Relecture finie

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@@ -71,26 +67,41 @@
 %% \address{Address\fnref{label3}}
 %% \fntext[label3]{}
 
 %% \address{Address\fnref{label3}}
 %% \fntext[label3]{}
 

-\title{ Multiperiod Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
+\title{Multiperiod Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}

 
 %% use optional labels to link authors explicitly to addresses:
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 %% \address[label2]{}
 
 %% use optional labels to link authors explicitly to addresses:
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-\author{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
+\author{Ali Kadhum Idrees, Karine Deschinkel, \\
+Michel Salomon, and Rapha\"el Couturier}

 %\thanks{are members in the AND team - DISC department - FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France.
 % e-mail: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}% <-this % stops a space
 %\thanks{}% <-this % stops a space
  
 %\thanks{are members in the AND team - DISC department - FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France.
 % e-mail: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}% <-this % stops a space
 %\thanks{}% <-this % stops a space
  

-
-\address{FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France. \\ e-mail: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}
+\address{FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France. \\ 
+e-mail: ali.idness@edu.univ-fcomte.fr, \\
+$\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}

 
 \begin{abstract}
 %One of  the fundamental challenges in Wireless Sensor Networks (WSNs)
 %is the coverage preservation and the extension of the network lifetime
 %continuously  and  effectively  when  monitoring a  certain  area  (or
 %region) of  interest. 
 
 \begin{abstract}
 %One of  the fundamental challenges in Wireless Sensor Networks (WSNs)
 %is the coverage preservation and the extension of the network lifetime
 %continuously  and  effectively  when  monitoring a  certain  area  (or
 %region) of  interest. 

-Coverage and lifetime are two paramount problems in  Wireless Sensor Networks (WSNs). In this paper, a method called Multiperiod Distributed Lifetime Coverage Optimization protocol (MuDiLCO), is proposed to maintain the coverage and to improve the lifetime in wireless sensor networks. The area  of interest is first divided into subregions and then the MuDiLCO protocol is distributed on the sensor nodes in each subregion. The proposed MuDiLCO protocol works into periods during which a sets of sensor nodes are scheduled to remaining active for a number of rounds during the sensing phase, to ensure coverage so as to maximize the lifetime of WSN. The  decision process is carried  out  by a leader node,  which  solves an integer program to produce the best representative sets to be used during the rounds of the sensing phase. Compared with some existing protocols, simulation results based on multiple criteria (energy consumption,coverage ratio, ...) show that the proposed protocol can prolong efficiently the network lifetime and improve the coverage performance.
+Coverage and  lifetime are  two paramount problems  in Wireless  Sensor Networks
+(WSNs). In this paper, a method called Multiperiod Distributed Lifetime Coverage
+Optimization  protocol (MuDiLCO)  is proposed  to maintain  the coverage  and to
+improve the lifetime in wireless sensor  networks. The area of interest is first
+divided  into subregions and  then the  MuDiLCO protocol  is distributed  on the
+sensor nodes in each subregion. The proposed MuDiLCO protocol works into periods
+during which sets of sensor nodes are scheduled to remain active for a number of
+rounds  during the  sensing phase,  to  ensure coverage  so as  to maximize  the
+lifetime of  WSN.  The decision process is  carried out by a  leader node, which
+solves an  integer program to  produce the best  representative sets to  be used
+during the rounds  of the sensing phase. Compared  with some existing protocols,
+simulation  results based  on  multiple criteria  (energy consumption,  coverage
+ratio, and  so on) show that  the proposed protocol can  prolong efficiently the
+network lifetime and improve the coverage performance.

 
 \end{abstract}
 
 
 \end{abstract}
 


@@ -104,18 +115,26 @@ Optimization, Scheduling, Distributed Computation.
 
 \section{Introduction}
  
 
 \section{Introduction}
  

-\indent  The fast developments  in the  low-cost sensor  devices and
-wireless  communications  have allowed  the  emergence  of the WSNs.  WSN
-includes  a large  number of  small, limited-power sensors that can
-sense, process and transmit data over a wireless communication. They
-communicate with each other by using multi-hop wireless communications, cooperate together to monitor the area of interest, 
-and the measured data can be reported to a monitoring center called sink  
-for analysis it~\cite{Sudip03}. There are several applications used the
-WSN including health, home, environmental, military, and industrial
-applications~\cite{Akyildiz02}. Sensor nodes run on batteries with
-limited capacities, and it is often costly or simply impossible to replace and/or recharge batteries, especially in
-remote and hostile environments. To achieve a long life of the network, it is important to conserve battery power.
-Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
+\indent  The   fast  developments  of  low-cost  sensor   devices  and  wireless
+communications have allowed the emergence of WSNs. A WSN includes a large number
+of small, limited-power sensors that can sense, process and transmit data over a
+wireless  communication. They  communicate with  each other  by  using multi-hop
+wireless communications and cooperate together  to monitor the area of interest,
+so that  each measured data can be  reported to a monitoring  center called sink
+for  further analysis~\cite{Sudip03}.  There are  several fields  of application
+covering  a wide  spectrum for  a  WSN, including  health, home,  environmental,
+military, and industrial applications~\cite{Akyildiz02}.
+
+On the one hand sensor nodes run on batteries with limited capacities, and it is
+often  costly  or  simply  impossible  to  replace  and/or  recharge  batteries,
+especially in remote and hostile environments. Obviously, to achieve a long life
+of the network  it is important to conserve  battery power.  Therefore, lifetime
+optimization is one of the most  critical issues in wireless sensor networks. On
+the other hand we must guarantee coverage over the area of interest.  To fulfill
+these two objectives, the main idea  is to take advantage of overlapping sensing
+regions to turn-off redundant sensor nodes  and thus save energy. In this paper,
+we concentrate  on the area coverage  problem, with the  objective of maximizing
+the network lifetime by using an optimized multirounds scheduling.

 
 % One of the major scientific research challenges in WSNs, which are addressed by a large number of literature during the last few years is to design energy efficient approaches for coverage and connectivity in WSNs~\cite{conti2014mobile}. The coverage problem is one  of the
 %fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and continuously
 
 % One of the major scientific research challenges in WSNs, which are addressed by a large number of literature during the last few years is to design energy efficient approaches for coverage and connectivity in WSNs~\cite{conti2014mobile}. The coverage problem is one  of the
 %fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and continuously


@@ -125,178 +144,199 @@ Therefore, lifetime optimisation is one of the most critical issues in wireless
 %leads to decrease the lifetime of the network. To extend the lifetime of the network, the main idea is to take advantage of the overlapping sensing regions  of some  sensor nodes to  save energy by  turning off
 %some  of them  during the  sensing phase~\cite{Misra05}. WSNs require energy-efficient solutions to improve the network lifetime that is constrained by the limited power of each sensor node ~\cite{Akyildiz02}. 
 
 %leads to decrease the lifetime of the network. To extend the lifetime of the network, the main idea is to take advantage of the overlapping sensing regions  of some  sensor nodes to  save energy by  turning off
 %some  of them  during the  sensing phase~\cite{Misra05}. WSNs require energy-efficient solutions to improve the network lifetime that is constrained by the limited power of each sensor node ~\cite{Akyildiz02}. 
 

-In this paper, we concentrate on the area coverage problem, with the objective of maximizing the network lifetime by using an optimized multirounds scheduling. 
+%In this paper,  we concentrate on the area coverage  problem, with the objective
+%of maximizing the network lifetime by using an optimized multirounds scheduling.

 %The area of interest is divided into subregions.
 
 % Each period includes four phases starts with a discovery phase to exchange information among the sensors of the subregion, in order  to choose in a  suitable manner a sensor node as leader to carry out a coverage strategy.  This coverage strategy involves the solving of an integer program by the leader,  to optimize the coverage and the lifetime in the subregion by producing a sets of sensor nodes in order to take the mission of coverage preservation during several rounds in the sensing phase. 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.  
 
 The remainder of the paper is organized as follows. The next section
 % Section~\ref{rw}
 %The area of interest is divided into subregions.
 
 % Each period includes four phases starts with a discovery phase to exchange information among the sensors of the subregion, in order  to choose in a  suitable manner a sensor node as leader to carry out a coverage strategy.  This coverage strategy involves the solving of an integer program by the leader,  to optimize the coverage and the lifetime in the subregion by producing a sets of sensor nodes in order to take the mission of coverage preservation during several rounds in the sensing phase. 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.  
 
 The remainder of the paper is organized as follows. The next section
 % Section~\ref{rw}

-reviews the related work in the field. Section~\ref{pd} is devoted to
-the description of MuDiLCO Protocol. Section~\ref{cp} gives  the coverage model formulation,  which is used
-to schedule the activation of sensors.  Section~\ref{exp}  shows the
-simulation results obtained using the discrete event simulator 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}.
-
-
-\section{Related works}
+reviews  the related works in  the field.   Section~\ref{pd} is  devoted  to the
+description of MuDiLCO protocol.  Section~\ref{exp} shows the simulation results
+obtained  using the discrete  event simulator  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}.
+
+\section{Related works} % Trop proche de l'etat de l'art de l'article de Zorbas ?

 \label{rw}
 
 \label{rw}
 

-\indent 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 WSNs. Cardei and Wu \cite{cardei2006energy} provide a taxonomy for coverage algorithms in WSNs according to several design choices:
+\indent  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 WSNs. Cardei  and Wu \cite{cardei2006energy} provide a  taxonomy for coverage
+algorithms in WSNs according to several design choices:

 \begin{itemize}
 \begin{itemize}

-\item Sensors scheduling Algorithms, i.e. centralized or distributed/localized algorithms.
-\item The objective of sensor coverage, i.e. to maximize the network lifetime
-or to minimize the number of sensors during the sensing period.
-\item The homogeneous or heterogeneous nature of the
-nodes, in terms of sensing or communication capabilities.
+\item  Sensors   scheduling  algorithm  implementation,   i.e.   centralized  or
+  distributed/localized algorithms.
+\item The objective of sensor coverage, i.e. to maximize the network lifetime or
+  to minimize the number of sensors during the sensing period.
+\item The homogeneous or heterogeneous nature  of the nodes, in terms of sensing
+  or communication capabilities.

 \item The node deployment method, which may be random or deterministic.
 \item The node deployment method, which may be random or deterministic.

-\item Additional requirements for energy-efficient
-coverage and connected coverage.
+\item  Additional  requirements  for  energy-efficient  coverage  and  connected
+  coverage.

 \end{itemize}
 
 \end{itemize}
 

-The choice of non-disjoint or disjoint cover sets (sensors participate or not in many cover sets) can be added to the above list.
+The choice of non-disjoint or disjoint cover sets (sensors participate or not in
+many cover sets) can be added to the above list.

 % The independency in the cover set (i.e. whether the cover sets are disjoint or non-disjoint) \cite{zorbas2010solving} is another design choice that can be added to the above list.
    
