ok pour les modifs de michel

[UIC2013.git] / bare_conf.tex

diff --git a/bare_conf.tex b/bare_conf.tex
index a6cc2772956ddb79a6606830bf2c4f4b8de55a8f..90482fc24915c489d7e9bdec96cec891811993f6 100755 (executable)
--- a/bare_conf.tex
+++ b/bare_conf.tex
@@ -36,7 +36,6 @@
 
 \title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
 
 
 \title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
 

-

 % author names and affiliations
 % use a multiple column layout for up to three different
 % affiliations
 % author names and affiliations
 % use a multiple column layout for up to three different
 % affiliations


@@ -77,6 +76,7 @@ network lifetime and improve the coverage performance.
 \IEEEpeerreviewmaketitle
 
 \section{Introduction}
 \IEEEpeerreviewmaketitle
 
 \section{Introduction}

+

 \noindent Recent years have witnessed significant advances in wireless
 communications and embedded micro-sensing MEMS technologies which have
 made  emerge wireless  sensor networks  as one  of the  most promising
 \noindent Recent years have witnessed significant advances in wireless
 communications and embedded micro-sensing MEMS technologies which have
 made  emerge wireless  sensor networks  as one  of the  most promising


@@ -109,13 +109,17 @@ service  for  applications.  In  this  paper  we  concentrate on  area
 coverage  problem,  with  the  objective  of  maximizing  the  network
 lifetime  by using  an adaptive  scheduling. The  area of  interest is
 divided into subregions and an activity scheduling for sensor nodes is
 coverage  problem,  with  the  objective  of  maximizing  the  network
 lifetime  by using  an adaptive  scheduling. The  area of  interest is
 divided into subregions and an activity scheduling for sensor nodes is

-planned for  each subregion.  Our scheduling  scheme considers rounds,
-where a  round starts with  a discovery phase to  exchange information
-between  sensors of  the subregion,  in  order to  choose in  suitable
-manner a sensor  node to carry out a  coverage strategy. This coverage
-strategy involves the solving  of an integer program which provides
-the activation  of the  sensors for the  sensing phase of  the current
-round.
+planned for  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 much node failures.
+Our scheduling  scheme considers rounds,  where a round starts  with a
+discovery  phase  to  exchange  information  between  sensors  of  the
+subregion,  in order to  choose in  suitable manner  a sensor  node to
+carry  out a coverage  strategy. This  coverage strategy  involves the
+solving of  an integer  program which provides  the activation  of the
+sensors for the sensing phase of the current round.

 
 The remainder of the paper is organized as follows.  The next section
 % Section~\ref{rw}
 
 The remainder of the paper is organized as follows.  The next section
 % Section~\ref{rw}


@@ -128,15 +132,15 @@ OMNET++  \cite{varga}. They  fully demonstrate  the usefulness  of the
 proposed  approach.   Finally, we  give  concluding  remarks and  some
 suggestions for future works in Section~\ref{sec:conclusion}.
 
 proposed  approach.   Finally, we  give  concluding  remarks and  some
 suggestions for future works in Section~\ref{sec:conclusion}.
 

-\section{\uppercase{Related works}}
+\section{Related Works}

 \label{rw}
 \label{rw}

-\noindent 
-This section  is dedicated to  the various approaches proposed  in the
-literature for  the coverage lifetime maximization  problem, where the
-objective  is to optimally  schedule sensors'  activities in  order to
-extend  network  lifetime in  a  randomly  deployed  network. As  this
-problem is subject  to a wide range of  interpretations, we suggest to
-recall main definitions and assumptions related to our work.
+
+\noindent This section is dedicated to the various approaches proposed
+in  the literature  for  the coverage  lifetime maximization  problem,
+where the  objective is to  optimally schedule sensors'  activities in
+order to  extend network lifetime  in a randomly deployed  network. As
+this problem is subject to a wide range of interpretations, we suggest
+to recall main definitions and assumptions related to our work.

 
 %\begin{itemize}
 %\item Area Coverage: The main objective is to cover an area. The area coverage requires
 
 %\begin{itemize}
 %\item Area Coverage: The main objective is to cover an area. The area coverage requires


@@ -168,8 +172,6 @@ number  of  primary points  that  are  covered  in each  round,  while
 minimizing  overcoverage (points  covered by  multiple  active sensors
 simultaneously).
 
 minimizing  overcoverage (points  covered by  multiple  active sensors
 simultaneously).
 

