraints. They are included  two heuristic methods  within the CG framework so as to accelerate the solution process. 
 In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution  taking into consideration frequent nodes failure.
 Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
@@ -200,7 +307,7 @@ The main contributions of our DiLCO Protocol can be summarized as follows:
 
 \fi
 
-\section{ The DiLCO Protocol Description}
+\section{\uppercase{Description of the DiLCO protocol}}
 \label{sec:The DiLCO Protocol Description}
 
 \noindent In this section, we  introduce the DiLCO protocol which is distributed
@@ -224,7 +331,7 @@ simple  energy model that  takes communication,  sensing and  computation energy
 consumptions into account to evaluate the performance of our protocol. 
 \fi
 
-\subsection{ Assumptions and models}
+\subsection{Assumptions and models}
 
 \noindent  We consider  a sensor  network composed  of static  nodes distributed
 independently and uniformly at random.  A high density deployment ensures a high
@@ -324,7 +431,7 @@ phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
 Decision) are  energy consuming for all the  nodes, even nodes that  will not be
 retained by the leader to keep watch over the corresponding area.
 
-During the excution of the DiLCO protocol, two kinds of packets will be used:
+During the execution of the DiLCO protocol, two kinds of packets will be used:
 %\begin{enumerate}[(a)]
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
@@ -365,7 +472,7 @@ Active-Sleep packet to know its state for the coming sensing phase.
 \subsubsection{Information Exchange Phase}
 
 Each sensor node $j$ sends its position, remaining energy $RE_j$, and
-the number of neighbours  $NBR_j$ to all wireless sensor nodes in
+the number of neighbors  $NBR_j$ to all wireless sensor nodes in
 its subregion by using an INFO packet and then listens to the packets
 sent from  other nodes.  After that, each  node will  have information
 about  all the  sensor  nodes in  the  subregion.  In  our model,  the
@@ -380,7 +487,7 @@ independently  for each  round.  All the  sensor  nodes cooperate  to
 select WSNL.  The nodes in the  same subregion will  select the leader
 based on  the received  information from all  other nodes in  the same
 subregion.  The selection criteria  in order  of priority  are: larger
-number  of neighbours,  larger remaining  energy, and  then in  case of
+number  of neighbors,  larger remaining  energy, and  then in  case of
 equality, larger index. 
 
 \subsubsection{Decision phase}
@@ -457,7 +564,7 @@ The sensor node enter in listening mode waiting to receive ActiveSleep packet fr
 \fi
 
 
-\section{Coverage problem formulation}
+\section{\uppercase{Coverage problem formulation}}
 \label{cp}
 
 \indent Our model is based on the model proposed by \cite{pedraza2006} where the
@@ -500,10 +607,9 @@ We define the Overcoverage variable $\Theta_{p}$ as:
 \end{array} \right.
 \label{eq13} 
 \end{equation}
-\noindent More precisely, $\Theta_{p}$ represents the number of active
-sensor  nodes  minus  one  that  cover the  primary  point  $p$.\\
-The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
-by:
+\noindent More  precisely, $\Theta_{p}$ represents  the number of  active sensor
+nodes minus  one that  cover the primary  point~$p$. The  Undercoverage variable
+$U_{p}$ of the primary point $p$ is defined by:
 \begin{equation}
 U_{p} = \left \{ 
 \begin{array}{l l}
@@ -654,22 +760,35 @@ ActiveSleep  packet. To  compute the  energy  needed by  a node  to transmit  or
 receive such  packets, we  use the equation  giving the  energy spent to  send a
 1-bit-content   message  defined   in~\cite{raghunathan2002energy}   (we  assume
 symmetric  communication costs), and  we set  their respective  size to  112 and
-24~bits. The energy required to send or receive a 1-bit is equal to $0.2575 mW$.
+24~bits. The energy required to send  or receive a 1-bit-content message is thus
+is equal to 0.2575 mW.
 
 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
-$E_{th}=36$~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 has
-been computed  by multiplying the energy  consumed in active state  (9.72 mW) by
-the time in  second for one round (3600 seconds).  According  to the interval of
-initial energy, a sensor may be active during at most 20 rounds.
-
-In the simulations,  we introduce the following performance  metrics to evaluate
+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.
+
+In the simulations,  we introduce the follow80ing performance  metrics to evaluate
 the efficiency of our approach:
 
 %\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
@@ -700,29 +819,15 @@ Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round
 
 \fi
 
-\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  Energy Consumption}:}  Energy Consumption (EC)  can be seen  as the
+\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:
- \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},
-\end{equation*}
-
-%\begin{equation*}
-%\scriptsize
-%\mbox{EC} =  \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
-%\end{equation*}
+  \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},
+  \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
@@ -735,15 +840,17 @@ 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).
 