 \subsection{Centralized Approaches}
 %{\bf Centralized approaches}
 % The independency in the cover set (i.e. whether the cover sets are disjoint or non-disjoint) \cite{zorbas2010solving} is another design choice that can be added to the above list.
    
 \subsection{Centralized Approaches}
 %{\bf Centralized approaches}

-The major approach is
-to divide/organize  the sensors into  a suitable number of  set covers
-where each  set completely covers  an interest region and  to activate
-these set covers successively. The centralized algorithms always provide nearly or close to optimal solution since the algorithm has global view of the whole network. Note that centralized algorithms have the advantage of requiring very low processing power from the sensor nodes, which usually have
-limited processing capabilities. 
-
-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
-\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
-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 $n$
-is the number of  sensors. Abrams et al.~\cite{abrams2004set}  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  includes an area, summed over  all areas, is maximized.
-Their        work        builds        upon       previous        work
-in~\cite{Slijepcevic01powerefficient} and the  generated cover sets do
-not provide complete coverage of the monitoring zone.
-\cite{cardei2005improving} propose a method to efficiently
-compute the maximum  number of disjoint set covers  such that each set
-can  monitor all  targets. They  first  transform the  problem into  a
-maximum  flow   problem, which  is  formulated  as   a  mixed  integer
-programming (MIP). Then their heuristic  uses the output of the MIP to
-compute  disjoint  set  covers.  Results  show  that  this  heuristic
-provides  a   number  of  set  covers  slightly   larger  compared  to
-\cite{Slijepcevic01powerefficient}  but with  a larger  execution time
-due  to the complexity  of the  mixed integer  programming resolution.
-
-Zorbas  et  al.  \cite{zorbas2010solving}  presented a centralised greedy
-algorithm for the efficient production of both node disjoint
-and non-disjoint cover sets. Compared to algorithm's results  of  Slijepcevic and Potkonjak
-\cite{Slijepcevic01powerefficient},  their   heuristic  produces  more
-disjoint cover sets with a slight growth rate in execution time. When producing non-disjoint cover sets, both Static-CCF and Dynamic-CCF provide cover sets offering longer network lifetime than those produced by
-\cite{cardei2005energy}. Also, they require a smaller number of node participations in order to
-achieve these results.
-
-In the  case of non-disjoint algorithms  \cite{pujari2011high}, sensors may
-participate  in more  than  one cover  set.   In some  cases, this  may
-prolong  the lifetime  of the  network in  comparison to  the disjoint
-cover set algorithms, but  designing algorithms for non-disjoint cover
-sets  generally induces a  higher order  of complexity.   Moreover, in
-case of a sensor's  failure, non-disjoint scheduling policies are less
-resilient and less  reliable because a sensor may  be involved in more
-than one  cover sets.  For instance,  Cardei et al.~\cite{cardei2005energy}
-present a  linear programming (LP)  solution and a greedy  approach to
-extend the  sensor network lifetime  by organizing the sensors  into a
-maximal  number of  non-disjoint cover  sets. Simulation  results show
-that by allowing sensors to  participate in multiple sets, the network
-lifetime         increases        compared         with        related
-work~\cite{cardei2005improving}.   In~\cite{berman04}, the
-authors  have formulated  the lifetime  problem and  suggested another
-(LP)  technique to  solve this  problem. A  centralized  solution  based      on      the     Garg-K\"{o}nemann
-algorithm~\cite{garg98}, provably near
-the optimal solution,    is also proposed.
+The major approach  is to divide/organize the sensors into  a suitable number of
+set covers where  each set completely covers an interest  region and to activate
+these set covers successively.  The centralized algorithms always provide nearly
+or close  to optimal solution since the  algorithm has global view  of the whole
+network. Note that  centralized algorithms have the advantage  of requiring very
+low  processing  power  from  the  sensor  nodes,  which  usually  have  limited
+processing  capabilities. The  main drawback  of this  kind of  approach  is its
+higher cost in communications, since the  node that will take the decision needs
+information from all the  sensor nodes. Moreover, centralized approaches usually
+suffer from the scalability problem, making them less competitive as the network
+size increases.
+
+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 \cite{Slijepcevic01powerefficient} proposed
+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 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  $n$  is  the  number  of
+sensors.   Abrams  et   al.~\cite{abrams2004set}  designed  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.  Their work builds upon previous work
+in~\cite{Slijepcevic01powerefficient}  and  the  generated  cover  sets  do  not
+provide complete coverage of the monitoring zone.
+
+\cite{cardei2005improving} proposed a method to efficiently  compute the maximum
+number of disjoint  set covers such that each set can  monitor all targets. They
+first transform the problem into a  maximum flow problem, which is formulated as
+a mixed integer  programming (MIP). Then their heuristic uses  the output of the
+MIP to compute disjoint set covers.  Results show that this heuristic provides a
+number      of     set      covers     slightly      larger      compared     to
+\cite{Slijepcevic01powerefficient}, but with a  larger execution time due to the
+complexity of the mixed integer programming resolution.
+
+Zorbas et al.  \cite{zorbas2010solving} presented a centralized greedy algorithm
+for  the efficient  production  of  both node  disjoint  and non-disjoint  cover
+sets.   Compared   to  algorithm's   results   of   Slijepcevic  and   Potkonjak
+\cite{Slijepcevic01powerefficient}, their heuristic produces more disjoint cover
+sets with  a slight growth rate  in execution time.  When producing non-disjoint
+cover sets,  both Static-CCF  and Dynamic-CCF algorithms,  where CCF  means that
+they  use a cost  function called  Critical Control  Factor, provide  cover sets
+offering     longer    network     lifetime    than     those     produced    by
+\cite{cardei2005energy}.   Also,  they   require  a   smaller  number   of  node
+participations in order to achieve these results.
+
+In  the  case  of  non-disjoint algorithms  \cite{pujari2011high},  sensors  may
+participate in  more than one  cover set.  In  some cases, this may  prolong the
+lifetime of the network in comparison  to the disjoint cover set algorithms, but
+designing  algorithms for  non-disjoint cover  sets generally  induces  a higher
+order  of complexity.   Moreover, in  case of  a sensor's  failure, non-disjoint
+scheduling policies are less resilient and less reliable because a sensor may be
+involved   in   more  than   one   cover   sets.    For  instance,   Cardei   et
+al.~\cite{cardei2005energy}  present a  linear programming  (LP) solution  and a
+greedy approach to extend the  sensor network lifetime by organizing the sensors
+into a maximal  number of non-disjoint cover sets.  Simulation results show that
+by  allowing sensors  to  participate  in multiple  sets,  the network  lifetime
+increases     compared     with     related     work~\cite{cardei2005improving}.
+In~\cite{berman04},  the  authors  have  formulated  the  lifetime  problem  and
+suggested another (LP)  technique to solve this problem.  A centralized solution
+based  on  the  Garg-K\"{o}nemann  algorithm~\cite{garg98},  provably  near  the
+optimal solution, is also proposed.

 
 \subsection{Distributed approaches}
 %{\bf Distributed approaches}
 
 \subsection{Distributed approaches}
 %{\bf Distributed approaches}

-In distributed $\&$ localized coverage algorithms, the required computation to schedule the activity of sensor nodes will be done by the cooperation among the neighbours nodes. These algorithms may require more computation power  for the processing by the cooperated sensor nodes but they are more scaleable for large WSNs.  Localized and distributed algorithms generally result in non-disjoint set covers. 
-
-Some      distributed     algorithms      have      been     developed
-in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02, yardibi2010distributed}  to perform the
-scheduling so as to coverage preservation.   Distributed algorithms typically  operate in  rounds for
-a predetermined  duration. At  the  beginning of  each  round, a  sensor
-exchanges 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 made on simple greedy criteria like  the largest uncovered
-area   \cite{Berman05efficientenergy},   maximum   uncovered   targets
-\cite{lu2003coverage}.   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 the node ID
-and the node location  to its neighbors at the beginning  of each round. A
-sensor determines  its status by  a rule named off-duty  eligible rule,
-which tells  him to  turn off if  its sensing  area is covered  by its
-neighbors. A  back-off scheme is  introduced to let each  sensor delay
-the decision process  with a random period of time,  in order to avoid
-simultaneous conflicting decisions between nodes and  lack of coverage on any area.
-\cite{prasad2007distributed}  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
-prioritizes 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. 
-
-The authors in \cite{yardibi2010distributed}  developed a distributed adaptive sleep scheduling algorithm (DASSA) for WSNs with partial coverage. DASSA does not require location information of sensors while maintaining connectivity and satisfying a user defined coverage target. In DASSA, nodes use the residual energy levels and feedback from the sink for scheduling the activity of their neighbors. This feedback mechanism reduces the randomness in scheduling that would otherwise occur due to the absence of location information. 
-
-In \cite{ChinhVu},  the author proposed a novel  distributed heuristic, called
-Distributed Energy-efficient  Scheduling for k-coverage  (DESK), which
-ensures that the energy consumption  among the sensors is balanced and
-the lifetime  maximized while the coverage  requirement is maintained.
-This  heuristic   works  in  rounds,  requires   only  1-hop  neighbor
-information,  and each  sensor decides  its status  (active  or sleep)
-based    on    the    perimeter    coverage    model    proposed    in
+In distributed  and localized coverage  algorithms, the required  computation to
+schedule the  activity of  sensor nodes  will be done  by the  cooperation among
+neighboring nodes. These  algorithms may require more computation  power for the
+processing  by the cooperating  sensor nodes,  but they  are more  scalable for
+large  WSNs.    Localized  and   distributed  algorithms  generally   result  in
+non-disjoint set covers.
+
+Some        distributed       algorithms        have        been       developed
+in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02,    yardibi2010distributed}
+to perform  the scheduling so  as to preserve coverage.   Distributed algorithms
+typically operate  in rounds for a  predetermined duration. At  the beginning of
+each  round, a  sensor  exchanges 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 made on  simple greedy criteria like the largest uncovered
+area    \cite{Berman05efficientenergy}     or    maximum    uncovered    targets
+\cite{lu2003coverage}.  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  the node~ID and  the node
+location to  its neighbors at the  beginning of each round.  A sensor determines
+its status by a  rule named off-duty eligible rule, which tells  him to turn off
+if its sensing area is covered by its neighbors. A back-off scheme is introduced
+to let each sensor  delay the decision process with a random  period of time, in
+order  to avoid  simultaneous conflicting  decisions between  nodes and  lack of
+coverage  on  any  area.    \cite{prasad2007distributed}  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 prioritizes 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.
+
+The  authors in \cite{yardibi2010distributed}  developed a  Distributed Adaptive
+Sleep Scheduling Algorithm  (DASSA) for WSNs with partial  coverage.  DASSA does
+not require  location information of sensors while  maintaining connectivity and
+satisfying a  user defined  coverage target.  In  DASSA, nodes use  the residual
+energy levels  and feedback from the  sink for scheduling the  activity of their
+neighbors.  This  feedback mechanism reduces  the randomness in  scheduling that
+would  otherwise  occur   due  to  the  absence  of   location  information.  In
+\cite{ChinhVu},  the  author  proposed  a novel  distributed  heuristic,  called
+Distributed  Energy-efficient Scheduling  for k-coverage  (DESK),  which ensures
+that  the energy  consumption among  the sensors  is balanced  and  the lifetime
+maximized while the coverage requirement is maintained.  This heuristic works in
+rounds, requires only one-hop neighbor  information, and each sensor decides its
+status  (active or  sleep) based  on the  perimeter coverage  model  proposed in

 \cite{Huang:2003:CPW:941350.941367}.
 