-\newpage
-

 {\bf Lifetime}
 
 Various   definitions   exist   for   the   lifetime   of   a   sensor
 {\bf Lifetime}
 
 Various   definitions   exist   for   the   lifetime   of   a   sensor


@@ -202,13 +204,13 @@ the time intervals to be activated.
 {\bf Distributed approaches}
 
 Some      distributed     algorithms      have      been     developed
 {\bf Distributed approaches}
 
 Some      distributed     algorithms      have      been     developed

-in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02} to perform the schelduling.     Distributed
-algorithms typically operate in  rounds for predetermined duration. At
-the beginning  of each round,  a sensor exchange information  with its
-neighbors and makes a decision to  either remain turned on or to go to
-sleep for the round. This decision is basically based on simple greedy
-criteria       like       the       largest       uncovered       area
-\cite{Berman05efficientenergy},      maximum     uncovered     targets
+in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}  to perform the
+scheduling.   Distributed algorithms typically  operate in  rounds for
+predetermined  duration. At  the  beginning of  each  round, a  sensor
+exchange information with its neighbors and makes a decision to either
+remain turned  on or to  go to sleep  for the round. This  decision is
+basically based  on simple greedy criteria like  the largest uncovered
+area   \cite{Berman05efficientenergy},   maximum   uncovered   targets

 \cite{1240799}.   In \cite{Tian02}, the  scheduling scheme  is divided
 into rounds, where each round  has a self-scheduling phase followed by
 a sensing phase.  Each sensor  broadcasts a message containing node ID
 \cite{1240799}.   In \cite{Tian02}, the  scheduling scheme  is divided
 into rounds, where each round  has a self-scheduling phase followed by
 a sensing phase.  Each sensor  broadcasts a message containing node ID


@@ -222,7 +224,7 @@ of       the       area        is       no       longer       covered.
 \cite{Prasad:2007:DAL:1782174.1782218}  defines a model  for capturing
 the dependencies  between different cover sets  and proposes localized
 heuristic  based on this  dependency.  The  algorithm consists  of two
 \cite{Prasad:2007:DAL:1782174.1782218}  defines a model  for capturing
 the dependencies  between different cover sets  and proposes localized
 heuristic  based on this  dependency.  The  algorithm consists  of two

-phases, an initial setup phase during which each sensor computes and
+phases, an initial  setup phase during which each  sensor computes and

 prioritize the  covers and  a sensing phase  during which  each sensor
 first decides  its on/off status, and  then remains on or  off for the
 rest  of the  duration.  Authors  in \cite{chin2007}  propose  a novel
 prioritize the  covers and  a sensing phase  during which  each sensor
 first decides  its on/off status, and  then remains on or  off for the
 rest  of the  duration.  Authors  in \cite{chin2007}  propose  a novel


@@ -262,10 +264,10 @@ these set covers successively.
 
 First algorithms  proposed in the  literature consider that  the cover
 sets  are  disjoint: a  sensor  node appears  in  exactly  one of  the
 
 First algorithms  proposed in the  literature consider that  the cover
 sets  are  disjoint: a  sensor  node appears  in  exactly  one of  the

-generated  cover   sets.   For  instance,   Slijepcevic  and  Potkonjak
+generated  cover  sets.    For  instance,  Slijepcevic  and  Potkonjak

 \cite{Slijepcevic01powerefficient}   propose    an   algorithm   which
 allocates sensor nodes in mutually independent sets to monitor an area
 \cite{Slijepcevic01powerefficient}   propose    an   algorithm   which
 allocates sensor nodes in mutually independent sets to monitor an area

-divided into several fields. Their algorithm builds a cover set by
+divided into  several fields.  Their algorithm builds  a cover  set by

 including in  priority the sensor  nodes which cover  critical fields,
 that  is to  say fields  that are  covered by  the smallest  number of
 sensors. The time complexity of  their heuristic is $O(n^2)$ where $n$
 including in  priority the sensor  nodes which cover  critical fields,
 that  is to  say fields  that are  covered by  the smallest  number of
 sensors. The time complexity of  their heuristic is $O(n^2)$ where $n$