+
 \iffalse 
-\item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power,
-therefore it is important that the proposed algorithm has the shortest
-possible execution  time. The energy of  a sensor node  must be mainly
-used   for  the  sensing   phase,  not   for  the   pre-sensing  ones.   
+\item {{\bf  Execution Time}:}  a sensor node  has limited energy  resources and
+  computing power, therefore it is important that the proposed algorithm has the
+  shortest possible execution  time. The energy of a sensor  node must be mainly
+  used for the sensing phase, not for the pre-sensing ones.
  
-\item {{\bf Stopped simulation runs}:} A simulation
-ends  when the  sensor network  becomes
-disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.
+\item {{\bf Stopped simulation runs}:} A simulation ends when the sensor network
+  becomes disconnected (some nodes are dead and are not able to send information
+  to the base station). We report the number of simulations that are stopped due
+  to network disconnections and for which round it occurs.
 
 \fi
 
@@ -752,7 +859,7 @@ disconnected (some nodes are dead and are not able to send information to the ba
 
 
 %\subsection{Performance Analysis for different subregions}
-\subsection{Performance Analysis}
+\subsection{Performance analysis}
 \label{sub1}
 
 In this subsection, we first focus  on the performance of our DiLCO protocol for
@@ -769,7 +876,7 @@ second one, 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.
 
-\subsubsection{Coverage Ratio} 
+\subsubsection{Coverage ratio} 
 
 Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. It
 can  be seen  that both  DESK and  GAF provide  a little  better  coverage ratio
@@ -777,11 +884,11 @@ compared to DiLCO  in the first thirty periods. This can  be easily explained by
 the number of  active nodes: the optimization process  of our protocol activates
 less nodes  than DESK  or GAF, resulting  in a  slight decrease of  the coverage
 ratio. In case of DiLCO-2  (respectively DiLCO-4), the coverage ratio exhibits a
-fast decrease with  the number of periods and reaches zero  value in period {\bf
-  X} (respectively {\bf Y}), whereas the  other versions of DiLCO, DESK, and GAF
-ensure a coverage  ratio above 50\% for subsequent periods.  We believe that the
-results obtained with  these two methods can be explained  by a high consumption
-of energy and we will check this assumption in the next subsection.
+fast decrease  with the number  of periods and  reaches zero value  in period~18
+(respectively 46), whereas  the other versions of DiLCO, DESK,  and GAF ensure a
+coverage ratio above  50\% for subsequent periods.  We  believe that the results
+obtained with these two methods can be explained by a high consumption of energy
+and we will check this assumption in the next subsection.
 
 Concerning  DiLCO-8, DiLCO-16,  and  DiLCO-32,  these methods  seem  to be  more
 efficient than DESK  and GAF, since they can provide the  same level of coverage
@@ -794,7 +901,7 @@ nodes, and thus allow to extend the network lifetime.
 \begin{figure}[t!]
 \centering
  \includegraphics[scale=0.45] {R/CR.pdf} 
-\caption{The Coverage Ratio}
+\caption{Coverage ratio}
 \label{fig3}
 \end{figure} 
 
@@ -803,68 +910,93 @@ nodes, and thus allow to extend the network lifetime.
 %slightly more efficient than other protocols, because they subdivides
 %the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%
 
-\subsubsection{Energy Consumption}
-
-% MICHEL - TO BE CONTINUED
-
-Based on  previous results in  figure~\ref{fig3}, we keep DiLCO-16  and DiLCO-32
-and we  compare their performances in  terms of energy consumption  with the two
-other  approaches. We  measure the  energy consumed  by the  sensors  during the
-communication,  listening, computation,  active, and  sleep modes  for different
-network  densities.  Figure~\ref{fig95} illustrates  the energy  consumption for
-different network sizes.
-% for $Lifetime95$ and $Lifetime50$. 
-We  denote by  $DiLCO-/50$ (respectively  $DiLCO-/95$) as  the amount  of energy
-consumed  during which the  network can  satisfy an  area coverage  greater than
-$50\%$ (repectively  $95\%$) and  we refer  to the same  definition for  the two
-other approaches.
+\subsubsection{Energy consumption}
+
+Based on  the results shown in  Figure~\ref{fig3}, we focus on  the DiLCO-16 and
+DiLCO-32 versions of our protocol,  and we compare their energy consumption with
+the DESK and GAF approaches. For each sensor node we measure the energy consumed
+according to its successive status,  for different network densities.  We denote
+by $\mbox{\it  Protocol}/50$ (respectively $\mbox{\it  Protocol}/95$) the amount
+of energy consumed  while the area coverage is  greater than $50\%$ (repectively
+$95\%$),  where  {\it  Protocol}  is  one  of the  four  protocols  we  compare.
+Figure~\ref{fig95} presents  the energy consumptions observed  for network sizes
+going from 50  to 250~nodes. Let us  notice that the same network  sizes will be
+used for the different performance metrics.
+
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/EC.pdf} 
-\caption{The Energy Consumption}
+\caption{Energy consumption}
 \label{fig95}
 \end{figure} 
 