 \cite{Huang:2003:CPW:941350.941367}.
 

-

 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
 %heterogeneous energy wireless sensor networks. 
 %In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions. 
 
 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
 %heterogeneous energy wireless sensor networks. 
 %In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions. 
 

-The works presented in \cite{Bang, Zhixin, Zhang}  focuses on a Coverage-Aware, Distributed  Energy- Efficient and distributed clustering methods respectively, which aims to extend the network lifetime, while the coverage is ensured.
-S.  Misra  et al.  \cite{Misra}  proposed  a  localized algorithm  for
-coverage in  sensor networks. The algorithm conserve  the energy while
-ensuring  the network coverage  by activating  the subset  of sensors,
-with  the  minimum  overlap  area. The proposed  method  preserves  the
-network connectivity by formation of the network backbone. 
-More    recently,   Shibo   et
-al. \cite{Shibo}  expressed the coverage  problem as a  minimum weight
-submodular  set cover  problem  and proposed  a Distributed  Truncated
-Greedy Algorithm  (DTGA) to  solve it. They  take advantage  from both
-temporal  and spatial  correlations between  data sensed  by different
-sensors,  and   leverage  prediction,  to  improve   the  lifetime. 
-
-In \cite{xu2001geography}, Xu et al. proposed an algorithm, called Geographical Adaptive Fidelity (GAF), which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
-
-Some other approaches (outside the scope of our work) do  not consider a synchronized and predetermined
-period  of time  where the  sensors are  active or  not.  Indeed, each
-sensor  maintains its  own timer  and its  wake-up time is randomized
-\cite{Ye03} or regulated \cite{cardei2005maximum} over time. 
-
-The MuDiLCO protocol (for Multiperiod Distributed Lifetime Coverage Optimization protocol) presented in this paper is an extension of the approach explained in~\cite{idrees2014coverage}. In~\cite{idrees2014coverage}, the protocol is deployed over only two subregions. Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity. Compared to our previous paper, we study here the possibility of dividing the sensing phase into multiple rounds and we also add a model of energy consumption to assess the efficiency of our approach.
+The  works presented in  \cite{Bang, Zhixin,  Zhang} focuses  on coverage-aware,
+distributed energy-efficient,  and distributed clustering  methods respectively,
+which aims  to extend the network  lifetime, while the coverage  is ensured.  S.
+Misra et al.  \cite{Misra} proposed a localized algorithm for coverage in sensor
+networks. The algorithm conserve the  energy while ensuring the network coverage
+by activating the subset of sensors  with the minimum overlap area. The proposed
+method preserves the network connectivity  by formation of the network backbone.
+More recently,  Shibo et  al. \cite{Shibo} expressed  the coverage problem  as a
+minimum weight submodular set cover problem and proposed a Distributed Truncated
+Greedy Algorithm (DTGA) to solve it.  They take advantage from both temporal and
+spatial  correlations between  data sensed  by different  sensors,  and leverage
+prediction,  to   improve  the   lifetime.  In  \cite{xu2001geography},   Xu  et
+al. proposed  an algorithm, called  Geographical Adaptive Fidelity  (GAF), which
+uses geographic location  information to divide the area  of interest into fixed
+square grids. Within each grid, it keeps only one node staying awake to take the
+responsibility of sensing and communication.
+
+Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
+synchronized and  predetermined period of time  where the sensors  are active or
+not.   Indeed, each  sensor maintains  its  own timer  and its  wake-up time  is
+randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
+
+The MuDiLCO protocol (for Multiperiod Distributed Lifetime Coverage Optimization
+protocol) presented  in this  paper is an  extension of the  approach introduced
+in~\cite{idrees2014coverage}.  In~\cite{idrees2014coverage},   the  protocol  is
+deployed over  only two  subregions. Simulation results  have shown that  it was
+more  interesting  to  divide  the  area  into  several  subregions,  given  the
+computation complexity. Compared to our previous paper, in this one we study the
+possibility of dividing  the sensing phase into multiple rounds  and we also add
+an  improved  model  of energy  consumption  to  assess  the efficiency  of  our
+approach.
+

 %The main contributions of our MuDiLCO Protocol can be summarized as follows:
 %(1) The high coverage ratio, (2) The reduced number of active nodes, (3) The distributed optimization over the subregions in the area of interest, (4) The distributed dynamic leader election at each round based on some priority factors that led to energy consumption balancing among the nodes in the same subregion, (5) The primary point coverage model to represent each sensor node in the network, (6) 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 for a multirounds to take the mission of the coverage in each subregion, (7) The very low energy consumption, (8) The higher network lifetime.
 %\section{Preliminaries}
 %\label{Pr}
 
 %The main contributions of our MuDiLCO Protocol can be summarized as follows:
 %(1) The high coverage ratio, (2) The reduced number of active nodes, (3) The distributed optimization over the subregions in the area of interest, (4) The distributed dynamic leader election at each round based on some priority factors that led to energy consumption balancing among the nodes in the same subregion, (5) The primary point coverage model to represent each sensor node in the network, (6) 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 for a multirounds to take the mission of the coverage in each subregion, (7) The very low energy consumption, (8) The higher network lifetime.
 %\section{Preliminaries}
 %\label{Pr}
 

-
-
-

 %Network Lifetime
 
 %\subsection{Network Lifetime}
 %Network Lifetime
 
 %\subsection{Network Lifetime}


@@ -313,10 +353,7 @@ The MuDiLCO protocol (for Multiperiod Distributed Lifetime Coverage Optimization
 %active sensor node without  connectivity towards a base station cannot
 %transmit information on an event in the area that it monitors.
 
 %active sensor node without  connectivity towards a base station cannot
 %transmit information on an event in the area that it monitors.
 

-
-
-
-\section{ The MuDiLCO Protocol Description}
+\section{MuDiLCO protocol description}

 \label{pd}
 
 %Our work will concentrate on the area coverage by design
 \label{pd}
 
 %Our work will concentrate on the area coverage by design


@@ -331,36 +368,36 @@ The MuDiLCO protocol (for Multiperiod Distributed Lifetime Coverage Optimization
 %minimizing  overcoverage (points  covered by  multiple  active sensors
 %simultaneously).
 
 %minimizing  overcoverage (points  covered by  multiple  active sensors
 %simultaneously).
 

-
-

 %In this section, we introduce a Multiperiod Distributed Lifetime Coverage Optimization protocol, which is called MuDiLCO. It is  distributed on each subregion in the area of interest. It is based on two efficient techniques: network
 %leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.  
 %The main features of our MuDiLCO protocol:
 %i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into periods, which consists in round(s), iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi)  it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative non-disjoint sets of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our Protocol.
 
 %In this section, we introduce a Multiperiod Distributed Lifetime Coverage Optimization protocol, which is called MuDiLCO. It is  distributed on each subregion in the area of interest. It is based on two efficient techniques: network
 %leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.  
 %The main features of our MuDiLCO protocol:
 %i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into periods, which consists in round(s), iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi)  it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative non-disjoint sets of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our Protocol.
 

+\subsection{Assumptions}

 
 

-\subsection{ Assumptions and Models}
-We consider  a randomly and  uniformly deployed network  consisting of
-static  wireless sensors. The  wireless sensors  are deployed  in high
-density to ensure initially a high coverage ratio of the interested area. We
-assume that  all nodes are  homogeneous in terms of  communication and
-processing capabilities and heterogeneous in term of energy provision.
-The  location  information is  available  to  the  sensor node  either
-through hardware such as embedded GPS or through location discovery
-algorithms.   
-\indent We consider a boolean  disk coverage model which is the most
-widely used sensor coverage model in the literature. Each sensor has a
-constant sensing range $R_s$. All  space points within a disk centered
-at  the sensor with  the radius  of the  sensing range  is said  to be
-covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$.
-In  fact,   Zhang  and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the
-previous hypothesis, a complete coverage of a convex area implies
-connectivity among the working nodes in the active mode.
-
-\indent Instead of working with the coverage area, we consider for each
-sensor a set of points called  primary points. We also assume that the
-sensing disk defined  by a sensor is covered if all the primary points of
-this sensor are covered. The choice of number and locations of primary points is the subject of another study not presented here.
+We  consider a  randomly and  uniformly  deployed network  consisting of  static
+wireless sensors.  The sensors are  deployed in high density to ensure initially
+a high  coverage ratio  of the interested  area.  We  assume that all  nodes are
+homogeneous  in   terms  of  communication  and   processing  capabilities,  and
+heterogeneous  from the  point  of view  of  energy provision.   Each sensor  is
+supposed  to get information  on its  location either  through hardware  such as
+embedded GPS or through location discovery algorithms.
+   
+To model  a sensor node's coverage  area, we consider the  boolean disk coverage
+model   which  is  the   most  widely   used  sensor   coverage  model   in  the
+literature. Thus, each  sensor has a constant sensing range  $R_s$ and all space
+points within  the disk centered  at the sensor  with the radius of  the sensing
+range  is  said  to  be  covered  by  this sensor.   We  also  assume  that  the
+communication   range  satisfies   $R_c  \geq   2R_s$.   In   fact,   Zhang  and
+Zhou~\cite{Zhang05} proved that if  the transmission range fulfills the previous
+hypothesis, a complete coverage of  a convex area implies connectivity among the
+working nodes in the active mode.
+
+Instead  of working  with a  continuous coverage  area, we  make it  discrete by
+considering for each sensor a set of points called primary points. Consequently,
+we assume  that the sensing disk  defined by a sensor  is covered if  all of its
+primary points are covered. The choice of number and locations of primary points
+is the subject of another study not presented here.