@@ -274,7 +276,7 @@ technique  to achieve energy  savings by  organizing the  sensor nodes
 into a maximum number of  disjoint dominating sets which are activated
 successively. The dominating sets do not guarantee the coverage of the
 whole        region        of        interest.        Abrams        et
 into a maximum number of  disjoint dominating sets which are activated
 successively. The dominating sets do not guarantee the coverage of the
 whole        region        of        interest.        Abrams        et

-al.~\cite{Abrams:2004:SKA:984622.984684}   design  three  approximation
+al.~\cite{Abrams:2004:SKA:984622.984684}  design  three  approximation

 algorithms  for a  variation of  the  set k-cover  problem, where  the
 objective is to partition the sensors into covers such that the number
 of covers that  include an area, summed over  all areas, is maximized.
 algorithms  for a  variation of  the  set k-cover  problem, where  the
 objective is to partition the sensors into covers such that the number
 of covers that  include an area, summed over  all areas, is maximized.


@@ -340,10 +342,10 @@ scheduling strategy. We  give a brief answer to  these three questions
 to describe our  approach before going into details  in the subsequent
 sections.
 \begin{itemize}
 to describe our  approach before going into details  in the subsequent
 sections.
 \begin{itemize}

-\item {\bf  How must  the phases for  information exchange,
-  decision  and sensing be planned over  time?}  Our  algorithm divides  the time
-  line  into  a  number  of  rounds. Each  round  contains  4  phases:
-  Information Exchange, Leader Election, Decision, and Sensing.
+\item {\bf How must the  phases for information exchange, decision and
+  sensing be planned over time?}   Our algorithm divides the time line
+  into a number  of rounds. Each round contains  4 phases: Information
+  Exchange, Leader Election, Decision, and Sensing.

 
 \item {\bf What are the rules to decide which node has to be turned on
   or off?}  Our algorithm tends to limit the overcoverage of points of
 
 \item {\bf What are the rules to decide which node has to be turned on
   or off?}  Our algorithm tends to limit the overcoverage of points of


@@ -369,7 +371,7 @@ sections.
   decision is made by a leader in each subregion.
 \end{itemize}
 
   decision is made by a leader in each subregion.
 \end{itemize}
 

-\section{\uppercase{Activity scheduling}}
+\section{Activity Scheduling}

 \label{pd}
 
 We consider  a randomly and  uniformly deployed network  consisting of
 \label{pd}
 
 We consider  a randomly and  uniformly deployed network  consisting of


@@ -412,7 +414,7 @@ Election,  Decision) are energy  consuming for  some nodes,  even when
 they do not  join the network to monitor the  area. Below, we describe
 each phase in more detail.
 
 they do not  join the network to monitor the  area. Below, we describe
 each phase in more detail.
 

-\subsection{\textbf INFOrmation Exchange Phase}
+\subsection{INFOrmation Exchange Phase}

 
 Each sensor node $j$ sends  its position, remaining energy $RE_j$, and
 the number of local neighbors  $NBR_j$ to all wireless sensor nodes in
 
 Each sensor node $j$ sends  its position, remaining energy $RE_j$, and
 the number of local neighbors  $NBR_j$ to all wireless sensor nodes in


@@ -426,7 +428,7 @@ active mode.
 
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 
 
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 

-\subsection{\textbf Leader Election Phase}
+\subsection{Leader Election Phase}

 This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL)
 which  will  be  responsible  of executing  coverage  algorithm.  Each
 subregion  in  the   area  of  interest  will  select   its  own  WSNL
 This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL)
 which  will  be  responsible  of executing  coverage  algorithm.  Each
 subregion  in  the   area  of  interest  will  select   its  own  WSNL


@@ -437,7 +439,7 @@ subregion.  The selection criteria  in order  of priority  are: larger
 number  of neighbors,  larger remaining  energy, and  then in  case of
 equality, larger index.
 
 number  of neighbors,  larger remaining  energy, and  then in  case of
 equality, larger index.
 