-The  results show  that  DiLCO-16/50, DiLCO-32/50,  DiLCO-16/95 and  DiLCO-32/95
-protocols  are  the  most  competitive  from the  energy  consumption  point  of
-view. The  other approaches have a  high energy consumption due  to activating a
-larger number of redundant nodes.
+The  results  depict the  good  performance of  the  different  versions of  our
+protocol.   Indeed,  the protocols  DiLCO-16/50,  DiLCO-32/50, DiLCO-16/95,  and
+DiLCO-32/95  consume less  energy than  their DESK  and GAF  counterparts  for a
+similar level of area coverage.   This observation reflects the larger number of
+nodes set active by DESK and GAF.
 
 
 %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. 
 %As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.  
 
-\subsubsection{Execution Time}
-We observe the impact of the network size and of the number of subregions on the computation time. We report the average execution times in seconds needed to solve the optimization problem for the different approaches and various numbers of sensors. 
-The original execution time is computed on a laptop DELL with intel Core i3 2370 M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6}\right)$ and reported on Figure~\ref{fig8}.
+\subsubsection{Execution time}
+
+Another interesting point to investigate  is the evolution of the execution time
+with the size of the WSN and  the number of subregions. Therefore, we report for
+every version of  our protocol the average execution times  in seconds needed to
+solve the optimization problem for  different WSN sizes. The execution times are
+obtained on a laptop DELL  which has an Intel Core~i3~2370~M~(2.4~GHz) dual core
+processor and a MIPS rating equal to 35330. The corresponding execution times on
+a MEDUSA II sensor node are then  extrapolated according to the MIPS rate of the
+Atmels  AVR  ATmega103L  microcontroller  (6~MHz),  which  is  equal  to  6,  by
+multiplying    the    laptop     times    by    $\left(\frac{35330}{2}    \times
+\frac{1}{6}\right)$.  The  expected times  on  a  sensor  node are  reported  on
+Figure~\ref{fig8}.
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/T.pdf}  
-\caption{Execution Time (in seconds)}
+\caption{Execution time in seconds}
 \label{fig8}
 \end{figure} 
 
-
-Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison with other DiLCO versions, because the activity scheduling is tackled by a larger number of leaders  and each leader solves an integer problem with a limited number of variables and constraints. Conversely, DiLCO-2 requires to solve an optimization problem with half of the network nodes and thus presents  a high execution time. Nevertheless if we refer to figure~\ref{fig3}, we observe that DiLCO-32 is slightly less efficient than DilCO-16 to maintain as long as possible high coverage. Excessive subdivision of the area of interest prevents to ensure good coverage especially on the borders of the subregions.
+Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison
+with  other DiLCO  versions, because  the activity  scheduling is  tackled  by a
+larger  number of  leaders and  each  leader solves  an integer  problem with  a
+limited number  of variables and  constraints.  Conversely, DiLCO-2  requires to
+solve an optimization problem with half of the network nodes and thus presents a
+high execution time.  Nevertheless if  we refer to Figure~\ref{fig3}, we observe
+that DiLCO-32  is slightly less efficient  than DilCO-16 to maintain  as long as
+possible high  coverage. In fact excessive  subdivision of the  area of interest
+prevents   to  ensure   good  coverage   especially  on   the  borders   of  the
+subregions. Thus,  the optimal number of  subregions can be seen  as a trade-off
+between execution time and coverage performance.
 
 %The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more.  We think that in distributed fashion the solving of the  optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal  with very large networks,  a distributed method is clearly required.
 