 
 %By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless
 %sensor node  and its $R_s$,  we calculate the primary  points directly
 
 %By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless
 %sensor node  and its $R_s$,  we calculate the primary  points directly


@@ -375,106 +412,126 @@ this sensor are covered. The choice of number and locations of primary points is
 %Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS  or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list $L$.
 %The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader after the decision to apply multi-round activity scheduling during the sensing phase. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will produce the cover sets of sensor nodes to take the mission of coverage during the sensing phase for $T$ rounds. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's schedule for $T$ rounds during the period of sensing, either Active or sleep until the starting of next period. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep based on it's schedule for $T$ rounds during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, which are includes $T$ rounds, all the sensor nodes in the same subregion will start new period by executing the MuDiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
 
 %Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS  or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list $L$.
 %The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader after the decision to apply multi-round activity scheduling during the sensing phase. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will produce the cover sets of sensor nodes to take the mission of coverage during the sensing phase for $T$ rounds. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's schedule for $T$ rounds during the period of sensing, either Active or sleep until the starting of next period. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep based on it's schedule for $T$ rounds during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, which are includes $T$ rounds, all the sensor nodes in the same subregion will start new period by executing the MuDiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
 

-\subsection{The Main Idea}
-The   area  of  interest   can  be  divided using the
-divide-and-conquer strategy into smaller areas,  called subregions and
-then  our MuDiLCO protocol  will be implemented  in each  subregion
-simultaneously. \\
+\subsection{Background idea}

 
 

-\noindent Our MuDiLCO protocol works in periods fashion as shown in figure~\ref{fig2}.
+The  area of  interest  can be  divided  using the  divide-and-conquer
+strategy into  smaller areas, called subregions, and  then our MuDiLCO
+protocol will be implemented in each subregion in a distributed way.
+
+As can  be seen  in Figure~\ref{fig2}, our  protocol works  in periods
+fashion, where  each is  divided into 4  phases: Information~Exchange,
+Leader~Election,  Decision, and  Sensing.  Each  sensing phase  may be
+itself divided  into $T$ rounds  and for each  round a set  of sensors
+(said a cover set) is responsible for the sensing task.

 \begin{figure}[ht!]
 \centering
 \includegraphics[width=95mm]{Modelgeneral.pdf} % 70mm
 \begin{figure}[ht!]
 \centering
 \includegraphics[width=95mm]{Modelgeneral.pdf} % 70mm

-\caption{MuDiLCO protocol}
+\caption{The MuDiLCO protocol scheme executed on each node}

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

-Each period is divided into 4 phases: Information  Exchange,
-Leader  Election, Decision,  and  Sensing.  Each sensing phase may be itself divided into $T$ rounds.
+%Each period is divided into 4 phases: Information  Exchange,
+%Leader  Election, Decision,  and  Sensing.  Each sensing phase may be itself divided into $T$ rounds.

 % set cover responsible for the sensing task.  
 % set cover responsible for the sensing task.  

-For each round a set of sensors (said a cover set) is responsible for the sensing task.
-This protocol is reliable  against an unexpected node failure  because it works
-in periods. On the one hand,  if a node  failure is  detected before
-making the decision, the node will not participate to this phase, and,
-on the other hand, if the  node failure occurs after the decision, the
-sensing task of the network  will be temporarily affected: only during
-the period of sensing until a new period starts.  
-The energy
-consumption  and  some other  constraints  can  easily  be taken  into
-account  since  the  sensors   can  update  and  then  exchange  their
+%For each round a set of sensors (said a cover set) is responsible for the sensing task.
+
+This protocol is reliable  against an unexpected node failure, because
+it works  in periods. On the one  hand, if a node  failure is detected
+before  making the  decision, the  node will  not participate  to this
+phase, and,  on the other hand,  if the node failure  occurs after the
+decision,  the  sensing  task  of  the  network  will  be  temporarily
+affected: only during the period of sensing until a new period starts.
+
+The energy consumption and some  other constraints can easily be taken
+into account,  since the  sensors can update  and then  exchange their

 information (including their residual energy) at the beginning of each
 information (including their residual energy) at the beginning of each

-period.  However,   the  pre-sensing  phases   (Information Exchange,  Leader
-Election,  Decision) are energy  consuming for  some nodes,  even when
-they do not  join the network to monitor the  area. 
+period.  However, the pre-sensing phases (Information Exchange, Leader
+Election, and Decision) are energy consuming for some nodes, even when
+they do not join the network to monitor the area.

 
 %%%%%%%%%%%%%%%%%parler optimisation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
 %%%%%%%%%%%%%%%%%parler optimisation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 

-We define two types of packets used by MuDiLCO protocol :
+We  define two  types of  packets that  will be  used by  the proposed
+protocol:

 \begin{enumerate}[(a)] 
 \begin{enumerate}[(a)] 

-\item INFO packet: sent by each sensor node to all the nodes inside a subregion for information exchange.
-\item ActiveSleep packet: sent by the leader to all the nodes inside a subregion to inform them to be Active or Sleep during the sensing phase.
+\item INFO packet:  a such packet will be sent by  each sensor node to
+  all the nodes inside a subregion for information exchange.
+\item Active-Sleep packet: sent by the leader to all the nodes inside a
+  subregion to inform them to remain  Active or to go Sleep during the
+  sensing phase.

 \end{enumerate}
 
 \end{enumerate}
 

-There are five status for each sensor node in the network :
+There are five status for each sensor node in the network:

 \begin{enumerate}[(a)] 
 \begin{enumerate}[(a)] 

-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: sensor  node is waiting for a  decision (to be active
+  or not);
+\item COMPUTATION: sensor node has  been elected as leader and applies
+  the optimization process;
+\item ACTIVE: sensor node participate to the monitoring of the area;
+\item SLEEP: sensor node is turned off to save energy;
+\item COMMUNICATION: sensor node is transmitting or receiving packet.

 \end{enumerate}
 
 Below, we describe each phase in more details.
 
 \subsection{Information Exchange Phase}
 
 \end{enumerate}
 
 Below, we describe each phase in more details.
 
 \subsection{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
-its subregion by using an INFO packet (containing information on position coordinates, current remaining energy, sensor node id, number of its one-hop live neighbors)  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
-remaining energy corresponds to the time that a sensor can live in the
-active mode.
+Each sensor node $j$ sends its position, remaining energy $RE_j$, and the number
+of neighbors $NBR_j$  to all wireless sensor nodes in its  subregion by using an
+INFO packet  (containing information on position  coordinates, current remaining
+energy, sensor node ID, number of its one-hop live neighbors) and then waits for
+packets sent by other nodes.  After  that, each node will have information about
+all  the sensor  nodes in  the subregion.   In our  model, the  remaining energy
+corresponds to the time that a sensor can live in the active mode.

 
 %\subsection{\textbf Working Phase:}
 
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 
 
 %\subsection{\textbf Working Phase:}
 
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 

-\subsection{Leader Election Phase}
-This step includes choosing the Wireless  Sensor Node  Leader (WSNL),
-which  will  be  responsible  for executing  the coverage  algorithm.  Each
+\subsection{Leader Election phase}
+
+This step consists in choosing the Wireless Sensor Node Leader (WSNL),
+which will be responsible  for executing the coverage algorithm.  Each

 subregion  in  the   area  of  interest  will  select   its  own  WSNL
 subregion  in  the   area  of  interest  will  select   its  own  WSNL

-independently  for each  period.  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
-equality, larger index. Observations on previous simulations suggest to use the number of $1-hop$ neighbours as the primary criterion to reduce energy consumption due to the communication.
-
-%the more priority selection factor is the number of $1-hop$ neighbours, $NBR j$, which can  minimize the energy consumption during the communication Significantly.  
+independently  for each  period.  All  the sensor  nodes  cooperate to
+elect a WSNL.  The nodes in  the same subregion will select the leader
+based on  the received informations from  all other nodes  in the same
+subregion.  The selection criteria are, in order of importance: larger
+number of  neighbors, larger  remaining energy, and  then in  case of
+equality, larger  index. Observations on  previous simulations suggest
+to use  the number of one-hop  neighbors as the  primary criterion to
+reduce energy consumption due to the communications.
+
+%the more priority selection factor is the number of $1-hop$ neighbors, $NBR j$, which can  minimize the energy consumption during the communication Significantly.  

 %The pseudo-code for leader election phase is provided in Algorithm~1.
 
 %Where $E_{th}$ is the minimum energy needed to stay active during the sensing phase. As shown in Algorithm~1, the more priority selection factor is the number of $1-hop$ neighbours, $NBR j$, which can  minimize the energy consumption during the communication Significantly.  
 
 %The pseudo-code for leader election phase is provided in Algorithm~1.
 
 %Where $E_{th}$ is the minimum energy needed to stay active during the sensing phase. As shown in Algorithm~1, the more priority selection factor is the number of $1-hop$ neighbours, $NBR j$, which can  minimize the energy consumption during the communication Significantly.  
 

-

 \subsection{Decision phase}
 \subsection{Decision phase}

-The  WSNL will  solve an  integer  program to
-select which cover sets will be activated in the following sensing phase
-to cover  the subregion. The integer program will produce $T$ cover sets (for $T$ rounds). WSNL will send  Active-Sleep packet to each
-sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in each round of the sensing phase.
-\indent  The integer  program   is   based   on  the   model   proposed   by
-\cite{pedraza2006} with some modification, where the objective is  to find a maximum number of
-disjoint  cover sets.   To accomplish  this goal,  authors  proposed an
-integer program, which forces undercoverage and overcoverage of targets
-to  become  minimal at  the  same  time.   They use  binary  variables
-$x_{jl}$ to indicate  if sensor $j$ belongs to cover  set $l$.  In our
-model, we  consider  binary  variables $X_{t,j}$,  which  determine the possiblity of activation of sensor $j$ during the round $t$ of a given sensing phase. We also consider primary points  as targets.   The set  of primary  points is
-denoted by $P$ and the set of sensors by $J$. Only sensors able to be alive during at least one round are involved in the integer program.
+
+Each WSNL  will solve  an integer program  to select which  cover sets
+will  be  activated  in  the  following sensing  phase  to  cover  the
+subregion to which  it belongs.  The integer program  will produce $T$
+cover sets,  one for each round.   The WSNL will  send an Active-Sleep
+packet  to each  sensor  in  the subregion  based  on the  algorithm's
+results,  indicating if the  sensor should  be active  or not  in each
+round of the sensing phase. The  integer program is based on the model
+proposed  by  \cite{pedraza2006}  with  some modification,  where  the
+objective  is to find  a maximum  number of  disjoint cover  sets.  To
+fulfill  this goal,  the  authors proposed  an  integer program  which
+forces undercoverage and overcoverage  of targets to become minimal at
+the  same time.   They use  binary variables  $x_{jl}$ to  indicate if
+sensor $j$ belongs to cover set $l$.  In our model, we consider binary
+variables  $X_{t,j}$  to determine  the  possibility  of activation  of
+sensor $j$  during the  round $t$  of a given  sensing phase.  We also
+consider  primary points  as targets.   The set  of primary  points is
+denoted by $P$ and the set of  sensors by $J$. Only sensors able to be
+alive during at least one round are involved in the integer program.