-\subsection{\textbf Decision Phase}
+\subsection{Decision Phase}

 The  WSNL will  solve an  integer  program (see  section~\ref{cp})  to
 select which sensors will be  activated in the following sensing phase
 to cover  the subregion.  WSNL will send  Active-Sleep packet  to each
 The  WSNL will  solve an  integer  program (see  section~\ref{cp})  to
 select which sensors will be  activated in the following sensing phase
 to cover  the subregion.  WSNL will send  Active-Sleep packet  to each


@@ -445,12 +447,12 @@ sensor in the subregion based on algorithm's results.
 %The main goal in this step after choosing the WSNL is to produce the best representative active nodes set that will take the responsibility of covering the whole region $A^k$ with minimum number of sensor nodes to prolong the lifetime in the wireless sensor network. For our problem, in each round we need to select the minimum set of sensor nodes to improve the lifetime of the network and in the same time taking into account covering the region $A^k$ . We need an optimal solution with tradeoff between our two conflicting objectives.
 %The above region coverage problem can be formulated as a Multi-objective optimization problem and we can use the Binary Particle Swarm Optimization technique to solve it. 
 
 %The main goal in this step after choosing the WSNL is to produce the best representative active nodes set that will take the responsibility of covering the whole region $A^k$ with minimum number of sensor nodes to prolong the lifetime in the wireless sensor network. For our problem, in each round we need to select the minimum set of sensor nodes to improve the lifetime of the network and in the same time taking into account covering the region $A^k$ . We need an optimal solution with tradeoff between our two conflicting objectives.
 %The above region coverage problem can be formulated as a Multi-objective optimization problem and we can use the Binary Particle Swarm Optimization technique to solve it. 
 

-\subsection{\textbf Sensing Phase}
+\subsection{Sensing Phase}

 Active  sensors  in the  round  will  execute  their sensing  task  to
 preserve maximal  coverage in the  region of interest. We  will assume
 that the cost  of keeping a node awake (or sleep)  for sensing task is
 the same  for all wireless sensor  nodes in the  network.  Each sensor
 Active  sensors  in the  round  will  execute  their sensing  task  to
 preserve maximal  coverage in the  region of interest. We  will assume
 that the cost  of keeping a node awake (or sleep)  for sensing task is
 the same  for all wireless sensor  nodes in the  network.  Each sensor

-will  receive an  Active-Sleep packet  from WSNL  informing it  to stay
+will receive  an Active-Sleep  packet from WSNL  informing it  to stay

 awake or  go sleep  for a time  equal to  the period of  sensing until
 starting a new round.
 
 awake or  go sleep  for a time  equal to  the period of  sensing until
 starting a new round.
 


@@ -537,7 +539,7 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 \label{fig2}
 \end{figure}
 
 \label{fig2}
 \end{figure}
 

-\section{\uppercase{Coverage problem formulation}}
+\section{Coverage Problem Formulation}

 \label{cp}
 %We can formulate our optimization problem as energy cost minimization by minimize the number of active sensor nodes and maximizing the coverage rate at the same time in each $A^k$ . This optimization problem can be formulated as follow: Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake is the same for all wireless sensor nodes in the network. We can define the decision parameter  $X_j$ as in \eqref{eq11}:\\
 
 \label{cp}
 %We can formulate our optimization problem as energy cost minimization by minimize the number of active sensor nodes and maximizing the coverage rate at the same time in each $A^k$ . This optimization problem can be formulated as follow: Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake is the same for all wireless sensor nodes in the network. We can define the decision parameter  $X_j$ as in \eqref{eq11}:\\
 


@@ -566,8 +568,8 @@ indicator function of whether the point $p$ is covered, that is:
 \end{array} \right.
 %\label{eq12} 
 \end{equation}
 \end{array} \right.
 %\label{eq12} 
 \end{equation}

-The number of sensors that are covering point $p$ is equal to 
-$\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+The number of active sensors that cover the primary point $p$ is equal
+to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:

 \begin{equation}
 X_{j} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 X_{j} = \left \{ 
 \begin{array}{l l}


@@ -580,7 +582,7 @@ We define the Overcoverage variable $\Theta_{p}$ as:
 \begin{equation}
  \Theta_{p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
  \Theta_{p} = \left \{ 
 \begin{array}{l l}

-  0            & \mbox{if point $p$ is not covered,}\\
+  0 & \mbox{if point $p$ is not covered,}\\

   \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
 \end{array} \right.
 \label{eq13} 
   \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
 \end{array} \right.
 \label{eq13} 