+\subsubsection{Network lifetime}
 
-\subsubsection{The Network Lifetime}
-In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. The term $/50$ (respectively  $/95$) next to the name of the method refers to the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$)) 
+In the next figure, the network lifetime is illustrated. Obviously, the lifetime
+increases with  the network  size, whatever the  considered protocol,  since the
+correlated node  density also  increases.  A high  network density means  a high
+node redundancy  which allows  to turn-off  many nodes and  thus to  prolong the
+network lifetime.
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/LT.pdf}  
-\caption{The Network Lifetime}
+\caption{Network lifetime}
 \label{figLT95}
 \end{figure} 
 
-
-As highlighted by figure~\ref{figLT95}, the network lifetime obviously
-increases when the size of the network increases. For the same level of coverage, DiLCO outperforms DESK and GAF for the lifetime of the network. If we focus on level of coverage greater than $95\%$, The subdivision in $16$ subregions seems to be the most appropriate. 
-
+As  highlighted by  Figure~\ref{figLT95},  when the  coverage  level is  relaxed
+($50\%$) the network lifetime also  improves. This observation reflects the fact
+that  the higher  the coverage  performance, the  more nodes  must be  active to
+ensure the  wider monitoring.  For a  same level of  coverage, DiLCO outperforms
+DESK and GAF for the lifetime of  the network. More specifically, if we focus on
+the larger level  of coverage ($95\%$) in case of  our protocol, the subdivision
+in $16$~subregions seems to be the most appropriate.
 
 % with  our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
 % that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best 
@@ -872,29 +1004,33 @@ increases when the size of the network increases. For the same level of coverage
 % letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed
 % independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
 
+\section{\uppercase{Conclusion and future work}}
+\label{sec:Conclusion and Future Works} 
+
+A crucial problem in WSN is  to schedule the sensing activities of the different
+nodes  in order to  ensure both  coverage of  the area  of interest  and longest
+network lifetime. The inherent limitations of sensor nodes, in energy provision,
+communication and computing capacities,  require protocols that optimize the use
+of  the  available resources  to  fulfill the  sensing  task.   To address  this
+problem, this paper proposes a  two-step approach. Firstly, the field of sensing
+is  divided into  smaller  subregions using  the  concept of  divide-and-conquer
+method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage
+Optimization is applied in each  subregion to optimize the coverage and lifetime
+performances.   In a subregion,  our protocol  consists to  elect a  leader node
+which will then perform a sensor activity scheduling. The challenges include how
+to  select   the  most  efficient  leader   in  each  subregion   and  the  best
+representative set of active nodes to ensure a high level of coverage. To assess
+the performance of our approach, we  compared it with two other approaches using
+many performance metrics  like coverage ratio or network  lifetime. We have also
+study the  impact of the  number of subregions  chosen to subdivide the  area of
+interest,  considering  different  network  sizes.  The  experiments  show  that
+increasing the  number of subregions allows  to improves the  lifetime. The more
+there  are   subregions,  the  more   the  network  is  robust   against  random
+disconnection resulting from dead nodes.  However, for a given sensing field and
+network size  there is an optimal  number of subregions.  Therefore,  in case of
+our simulation  context a  subdivision in $16$~subregions  seems to be  the most
+relevant. The optimal number of subregions will be investigated in the future.
 
-
-
-\section{\uppercase{Conclusion and Future Works}}
-\label{sec:Conclusion and Future Works}
-In this paper, we have  addressed the problem of the coverage and the lifetime
-optimization in wireless  sensor networks. This is a key issue as
-sensor nodes have limited resources in terms of memory,  energy and
-computational power. To cope with this problem, the field of sensing
-is divided into smaller subregions using the concept of divide-and-conquer method, and then a DiLCO protocol for optimizing the coverage and lifetime performances in each subregion.
-The proposed protocol combines two efficient techniques:  network
-leader election and sensor activity scheduling, where the challenges
-include how to select the  most efficient leader in each subregion and
-the best representative set of active nodes to ensure a high level of coverage.
-We have compared this method with two other approaches using many metrics as coverage ratio, execution time, lifetime.
-Some experiments have been performed to study the choice of the number of
-subregions  which subdivide  the  sensing field,  considering different  network
-sizes. They show that as the number of subregions increases, so does the network
-lifetime. Moreover,  it makes  the DiLCO protocol  more robust  against random
-network  disconnection due  to node  failures.  However,  too  much subdivisions
-reduces the advantage  of the optimization. In fact, there  is a balance between
-the  benefit  from the  optimization  and the  execution  time  needed to  solve
-it. Therefore, the subdivision in $16$ subregions seems to be the most appropriate. 
 \iffalse
 \noindent In this paper, we have  addressed the problem of the coverage and the lifetime
 optimization in wireless  sensor networks. This is a key issue as
@@ -925,18 +1061,17 @@ optimization  methods. \iffalse The round  will still consist of 4 phases, but t
 The computation of all cover sets in one time is far more
 difficult, but will reduce the communication overhead. \fi
 \fi
-\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*{\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.
 
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