 
 %parler de la limite en energie Et pour un round
 
 
 %parler de la limite en energie Et pour un round
 

-\noindent  For  a primary  point  $p$,  let  $\alpha_{j,p}$ denote  the
-indicator function of whether the point $p$ is covered, that is:
+For  a primary  point  $p$, let  $\alpha_{j,p}$  denote the  indicator
+function of whether the point $p$ is covered, that is:

 \begin{equation}
 \alpha_{j,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 \alpha_{j,p} = \left \{ 
 \begin{array}{l l}


@@ -484,8 +541,8 @@ 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 active sensors that cover the primary point $p$ during round $t$ is equal
-to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
+The number of  active sensors that cover the  primary point $p$ during
+round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:

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


@@ -504,10 +561,10 @@ We define the Overcoverage variable $\Theta_{t,p}$ as:
 \end{array} \right.
 \label{eq13} 
 \end{equation}
 \end{array} \right.
 \label{eq13} 
 \end{equation}

-\noindent More precisely, $\Theta_{t,p}$ represents the number of active
-sensor  nodes  minus  one  that  cover the  primary  point  $p$ during the round $t$.\\
-The Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is defined
-by:
+More precisely, $\Theta_{t,p}$ represents  the number of active sensor
+nodes  minus one that  cover the  primary point  $p$ during  the round
+$t$.  The Undercoverage variable  $U_{t,p}$ of  the primary  point $p$
+during round $t$ is defined by:

 \begin{equation}
 U_{t,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 U_{t,p} = \left \{ 
 \begin{array}{l l}


@@ -517,33 +574,31 @@ U_{t,p} = \left \{
 \label{eq14} 
 \end{equation}
 
 \label{eq14} 
 \end{equation}
 

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

 \begin{equation}
 \begin{equation}

- Minimize   \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p}  \right)  \label{eq15} 
+ \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p}  \right)  \label{eq15} 

 \end{equation}
 
 \end{equation}
 

-\hspace{30 mm} Subject to\\
+Subject to

 \begin{equation}
 \begin{equation}

-  \sum_{j=1}^{J} \alpha_{j,p} * X_{t,j}   = \Theta_{t,p} - U_{t,p} + 1 \label{eq16} \hspace{6 mm} \forall p \in P, t = 1..T
+  \sum_{j=1}^{|J|} \alpha_{j,p} * X_{t,j}   = \Theta_{t,p} - U_{t,p} + 1 \label{eq16} \hspace{6 mm} \forall p \in P, t = 1,\dots,T

 \end{equation}
 
 \begin{equation}
 \end{equation}
 
 \begin{equation}

-  \sum_{t=1}^{T}  X_{t,j}   \leq  \floor*{RE_{j}/E_{th}} \hspace{6 mm} \forall j \in J, t = 1..T
+  \sum_{t=1}^{T}  X_{t,j}   \leq  \floor*{RE_{j}/E_{R}} \hspace{6 mm} \forall j \in J, t = 1,\dots,T

   \label{eq144} 
 \end{equation}
 
 \begin{equation}
   \label{eq144} 
 \end{equation}
 
 \begin{equation}

-X_{t,j} \in \lbrace0,1\rbrace,   \hspace{10 mm} \forall j \in J, t = 1..T \label{eq17} 
+X_{t,j} \in \lbrace0,1\rbrace,   \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17} 

 \end{equation}
 
 \begin{equation}
 \end{equation}
 
 \begin{equation}

-U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1..T  \label{eq18} 
+U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T  \label{eq18} 

 \end{equation}
 
 \begin{equation}
 \end{equation}
 
 \begin{equation}

- \Theta_{t,p} \geq 0  \hspace{10 mm}\forall p \in P, t = 1..T  \label{eq178} 
+ \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}

 \end{equation}
 
 %\begin{equation}
 \end{equation}
 
 %\begin{equation}


@@ -552,79 +607,101 @@ U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1..T  \label{e
 
 
 \begin{itemize}
 
 
 \begin{itemize}

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

   sensing during the round $t$ (1 if yes and 0 if not);
   sensing during the round $t$ (1 if yes and 0 if not);

-\item $\Theta_{t,p}$  : {\it overcoverage}, the number  of sensors minus
+\item $\Theta_{t,p}$ - {\it overcoverage}: the number of sensors minus

   one that are covering the primary point $p$ during the round $t$;
   one that are covering the primary point $p$ during the round $t$;

-\item $U_{t,p}$  : {\it undercoverage},  indicates whether or  not the primary point
-  $p$ is being covered during the round $t$(1 if not covered and 0 if covered).
+\item $U_{t,p}$  - {\it undercoverage}:  indicates whether or  not the
+  primary point  $p$ is being covered  during the round $t$  (1 if not
+  covered and 0 if covered).

 \end{itemize}
 
 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
 \end{itemize}
 
 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  balancing  the
-restriction  equations by taking  positive values. Constraint \ref{eq144} guarantees that the sensor has enough energy ($RE_j$ its remaining energy) to be alive during the selected rounds knowing that $E_{th}$ is the requiring energy to be alive during one round. 
-There are  two main         
-objectives.  First, we limit the overcoverage of primary points in order to
-activate a minimum number of sensors.  Second we prevent the absence of monitoring on
- some parts of the subregion by  minimizing the 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 our simulations priority is given to the coverage by choosing $W_{\theta}$ very large compared to $W_U$. 
+case,  overcoverage  and undercoverage  variables  help balancing  the
+restriction equations by taking  positive values. The constraint given
+by equation~(\ref{eq144}) guarantees that the sensor has enough energy
+($RE_j$ corresponds  to its remaining  energy) to be alive  during the
+selected rounds knowing that $E_{R}$  is the amount of energy required
+to be alive during one round.
+
+There are  two main objectives.   First, we limit the  overcoverage of
+primary  points in  order to  activate  a minimum  number of  sensors.
+Second  we prevent  the absence  of monitoring  on some  parts  of the
+subregion by minimizing the 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  our simulations
+priority is given to the  coverage by choosing $W_{\theta}$ very large
+compared to $W_U$.

 %The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase.
 
 %The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase.
 

-

 \subsection{Sensing phase}
 \subsection{Sensing phase}

-The sensing phase consists of $T$ rounds. Each sensor node in the subregion will receive  an Active-Sleep  packet from WSNL  informing it to stay awake or to go to sleep  for each round of the sensing phase. 
-% In each round during the sensing phase, there is a cover set of sensor nodes,  in which  the active  sensors will  execute  their sensing  task  to preserve maximal  coverage and lifetime in the subregion and this will continue until finishing the round $T$ and starting new period. 

 
 

+The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
+receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
+sleep for  each round of  the sensing phase.  Algorithm~\ref{alg:MuDiLCO}, which
+will be  executed by each node  at the beginning  of a period, explains  how the
+Active-Sleep packet is obtained.

 
 

+% In each round during the sensing phase, there is a cover set of sensor nodes,  in which  the active  sensors will  execute  their sensing  task  to preserve maximal  coverage and lifetime in the subregion and this will continue until finishing the round $T$ and starting new period. 

 
 

-\begin{algorithm}                
+\begin{algorithm}[h!]                

  % \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
  % \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 it's subregion} \; 
+  %\emph{Initialize the sensor node and determine it's position and subregion} \; 

   
   

-  \If{ $RE_j \geq E_{th}$ }{
-      \emph{ $s_j.status$ = LISTENING}\;
-      \emph{ Send and Receive INFO Packet to and from other nodes in the subregion}\;
+  \If{ $RE_j \geq E_{R}$ }{
+      \emph{$s_j.status$ = COMMUNICATION}\;
+      \emph{Send $INFO()$ packet to other nodes in the subregion}\;
+      \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 

       %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
       %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
       
       %\If{ the received INFO Packet = No. of nodes in it's subregion -1  }{
       %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
       %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
       
       %\If{ the received INFO Packet = No. of nodes in it's subregion -1  }{

-           \emph{Selection of LeaderID}\;
-           \If{ $ s_j.ID = LeaderID $}{ 
-               \emph{Execute Integer Program Algorithm $(Schedule_{T,J})$ }\;
-               \emph{ Send $ActiveSleep()$ Packet with $Schedule_{1..T,k}$  }\;
-                 \emph{UPDATE $RE_j $}\;
-                         }       
-           \Else{ 
-                 \emph{Wait $ActiveSleep()$ Packet from the Leader}\;
-                % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
-                 \emph{UPDATE $RE_j $}\;
-           }  
-    %  }
-
+      \emph{LeaderID = Leader election}\;
+      \If{$ s_j.ID = LeaderID $}{
+        \emph{$s_j.status$ = COMPUTATION}\;
+        \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
+          Execute Integer Program Algorithm($T,J$)}\;
+        \emph{$s_j.status$ = COMMUNICATION}\;
+        \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
+          with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
+        \emph{Update $RE_j $}\;
+      }          
+      \Else{
+        \emph{$s_j.status$ = LISTENING}\;
+        \emph{Wait $ActiveSleep()$ packet from the Leader}\;
+        % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
+        \emph{Update $RE_j $}\;
+      }  
+      %  }

   }
   \Else { Exclude $s_j$ from entering in the current sensing phase}
   }
   \Else { Exclude $s_j$ from entering in the current sensing phase}

-   
+  

  %   \emph{return X} \;
 \caption{MuDiLCO($s_j$)}
 \label{alg:MuDiLCO}
 
 \end{algorithm}
 
  %   \emph{return X} \;
 \caption{MuDiLCO($s_j$)}
 \label{alg:MuDiLCO}
 
 \end{algorithm}
 

-
-
-
-\section{Simulations}
+\section{Experimental study}

 \label{exp}
 \label{exp}

-\subsection{Simulation Framework}
-We conducted  a series of simulations to evaluate the
-efficiency and the relevance of our approach,  using the  discrete event
-simulator  OMNeT++  \cite{varga}. The simulation parameters are summarized in
-Table~\ref{table3}. \\
+\subsection{Simulation setup}
+
+We  conducted  a  series of  simulations  to  evaluate  the efficiency  and  the
+relevance  of   our  approach,  using  the  discrete   event  simulator  OMNeT++
+\cite{varga}.     The     simulation     parameters    are     summarized     in
+Table~\ref{table3}.  Each experiment  for  a network  is  run over  25~different
+random topologies and  the results presented hereafter are  the average of these
+25 runs.
+%Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions. 
+We  performed  simulations for  five  different  densities  varying from  50  to
+250~nodes. Experimental results are obtained from randomly generated networks in
+which  nodes  are 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  cover the  sensing field  with the  given sensing
+range.