@@ -615,23 +617,24 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \right.
 \end{equation}
 \begin{itemize}
 \right.
 \end{equation}
 \begin{itemize}

-\item  $X_{j}$ :  indicates  whether  or not  the sensor  $j$ is  actively
+\item $X_{j}$  : indicates whether or  not the sensor  $j$ is actively

   sensing in the round (1 if yes and 0 if not);
 \item $\Theta_{p}$  : {\it overcoverage}, the number  of sensors minus
   sensing in the round (1 if yes and 0 if not);
 \item $\Theta_{p}$  : {\it overcoverage}, the number  of sensors minus

-  one that are covering point $p$;
+  one that are covering the primary point $p$;

 \item $U_{p}$  : {\it undercoverage},  indicates whether or  not point
   $p$ is being covered (1 if not covered and 0 if covered).
 \end{itemize}
 
 \item $U_{p}$  : {\it undercoverage},  indicates whether or  not point
   $p$ is being covered (1 if not covered and 0 if covered).
 \end{itemize}
 

-The first group of constraints indicates that some point $p$ should be
-covered by  at least  one sensor and,  if it  is not always  the case,
-overcoverage and undercoverage  variables help balance the restriction
-equation  by taking positive  values. There  are two  main objectives.
-First we limit  overcoverage of primary points in  order to activate a
-minimum  number of  sensors.   Second  we prevent  that  parts of  the
-subregion are not monitored  by minimizing undercoverage.  The weights
-$w_\theta$ and $w_U$  must be properly chosen so  as to guarantee that
-the maximum number of points are covered during each round.
+The first group  of constraints indicates that some  primary point $p$
+should be covered by at least one  sensor and, if it is not always the
+case,  overcoverage  and  undercoverage  variables  help  balance  the
+restriction  equation by taking  positive values.  There are  two main
+objectives.  First we limit overcoverage of primary points in order to
+activate a minimum number of sensors.  Second we prevent that parts of
+the  subregion are  not  monitored by  minimizing undercoverage.   The
+weights  $w_\theta$  and  $w_U$  must  be properly  chosen  so  as  to
+guarantee that  the maximum number  of points are covered  during each
+round.

  
 %In equation \eqref{eq15}, there are two main objectives: the first one using  the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the  Undercoverage parameter  to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
 %at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.
  
 %In equation \eqref{eq15}, there are two main objectives: the first one using  the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the  Undercoverage parameter  to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
 %at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.


@@ -658,22 +661,24 @@ the maximum number of points are covered during each round.
 
 %\end{itemize}
 
 
 %\end{itemize}
 

-\section{\uppercase{Simulation Results}}
+\section{Simulation Results}

 \label{exp}
 
 \label{exp}
 

-In this section, we conducted a series of simulations, to evaluate the
+In this section, we conducted  a series of simulations to evaluate the

 efficiency  and relevance of  our approach,  using the  discrete event
 simulator  OMNeT++  \cite{varga}. We  performed  simulations for  five
 different densities varying from 50 to 250~nodes. Experimental results
 were  obtained from  randomly generated  networks in  which  nodes are
 efficiency  and relevance of  our approach,  using the  discrete event
 simulator  OMNeT++  \cite{varga}. We  performed  simulations for  five
 different densities varying from 50 to 250~nodes. Experimental results
 were  obtained from  randomly generated  networks in  which  nodes are

-deployed over a $(50 \times  25)~m^2 $ sensing field. For each network
-deployment,  we assume  that the  deployed nodes  can fully  cover the
-sensing field  with the given  sensing range.  10 simulation  runs are
-performed  with different  network topologies  for each  node density.
-The results  presented hereafter are the  average of these  10 runs. A
-simulation  ends when all  the nodes  are dead  or the  sensor network
-becomes disconnected  (some nodes may  not be able  to sent to  a base
-station an event they sense).
+deployed over a  $(50 \times 25)~m^2 $ sensing  field. 
+More precisely, the deployment is controlled at a coarse scale in
+  order to ensure that the  deployed nodes can fully cover the sensing
+  field with the given sensing range.
+10~simulation  runs  are performed  with
+different  network  topologies for  each  node  density.  The  results
+presented hereafter  are the  average of these  10 runs.  A simulation
+ends  when  all the  nodes  are dead  or  the  sensor network  becomes
+disconnected (some nodes may not be  able to sent to a base station an
+event they sense).