 
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}
 
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}


@@ -642,15 +719,15 @@ Parameter & Value  \\ [0.5ex]
 %heading
 \hline
 % inserts single horizontal line
 %heading
 \hline
 % inserts single horizontal line

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

 % inserting body of the table
 %\hline
 % inserting body of the table
 %\hline

-Nodes Number &  50, 100, 150, 200 and 250~nodes   \\
+Network size &  50, 100, 150, 200 and 250~nodes   \\

 %\hline
 %\hline

-Initial Energy  & 500-700~joules  \\  
+Initial energy  & 500-700~joules  \\  

 %\hline
 %\hline

-Sensing Time for One Round & 60 Minutes \\
-$E_{th}$ & 36 Joules\\
+Sensing time for one round & 60 Minutes \\
+$E_{R}$ & 36 Joules\\

 $R_s$ & 5~m   \\     
 %\hline
 $w_{\Theta}$ & 1   \\
 $R_s$ & 5~m   \\     
 %\hline
 $w_{\Theta}$ & 1   \\


@@ -662,28 +739,39 @@ $w_{U}$ & $|P^2|$
 \label{table3}
 % is used to refer this table in the text
 \end{table}
 \label{table3}
 % is used to refer this table in the text
 \end{table}

-
-25 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 25 runs. 
-%Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions. 
-We  performed  simulations for five different densities varying from 50 to 250~nodes. Experimental results are obtained from  randomly generated  networks in  which  nodes are
-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 cover the sensing field with the given sensing range.\\
-

   
   

-Our MuDiLCO protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5, and MuDiLCO-7, corresponding  to $T=1$, $T=3$, $T=5$ or $T=7$ ($T$ the number of rounds in one sensing period).  We call the method MuDiLCO-T for the general case. We compare MuDiLCO-T with two other methods. The first method, called DESK and proposed by ~\cite{ChinhVu} is a full distributed coverage algorithm. The second method, 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 on during the sensing phase time.\\
-
-
-
+Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
+and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of
+rounds  in one  sensing period).  In  the following,  the general  case will  be
+denoted by MuDiLCO-T.   We compare MuDiLCO-T with two  other methods.  The first
+method,  called  DESK and  proposed  by  \cite{ChinhVu}  is a  full  distributed
+coverage  algorithm.   The  second  method,  called  GAF~\cite{xu2001geography},
+consists in dividing the region  into fixed squares.  During the decision phase,
+in each  square, one sensor is then  chosen to remain active  during the sensing
+phase time.

 
 \subsection{Energy Model}
 
 
 \subsection{Energy Model}
 

-We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
-The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
+We  use an  energy consumption  model  proposed by~\cite{ChinhVu}  and based  on
+\cite{raghunathan2002energy} with slight  modifications.  The energy consumption
+for  sending/receiving the packets  is added,  whereas the  part related  to the
+sensing range is removed because we consider a fixed sensing range.
+

 % We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node. 
 %The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU. 
 %revoir la phrase
 
 % We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node. 
 %The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU. 
 %revoir la phrase
 

-For our energy consumption model, we refer to the sensor node (Medusa II) which uses Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The typical architecture of a sensor is composed of four subsystems : the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for
-transmitting/receiving messages, sensing subsystem that collects data, and the power supply which  powers the complete sensor node ~\cite{raghunathan2002energy}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second)  for the different status of the sensor is summarized in Table~\ref{table4}. The energy needed to send or receive a 1-bit is equal to $0.2575 mW$.
+For our  energy consumption model, we  refer to the sensor  node Medusa~II which
+uses an Atmels  AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The
+typical  architecture  of a  sensor  is composed  of  four  subsystems: the  MCU
+subsystem which is capable of computation, communication subsystem (radio) which
+is  responsible  for  transmitting/receiving  messages, sensing  subsystem  that
+collects  data, and  the  power supply  which  powers the  complete sensor  node
+\cite{raghunathan2002energy}. Each  of the first three subsystems  can be turned
+on or  off depending on  the current status  of the sensor.   Energy consumption
+(expressed in  milliWatt per second) for  the different status of  the sensor is
+summarized in Table~\ref{table4}.  The energy  needed to send or receive a 1-bit
+packet is equal to $0.2575~mW$.

 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}
 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}


@@ -694,17 +782,17 @@ transmitting/receiving messages, sensing subsystem that collects data, and the p
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines

-Sensor mode & MCU   & Radio & Sensing & Power (mWs) \\ [0.5ex]
+Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]

 \hline
 % inserts single horizontal line
 \hline
 % inserts single horizontal line

-Listening & ON & ON & ON & 20.05 \\
+LISTENING & on & on & on & 20.05 \\

 % inserting body of the table
 \hline
 % inserting body of the table
 \hline

-Active & ON & OFF & ON & 9.72 \\
+ACTIVE & on & off & on & 9.72 \\

 \hline
 \hline

-Sleep & OFF & OFF & OFF & 0.02 \\
+SLEEP & off & off & off & 0.02 \\

 \hline
 \hline

-Computation & ON & ON & ON & 26.83 \\
+COMPUTATION & on & on & on & 26.83 \\

 %\hline
 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
  \hline
 %\hline
 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
  \hline


@@ -714,59 +802,78 @@ Computation & ON & ON & ON & 26.83 \\
 % is used to refer this table in the text
 \end{table}
 
 % is used to refer this table in the text
 \end{table}
 

-For sake of  simplicity we ignore the energy needed to turn on the
-radio, to start up the sensor node, the transition from mode to another, etc. 
+For sake  of simplicity we  ignore the  energy needed to  turn on the  radio, to
+start up the sensor node, to move from one status to another, etc.

 %We also do not consider the need of collecting sensing data. PAS COMPRIS
 %We also do not consider the need of collecting sensing data. PAS COMPRIS

-Thus, when a sensor becomes active (i.e., it already decides it's status), it can turn its radio off to save battery. MuDiLCO uses two types of packets for communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24 bits respectively. 
-The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets.
-
-
-The initial energy of  each node is  randomly set in the interval $[500-700]$.  Each  sensor  node will  not participate in the next round if its remaining energy is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mWs) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.\\
-
+Thus, when  a sensor becomes active  (i.e., it already decides  it's status), it
+can turn its  radio off to save  battery. MuDiLCO uses two types  of packets for
+communication. The size of the  INFO packet and Active-Sleep packet are 112~bits
+and 24~bits  respectively.  The  value of energy  spent to send  a 1-bit-content
+message is  obtained by using  the equation in  ~\cite{raghunathan2002energy} to
+calculate  the energy cost  for transmitting  messages and  we propose  the same
+value for receiving the packets.
+
+The initial energy of each node  is randomly set in the interval $[500;700]$.  A
+sensor node  will not participate in the  next round if its  remaining energy is
+less than  $E_{R}=36~\mbox{Joules}$, the minimum  energy needed for the  node to
+stay alive  during one round.  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
+alive during at most 20 rounds.

 
 
 
 

-
- 

 \subsection{Metrics}
 
 \subsection{Metrics}
 

-We introduce the following performance metrics for evaluating our approach: 
+To evaluate our approach we consider the following performance metrics:

 
 

-\begin{enumerate}[i)]
+\begin{enumerate}[i]

   
   

-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area of a sensor field is  covered. In our case, we treated the sensing fields as a grid, and used each grid point as a sample point
-for calculating the coverage. The coverage ratio can be calculated by:
+\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area
+  of a sensor field is covered. In our case, the sensing field is represented as
+  a connected grid  of points and we use  each grid point as a  sample point for
+  calculating the coverage. The coverage ratio can be calculated by:

 \begin{equation*}
 \scriptsize
 \begin{equation*}
 \scriptsize

-\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100.
+\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,

 \end{equation*}
 \end{equation*}

-Where: $n^t$ is the number of covered grid points by the active sensors of all subregions during round $t$ in the current sensing phase and $N$ is total number of grid points in the sensing field of the network.
+where $n^t$ is  the number of covered  grid points by the active  sensors of all
+subregions during round $t$ in the current sensing phase and $N$ is total number
+of grid points in the sensing field of the network.

 %The accuracy of this method depends on the distance between grids. In our
 %simulations, the sensing field has been divided into 50 by 25 grid points, which means
 %there are $51 \times 26~ = ~ 1326$ points in total.
 % Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
 
 %The accuracy of this method depends on the distance between grids. In our
 %simulations, the sensing field has been divided into 50 by 25 grid points, which means
 %there are $51 \times 26~ = ~ 1326$ points in total.
 % Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
 

-\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
-in  order to  minimize  the communication  overhead  and maximize  the
-network lifetime. The Active Sensors Ratio is defined as follows:
+\item{{\bf Number  of Active Sensors Ratio  (ASR)}:} it is important  to have as
+  few  active  nodes  as  possible  in  each  round,in  order  to  minimize  the
+  communication overhead  and maximize the network lifetime.  The Active Sensors
+  Ratio is defined as follows:

 \begin{equation*}
 \begin{equation*}

-\scriptsize
-\mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$A_r^t$}}{\mbox{$S$}} \times 100 .
+\scriptsize  \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
+  \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,

 \end{equation*}
 \end{equation*}

-Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round $t$ in the current sensing phase, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
-
-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until the coverage ratio drops below a predefined threshold. We denoted by $Lifetime95$ (respectively  $Lifetime50$) as the amount of  time during which  the network  can  satisfy an area  coverage greater than $95\%$ (repectively $50\%$). We assume that the network
-is alive  until all  nodes have  been drained of  their energy  or the
-sensor network becomes disconnected. Network connectivity is important because an
-active sensor node without  connectivity towards a base station cannot
-transmit information on an event in the area that it monitors.
- 
-
-\item {{\bf Energy Consumption}:}
-
- Energy Consumption (EC) can be seen as the total energy consumed by the sensors during the $Lifetime95$ or $Lifetime50$ divided by the number of rounds. The EC can be computed as follow: \\
+where $A_r^t$ is the number of  active sensors in the subregion $r$ during round
+$t$ in the  current sensing phase, $|J|$  is the total number of  sensors in the
+network, and $R$ is the total number of the subregions in the network.
+
+\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  $Lifetime_{50}$) as  the amount of  time during
+  which  the  network   can  satisfy  an  area  coverage   greater  than  $95\%$
+  (respectively $50\%$). We assume that the network is alive until all nodes have
+  been   drained    of   their   energy   or   the    sensor   network   becomes
+  disconnected. Network connectivity is  important because an active sensor node
+  without connectivity towards a base  station cannot transmit information on an
+  event in the area that it monitors.
+
+\item {{\bf  Energy Consumption  (EC)}:} the average  energy consumption  can be
+  seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
+  $Lifetime_{50}$  divided  by the  number  of rounds.  EC  can  be computed  as
+  follows:

  \begin{equation*}
 \scriptsize
  \begin{equation*}
 \scriptsize

-\mbox{EC} =  \frac{\mbox{$\sum\limits_{d=1}^D \left( E^c_d + E^l_d + E^a_d + E^s_d + E^p_d \right)$ }}{\mbox{$D$}}   .
+\mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +
+  \sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},