 
 Our proposed coverage protocol uses the radio energy dissipation model
 defined by~\cite{HeinzelmanCB02} as  energy consumption model for each
 
 Our proposed coverage protocol uses the radio energy dissipation model
 defined by~\cite{HeinzelmanCB02} as  energy consumption model for each


@@ -683,7 +688,7 @@ range 24-60~joules, and each sensor node will consume 0.2 watts during
 the sensing period which will have  a duration of 60 seconds. Thus, an
 active  node will  consume  12~joules during  sensing  phase, while  a
 sleeping  node will  use  0.002  joules.  Each  sensor  node will  not
 the sensing period which will have  a duration of 60 seconds. Thus, an
 active  node will  consume  12~joules during  sensing  phase, while  a
 sleeping  node will  use  0.002  joules.  Each  sensor  node will  not

-participate in the next round if it's remaining energy is less than 12
+participate in the next round if its remaining energy is less than 12

 joules.  In  all  experiments  the  parameters  are  set  as  follows:
 $R_s=5m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
 
 joules.  In  all  experiments  the  parameters  are  set  as  follows:
 $R_s=5m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
 


@@ -711,7 +716,7 @@ number of rounds on the  average coverage ratio for 150 deployed nodes
 for the  three approaches.  It can be  seen that the  three approaches
 give  similar  coverage  ratios  during  the first  rounds.  From  the
 9th~round the  coverage ratio  decreases continuously with  the simple
 for the  three approaches.  It can be  seen that the  three approaches
 give  similar  coverage  ratios  during  the first  rounds.  From  the
 9th~round the  coverage ratio  decreases continuously with  the simple

-heuristic, while the other two strategies provide superior coverage to
+heuristic, while the two other strategies provide superior coverage to

 $90\%$ for five more rounds.  Coverage ratio decreases when the number
 of rounds increases  due to dead nodes. Although  some nodes are dead,
 thanks to  strategy~1 or~2,  other nodes are  preserved to  ensure the
 $90\%$ for five more rounds.  Coverage ratio decreases when the number
 of rounds increases  due to dead nodes. Although  some nodes are dead,
 thanks to  strategy~1 or~2,  other nodes are  preserved to  ensure the


@@ -791,40 +796,31 @@ expected, the Strategy with One Leader is usually slightly better than
 the second  strategy, because the  global optimization permit  to turn
 off more  sensors. Indeed,  when there are  two subregions  more nodes
 remain awake  near the border shared  by them. Note that  again as the
 the second  strategy, because the  global optimization permit  to turn
 off more  sensors. Indeed,  when there are  two subregions  more nodes
 remain awake  near the border shared  by them. Note that  again as the

-number of  rounds increase  the two leader  strategy becomes  the most
+number of  rounds increases  the two leader  strategy becomes  the most

 performing, since its takes longer  to have the two subregion networks
 simultaneously disconnected.
 
 performing, since its takes longer  to have the two subregion networks
 simultaneously disconnected.
 

-\subsection{The Network Lifetime}
+\subsection{The Number of Stopped Simulation Runs}

 
 

-We have defined the network lifetime  as the time until all nodes have
-been drained of their energy  or each sensor network monitoring a area
-becomes disconnected.  In figure~\ref{fig6}, the  network lifetime for
-different network sizes and for the three approaches is illustrated.
+We  will now  study  the number  of  simulation which  stopped due  to
+network  disconnection, per round  for each  of the  three approaches.
+Figure~\ref{fig6} illustrates the average number of stopped simulation
+runs per  round for 150 deployed  nodes.  It can be  observed that the
+heuristic is  the approach which  stops the earlier because  the nodes
+are  chosen   randomly.   Among  the  two   proposed  strategies,  the
+centralized  one  first  exhibits  network  disconnection.   Thus,  as
+explained previously, in case  of the strategy with several subregions
+the  optimization effectively  continues as  long  as a  network in  a
+subregion   is  still   connected.   This   longer   partial  coverage
+optimization participates in extending the lifetime.