 \end{equation*}
 
 %\begin{equation*}
 \end{equation*}
 
 %\begin{equation*}


@@ -774,106 +881,150 @@ transmit information on an event in the area that it monitors.
 %\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*}
 
 %\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*}
 

-Where: D is the number of rounds during $Lifetime95$ or $Lifetime50$. 
-The total energy consumed by the sensors (EC) comes through taking into consideration four main energy factors, which are $E^c_d$, $E^l_d$, $E^a_d$, $E^s_d$ and $E^p_d$.
-The energy consumption $E^c_d$ for wireless  communications  is  calculated by taking into account the  energy spent by  all the nodes while  transmitting and
-receiving  packets during round $d$. The $E^l_d$ represents the energy consumed by all the sensors during the listening mode before taking the decision to go Active or Sleep in round $d$. $E^a_d$ and $E^s_d$  refer to energy consumed in the active mode or in the sleeping mode. The $E^p_d$ refers to energy consumed by the computation (processing) to solve the integer program.
+where $M_L$ and  $T_L$ are respectively the number of  periods and rounds during
+$Lifetime_{95}$ or  $Lifetime_{50}$.  The total  energy consumed by  the sensors
+(EC) comes through taking into consideration four main energy factors. The first
+one ,  denoted $E^{\scriptsize \mbox{com}}_m$, represent  the energy consumption
+spent  by  all  the  nodes   for  wireless  communications  during  period  $m$.
+$E^{\scriptsize  \mbox{list}}_m$, the  next  factor, corresponds  to the  energy
+consumed by the sensors in LISTENING  status before receiving the decision to go
+active or  sleep in  period $m$. $E^{\scriptsize  \mbox{comp}}_m$ refers  to the
+energy needed  by all  the leader nodes  to solve  the integer program  during a
+period. Finally, $E^a_t$ and $E^s_t$  indicate the energy consummed by the whole
+network in round $t$.

 
 %\item {Network Lifetime:} 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 has become  disconnected.
 
 
 %\item {Network Lifetime:} 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 has become  disconnected.
 

-
-
-\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.

 
 \end{enumerate}
 
 
 \end{enumerate}
 

-

 %%%%%%%%%%%%%%%%%%%%%%%%VU JUSQU ICI**************************************************
 
 %%%%%%%%%%%%%%%%%%%%%%%%VU JUSQU ICI**************************************************
 

-
-

 \section{Results and analysis}
 \section{Results and analysis}

+

 \subsection{Coverage ratio} 
 \subsection{Coverage ratio} 

-Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.  
-\parskip 0pt    
+
+Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. We
+can notice that for the first thirty rounds both DESK and GAF provide a coverage
+which is a little bit better than the  one of MuDiLCO-T. This is due to the fact
+that in  comparison with MuDiLCO that  uses optimization to put  in SLEEP status
+redundant sensors,  more sensor  nodes remain  active with DESK  and GAF.   As a
+consequence,  when the  number of  rounds increases,  a larger  number  of nodes
+failures can be observed in DESK and  GAF, resulting in a faster decrease of the
+coverage ratio.  Furthermore,  our protocol allows to maintain  a coverage ratio
+greater than  50\% for  far more rounds.  Overall, the proposed  sensor activity
+scheduling based on optimization in  MuDiLCO maintains higher coverage ratios of
+the area of interest for a larger number of rounds. It also means that MuDiLCO-T
+save more  energy, with less  dead nodes, at  most for several rounds,  and thus
+should extend the network lifetime.
+

 \begin{figure}[h!]
 \centering
  \includegraphics[scale=0.5] {R1/CR.pdf} 
 \begin{figure}[h!]
 \centering
  \includegraphics[scale=0.5] {R1/CR.pdf} 

-\caption{The coverage ratio for 150 deployed nodes}
+\caption{Average coverage ratio for 150 deployed nodes}

 \label{fig3}
 \end{figure} 
 
 \label{fig3}
 \end{figure} 
 

-DESK and GAF provide a very little better coverage ratio than MuDiLCO-T (in the first thirty rounds. This is due to the fact that MuDiLCO  put in sleep mode redundant sensors using optimization (which slightly decreases the coverage ratio) while there are more active nodes in the case of DESK and GAF. When the number of rounds increases, coverage ratio produced by DESK and GAF decreases. This is due to dead nodes. However,  MuDiLCO-T maintains the coverage ratio greater than 50$\%$ for a larger number of rounds in comparison with DESK and GAF. Although some nodes are dead, sensor activity scheduling based on optimization in MuDiLCO allows to prolong the coverage of the area of interest. The simulation results shows the superiority of our method, that  keeps high coverage for a larger number of rounds, so the network lifetime is extended.
+\subsection{Active sensors ratio} 

 
 

+It is crucial to have as few active nodes as possible in each round, in order to
+minimize    the    communication    overhead    and   maximize    the    network
+lifetime. Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed
+nodes all along the network lifetime. It appears that up to round thirteen, DESK
+and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas
+MuDiLCO-T clearly outperforms  them with only 24.8\% of  active nodes. After the
+thirty  fifth round,  MuDiLCO-T exhibits  larger number  of active  nodes, which
+agrees with  the dual observation of  higher level of  coverage made previously.
+Obviously, in  that case DESK  and GAF have  less active nodes, since  they have
+activated many nodes at the beginning. Anyway, MuDiLCO-T activates the available
+nodes in a more efficient manner.

 
 

-\subsection{Active sensors ratio} 
- It is important to have as few active nodes as possible in each round,
-in  order to  minimize  the communication  overhead  and maximize  the
-network lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed nodes all along the network lifetime. 

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R1/ASR.pdf}  
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R1/ASR.pdf}  

-\caption{The active sensors ratio for 150 deployed nodes }
+\caption{Active sensors ratio for 150 deployed nodes}

 \label{fig4}
 \end{figure} 
 
 \label{fig4}
 \end{figure} 
 

-
-We can observe that DESK and GAF have 37.6 $\%$ and 44.8 $\%$ of active nodes and MuDiLCO-T competes perfectly with only 24.8$\%$  of active nodes for the first thirteen rounds.
-From the thirty fifth round, MuDiLCO-T has a larger number of active nodes in comparison with DESK and GAF but it maintains a higher level of coverage compared to the two other methods. DESK and GAF have less number of active nodes because many nodes are died.
-
-

 \subsection{Stopped simulation runs}
 %The results presented in this experiment, is to show the comparison of our MuDiLCO protocol with other two approaches from the point of view the stopped simulation runs per round. Figure~\ref{fig6} illustrates the percentage of stopped simulation
 %runs per round for 150 deployed nodes. 
 \subsection{Stopped simulation runs}
 %The results presented in this experiment, is to show the comparison of our MuDiLCO protocol with other two approaches from the point of view the stopped simulation runs per round. Figure~\ref{fig6} illustrates the percentage of stopped simulation
 %runs per round for 150 deployed nodes. 

-Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs per round for 150 deployed nodes. This figure gives the breakpoint for each of the methods.
+
+Figure~\ref{fig6} reports the cumulative  percentage of stopped simulations runs
+per round for  150 deployed nodes. This figure gives the  breakpoint for each of
+the methods.  DESK stops first,  after around 45~rounds, because it consumes the
+more energy by  turning on a large number of redundant  nodes during the sensing
+phase. GAF  stops secondly for the  same reason than  DESK.  MuDiLCO-T overcomes
+DESK and GAF because the  optimization process distributed on several subregions
+leads  to coverage  preservation and  so extends  the network  lifetime.  Let us
+emphasize that the  simulation continues as long as a network  in a subregion is
+still connected.
+
+%%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R1/SR.pdf} 
 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R1/SR.pdf} 
 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
 \label{fig6}
 \end{figure} 

-DESK stops first (around 45 rounds) because it consumes more energy for turning on a large number of redundant nodes during the sensing phase. GAF stops secondly for the same reason of DESK. MuDiLCO-T overcomes DESK and GAF because the optimization process distributed on several subregions  leads to coverage preservation and so extends the network lifetime.
-%%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-

 
 

-\subsection{Energy Consumption}
-We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it with the two other methods. Figures~\ref{fig95} and ~\ref{fig7} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$. 
+\subsection{Energy Consumption} \label{subsec:EC}

 
 

-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R1/EC95.pdf} 
-\caption{The Energy Consumption with $95\%-Lifetime$}
-\label{fig95}
-\end{figure} 
+We  measure  the  energy  consumed  by the  sensors  during  the  communication,
+listening, computation, active, and sleep status for different network densities
+and   compare   it   with   the  two   other   methods.    Figures~\ref{fig7}(a)
+and~\ref{fig7}(b)  illustrate  the  energy  consumption,  considering  different
+network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.

 
 

-The results show that MuDiLCO-T is 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 as well as the energy consumed during the different modes of the sensor node.\\
- 
-As shown in Figures~\ref{fig95}\ref{fig7} and \ref{fig7}, MuDiLCO-7 consumes more energy than the other versions of MuDiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of rounds and the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem.  

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

-\centering
-\includegraphics[scale=0.5]{R1/EC50.pdf} 
-\caption{The Energy Consumption with $Lifetime50$}
-\label{fig7}
+  \centering
+  \begin{tabular}{cl}
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/EC95.pdf}} & (a) \\
+    \verb+ + \\
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/EC50.pdf}} & (b)
+  \end{tabular}
+  \caption{Energy consumption for (a) $Lifetime_{95}$ and 
+    (b) $Lifetime_{50}$}
+  \label{fig7}

 \end{figure} 
 
 \end{figure} 
 

-
+The  results  show  that MuDiLCO-T  is  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 as  well as  the energy
+consumed during  the different  status of the  sensor node. Among  the different
+versions of our protocol, the MuDiLCO-7  one consumes more energy than the other
+versions. This is  easy to understand since the bigger the  number of rounds and
+the  number of  sensors involved  in the  integer program,  the larger  the time
+computation to  solve the optimization  problem. To improve the  performances of
+MuDiLCO-7, we  should increase the  number of subregions  in order to  have less
+sensors to consider in the integer program.

 
 %In fact,  a distributed optimization decision, which produces T rounds, on the subregions is  greatly reduced the cost of communications and the time of listening as well as the energy needed for sensing phase and computation so thanks to the partitioning of the initial network into several independent subnetworks and producing T rounds for each subregion periodically. 
 
 
 \subsection{Execution time}
 
 %In fact,  a distributed optimization decision, which produces T rounds, on the subregions is  greatly reduced the cost of communications and the time of listening as well as the energy needed for sensing phase and computation so thanks to the partitioning of the initial network into several independent subnetworks and producing T rounds for each subregion periodically. 
 