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

-%\centering
-% \begin{multicols}{6}

 \centering
 \centering

-\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
-\caption{The Network Lifetime }
+\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps} 
+\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }

 \label{fig6}
 \end{figure} 
 
 \label{fig6}
 \end{figure} 
 

-As  highlighted by figure~\ref{fig6},  the network  lifetime obviously
-increases when the  size of the network increase,  with our approaches
-that lead  to the larger  lifetime improvement.  By choosing  for each
-round the  well suited nodes  to cover the  region of interest  and by
-leaving sleep  the other ones  to be used  later in next  rounds, both
-proposed strategies efficiently prolong the lifetime. Comparison shows
-that the larger the sensor  number, the more our strategies outperform
-the heuristic.   Strategy~2, which uses  two leaders, is the  best one
-because it  is robust  to network disconnection  in one  subregion. It
-also  means   that  distributing  the  algorithm  in   each  node  and
-subdividing the sensing field  into many subregions, which are managed
-independently and simultaneously, is the most relevant way to maximize
-the lifetime of a network.
-

 \subsection{The Energy Consumption}
 
 In this experiment, we study the effect of the multi-hop communication
 \subsection{The Energy Consumption}
 
 In this experiment, we study the effect of the multi-hop communication


@@ -863,21 +859,22 @@ 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.
 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.

-Table~\ref{table1} gives  the average execution  times on a  laptop of
-the decision phase during one round.  They are given for the different
-approaches  and   various  numbers  of  sensors.   The   lack  of  any
-optimization explains why the  heuristic has very low execution times.
-Conversely, the  Strategy with One  Leader which requires to  solve an
-optimization  problem considering all  the nodes  presents redhibitory
-execution  times. Moreover,  increasing of  50~nodes the  network size
-multiplies the  time by almost a  factor of 10. The  Strategy with Two
-Leaders has more suitable times.  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 deal with very large networks a
+Table~\ref{table1} gives the average  execution times  in seconds
+on a laptop of the decision phase (solving of the optimization problem)
+during one  round.  They  are given for  the different  approaches and
+various numbers of sensors.  The lack of any optimization explains why
+the heuristic has very  low execution times.  Conversely, the Strategy
+with  One  Leader which  requires  to  solve  an optimization  problem
+considering  all  the  nodes  presents  redhibitory  execution  times.
+Moreover, increasing of 50~nodes  the network size multiplies the time
+by  almost a  factor of  10. The  Strategy with  Two Leaders  has more
+suitable times.  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   deal  with  very  large  networks  a

 distributed method is clearly required.
 
 \begin{table}[ht]
 distributed method is clearly required.
 
 \begin{table}[ht]

-\caption{The Execution Time(s) vs The Number of Sensors }
+\caption{The Execution Time(s) vs The Number of Sensors}

 % title of Table
 \centering
 
 % title of Table
 \centering
 


@@ -886,7 +883,7 @@ distributed method is clearly required.
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines

-Sensors Number & Strategy & Strategy  & Simple Heuristic \\ [0.5ex]
+Sensors Number & Strategy~1 & Strategy~2  & Simple Heuristic \\ [0.5ex]

  & (with Two Leaders) & (with One Leader) & \\ [0.5ex]
 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
 % inserts table
  & (with Two Leaders) & (with One Leader) & \\ [0.5ex]
 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
 % inserts table


@@ -911,28 +908,41 @@ Sensors Number & Strategy & Strategy  & Simple Heuristic \\ [0.5ex]
 % is used to refer this table in the text
 \end{table}
 
 % is used to refer this table in the text
 \end{table}
 

-\subsection{The Number of Stopped Simulation Runs}
+\subsection{The Network Lifetime}

 
 

-Finally, we will  study the number of simulation  which stopped due to
-network  disconnection, per round  for each  of the  three approaches.
-Figure~\ref{fig8}  illustrates the number  of stopped  simulation runs
-per  round  for 150  deployed  nodes.  It  can  be  observed that  the
-heuristic is  the approach which  stops the earlier because  the nodes
-are  chosen   randomly.   Among  the  two   proposed  strategies,  the
-centralized  one  first   exhibits  network  disconnection.  Thus,  as
-explained previously, in case  of the strategy with several subregions
-the  optimization effectively  continues as  long  as a  network in  a
-subregion   is  still   connected.   This   longer   partial  coverage
-optimization participates in extending the lifetime.
+Finally, we  have defined the network  lifetime as the  time until all
+nodes  have  been drained  of  their  energy  or each  sensor  network
+monitoring  an area becomes  disconnected.  In  figure~\ref{fig8}, the
+network  lifetime for different  network sizes  and for  both Strategy
+with Two  Leaders and the Simple  Heuristic is illustrated. 
+  We do  not consider  anymore the  centralized Strategy  with One
+  Leader, because, as shown above, this strategy results  in execution
+  times that quickly become unsuitable for a sensor network.

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

+%\centering
+% \begin{multicols}{6}

 \centering
 \centering

-\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps} 
-\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
+\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
+\caption{The Network Lifetime }

 \label{fig8}
 \end{figure} 
 
 \label{fig8}
 \end{figure} 
 

-\section{\uppercase{Conclusions and Future Works}}
+As  highlighted by figure~\ref{fig8},  the network  lifetime obviously
+increases when  the size  of the network  increase, with  our approach
+that leads to  the larger lifetime improvement.  By  choosing for each
+round the  well suited nodes  to cover the  region of interest  and by
+letting the other ones sleep in order to be used later in next rounds,
+our strategy efficiently prolongs the lifetime. Comparison shows that
+the larger  the sensor number  is, the more our  strategies outperform
+the Simple Heuristic.  Strategy~2, which uses two leaders, is the best
+one because it is robust to network disconnection in one subregion. It
+also  means   that  distributing  the  algorithm  in   each  node  and
+subdividing the sensing field  into many subregions, which are managed
+independently and simultaneously, is the most relevant way to maximize
+the lifetime of a network.
+
+\section{Conclusions and Future Works}

 \label{sec:conclusion}
 
 In this paper, we have  addressed the problem of coverage and lifetime
 \label{sec:conclusion}
 
 In this paper, we have  addressed the problem of coverage and lifetime


@@ -951,18 +961,22 @@ subregion.   The network lifetime  in each  subregion is  divided into
 rounds, each round consists  of four phases: (i) Information Exchange,
 (ii) Leader Election, (iii) an optimization-based Decision in order to
 select  the  nodes remaining  active  for  the  last phase,  and  (iv)
 rounds, each round consists  of four phases: (i) Information Exchange,
 (ii) Leader Election, (iii) an optimization-based Decision in order to
 select  the  nodes remaining  active  for  the  last phase,  and  (iv)

-Sensing. The  simulations results show  the relevance of  the proposed
+Sensing.  The  simulations results show the relevance  of the proposed

 protocol in  terms of lifetime, coverage ratio,  active sensors Ratio,
 energy saving,  energy consumption, execution time, and  the number of
 stopped simulation  runs due  to network disconnection.   Indeed, when
 dealing with  large and dense wireless sensor  networks, a distributed
 approach like the one we propose  allows to reduce the difficulty of a
 protocol in  terms of lifetime, coverage ratio,  active sensors Ratio,
 energy saving,  energy consumption, execution time, and  the number of
 stopped simulation  runs due  to network disconnection.   Indeed, when
 dealing with  large and dense wireless sensor  networks, a distributed
 approach like the one we propose  allows to reduce the difficulty of a

-single global optimization problem by partitioning it in many smaller
-problems,  one per  subregion, that  can  be solved  more easily.   In
-future,  we  plan to  study  and  propose  a coverage  protocol  which
+single global optimization problem  by partitioning it in many smaller
+problems, one per subregion, that can be solved more easily.
+
+In  future, we plan  to study  and propose  a coverage  protocol which

 computes  all  active  sensor  schedules  in  a  single  round,  using
 optimization  methods  such  as  swarms optimization  or  evolutionary
 computes  all  active  sensor  schedules  in  a  single  round,  using
 optimization  methods  such  as  swarms optimization  or  evolutionary

-algorithms. The computation of all cover sets in one round is far more
+algorithms.  This single  round  will still  consists  of 4  phases, but  the
+  decision phase will compute the schedules for several sensing phases
+  which aggregated together define a kind of meta-sensing phase.
+The computation of all cover sets in one round is far more

 difficult, but will reduce the communication overhead.
 
 % use section* for acknowledgement
 difficult, but will reduce the communication overhead.
 
 % use section* for acknowledgement