 
 \subsection{Execution time}

-We observe the impact of the network size and of the number of rounds $T$ on the computation time. Figure~\ref{fig77} gives the average execution times in seconds  (times to solve optimization problem) for different values of $T$. 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 $\left( \frac{35330}{2} \times 6\right)$ and reported on Figure~\ref{fig77} for different network sizes.

 
 

-Figure~\ref{fig77} shows that the execution time increases with the number of rounds $T$ taken into account for the scheduling of the sensing phase. MuDiLCO-7 results in execution time that quickly becomes unsuitable for a sensor network, especially when the sensor network size increases. 
-%While MuDiLCO-1, 3, and 5 solves the optimization process with suitable execution times to be used on wireless sensor network because it distributed on larger number of small subregions as well as it is used acceptable number of round(s) T.  We think that in distributed fashion the solving of the optimization problem to produce T rounds 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.
+We observe  the impact of the  network size and of  the number of  rounds on the
+computation  time.   Figure~\ref{fig77} gives  the  average  execution times  in
+seconds (times  needed to  solve optimization problem)  for different  values of
+$T$.   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{fig77}
+for different network sizes. 

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


@@ -882,62 +1033,91 @@ Figure~\ref{fig77} shows that the execution time increases with the number of ro
 \label{fig77}
 \end{figure} 
 
 \label{fig77}
 \end{figure} 
 

+As expected,  the execution time  increases with the number  of rounds
+$T$ taken into account for  scheduling of the sensing phase. The times
+obtained for $T=1,3$ or $5$  seems bearable, but for $T=7$ they become
+quickly  unsuitable for  a  sensor node,  especially  when the  sensor
+network  size increases.  Again,  we can  notice  that if  we want  to
+schedule the nodes activities for a large number of rounds, we need to
+choose a relevant number of  subregion in order to avoid a complicated
+and cumbersome  optimization. On the one  hand, a large  value for $T$
+permits  to reduce the  energy-overhead due  to the  three pre-sensing
+phases,  on the  other hand  a leader  node may  waste  a considerable
+amount of energy to solve the optimization problem.
+
+%While MuDiLCO-1, 3, and 5 solves the optimization process with suitable execution times to be used on wireless sensor network because it distributed on larger number of small subregions as well as it is used acceptable number of round(s) T.  We think that in distributed fashion the solving of the optimization problem to produce T rounds 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.

 
 \subsection{Network Lifetime}
 
 \subsection{Network Lifetime}

-In Figure~\ref{fig9} and in Figure~\ref{fig8}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different  network sizes. 
+
+The  next   two  figures,  Figures~\ref{fig8}(a)   and  \ref{fig8}(b),
+illustrate   the  network  lifetime   for  different   network  sizes,
+respectively  for $Lifetime_{95}$  and $Lifetime_{50}$.   Both figures
+show that the  network lifetime increases together with  the number of
+sensor nodes, whatever the protocol,  thanks to the node density which
+result in  more and more redundant  nodes that can  be deactivated and
+thus  save energy.  Compared  to the  other approaches,  our MuDiLCO-T
+protocol  maximizes the lifetime  of the  network.  In  particular the
+gain in  lifetime for a coverage  over 95\% is greater  than 38\% when
+switching from  GAF to  MuDiLCO-3.  The slight  decrease that  can bee
+observed for MuDiLCO-7 in  case of $Lifetime_{95}$ with large wireless
+sensor networks result from the difficulty of the optimization problem
+to be solved  by the integer program.  This  point was already noticed
+in subsection \ref{subsec:EC} devoted to the energy consumption, since
+network lifetime and energy consumption are directly linked.

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

-\centering
-\includegraphics[scale=0.5]{R1/LT95.pdf}  
-\caption{The Network Lifetime for $Lifetime95$}
-\label{fig9}
+  \centering
+  \begin{tabular}{cl}
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/LT95.pdf}} & (a) \\
+    \verb+ + \\
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/LT50.pdf}} & (b)
+  \end{tabular}
+  \caption{Network lifetime for (a) $Lifetime_{95}$ and 
+    (b) $Lifetime_{50}$}
+  \label{fig8}

 \end{figure} 
 
 \end{figure} 
 

-
-As highlighted by Figure~\ref{fig9}, network lifetime obviously
-increases when the size of the network increases. MuDiLCO-T (whatever values of $T$) maximizes the lifetime of the network compared with other approaches. The gain in lifetime for a coverage over $95\%$ is greater than $38\%$ between GAF and MuDiLCO-3.
-

 % By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest with a maximum number rounds and by letting the other nodes sleep in order to be used later in next rounds, our MuDiLCO-T protocol efficiently prolonges the network lifetime. 
 
 %In Figure~\ref{fig8}, Comparison shows that our MuDiLCO-T protocol, which are used distributed optimization on the subregions with the ability of producing T rounds, is 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 sensor 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.
 
 
 %We see that our MuDiLCO-7 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumption seems to be huge because it used a larger number of rounds T during performing the optimization decision in the subregions, which is led to decrease the network lifetime. On the other side, our MuDiLCO-1, 3, and 5 protocol seems to be more efficient in comparison with other approaches because they are prolonged the lifetime of the network more than DESK and GAF.
 % By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest with a maximum number rounds and by letting the other nodes sleep in order to be used later in next rounds, our MuDiLCO-T protocol efficiently prolonges the network lifetime. 
 
 %In Figure~\ref{fig8}, Comparison shows that our MuDiLCO-T protocol, which are used distributed optimization on the subregions with the ability of producing T rounds, is 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 sensor 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.
 
 
 %We see that our MuDiLCO-7 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumption seems to be huge because it used a larger number of rounds T during performing the optimization decision in the subregions, which is led to decrease the network lifetime. On the other side, our MuDiLCO-1, 3, and 5 protocol seems to be more efficient in comparison with other approaches because they are prolonged the lifetime of the network more than DESK and GAF.

- 

 
 
 
 

-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R1/LT50.pdf}  
-\caption{The Network Lifetime for $Lifetime50$}
-\label{fig8}
-\end{figure} 
-

 \section{Conclusion and Future Works}
 \label{sec:conclusion}
 
 \section{Conclusion and Future Works}
 \label{sec:conclusion}
 

-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 MuDiLCO protocol optimizes  coverage and  lifetime performances in each subregion.
-The  proposed  protocol  combines  two efficient  techniques:  network
-leader election  and sensor activity scheduling.
+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  we propose  a  protocol  which
+optimizes coverage  and lifetime  performances in each  subregion. Our
+protocol,  called MuDiLCO  (Multiperiod Distributed  Lifetime Coverage
+Optimization)  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 cover sets %of active nodes that will optimize the network lifetime
 %while taking the responsibility of covering the corresponding
 %subregion using more than one cover set during the sensing phase. 
 %,  where the challenges
 %include how to select the  most efficient leader in each subregion and
 %the best cover sets %of active nodes that will optimize the network lifetime
 %while taking the responsibility of covering the corresponding
 %subregion using more than one cover set during the sensing phase. 

-The activity scheduling in each subregion works in periods, each period consists  of four phases: (i) Information Exchange,
-(ii) Leader Election, (iii) Decision Phase
-to plan the activity of the sensors over $T$ rounds  (iv) Sensing Phase itself divided into T rounds. 
-
-Simulations results show the relevance  of the proposed MuDiLCO
-protocol in terms of lifetime, coverage ratio, active sensors ratio, energy consumption, execution time. Indeed, when
-dealing with large 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. Nevertheless, results also show that it is not possible to plan the activity of sensors  over too many rounds because the resulting optimization problem leads to too high resolution time and thus to an excessive energy consumption.
+The activity scheduling in each subregion works in periods, where each
+period consists of four  phases: (i) Information Exchange, (ii) Leader
+Election, (iii)  Decision Phase  to plan the  activity of  the sensors
+over $T$ rounds (iv) Sensing Phase itself divided into T rounds.
+
+Simulations  results show the  relevance of  the proposed  protocol in
+terms  of  lifetime,  coverage  ratio, active  sensors  ratio,  energy
+consumption, execution time. Indeed,  when dealing with large 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. Nevertheless,  results also show that it is not
+possible to plan the activity of sensors over too many rounds, because
+the resulting  optimization problem leads to too  high resolution time
+and thus to an excessive energy consumption.

 
 %In  future work, we plan  to study and propose adjustable sensing range coverage optimization protocol, which computes  all active sensor schedules in one time, by using
 %optimization  methods. This protocol can prolong the network lifetime by minimizing the number of the active sensor nodes near the borders by optimizing the sensing range of sensor nodes.
 
 %In  future work, we plan  to study and propose adjustable sensing range coverage optimization protocol, which computes  all active sensor schedules in one time, by using
 %optimization  methods. This protocol can prolong the network lifetime by minimizing the number of the active sensor nodes near the borders by optimizing the sensing range of sensor nodes.


@@ -970,7 +1150,6 @@ problems, one per subregion, that can be solved more easily. Nevertheless, resul
   
 \end{document}
 
   
 \end{document}
 

-

 %%\bibitem{}
 
 %\end{thebibliography}
 %%\bibitem{}
 
 %\end{thebibliography}

diff --git a/biblio.bib b/biblio.bib
index 6ff1c2bfb5a444aa0e27f53162de6b3f07f214bd..aa94f0872274e8f72e2d31a7876856984f3ff7c0 100755 (executable)
--- a/biblio.bib
+++ b/biblio.bib
@@ -11,7 +11,7 @@
 @ARTICLE{Zhang,
  author = "L. Zhang and Q. Zhu and J. Wang",
  title = "Adaptive Clustering for Maximizing Network Lifetime and Maintaining Coverage ",
 @ARTICLE{Zhang,
  author = "L. Zhang and Q. Zhu and J. Wang",
  title = "Adaptive Clustering for Maximizing Network Lifetime and Maintaining Coverage ",

- journal = {JOURNAL OF NETWORKS},
+ journal = {Journal of Networks},

  volume = {8},
  number = {3},
  pages = {616-622},
  volume = {8},
  number = {3},
  pages = {616-622},


@@ -66,7 +66,7 @@ wireless sensor networks",
 @ARTICLE{Shibo,
  author = " S. He and J. Chen and X. Li and X. Shen and Y. Sun ",
  title = "Leveraging Prediction to Improve the Coverage of Wireless Sensor Networks",
 @ARTICLE{Shibo,
  author = " S. He and J. Chen and X. Li and X. Shen and Y. Sun ",
  title = "Leveraging Prediction to Improve the Coverage of Wireless Sensor Networks",

- JOURNAL = {IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS},
+ JOURNAL = {IEEE Transations on Parallel Distributed Systems},

  VOLUME = {23},
  NUMBER = {4},
  PAGES = {701-712},
  VOLUME = {23},
  NUMBER = {4},
  PAGES = {701-712},


@@ -106,7 +106,7 @@ sensor networks",
  }
  
 @ARTICLE{Huang:2003:CPW:941350.941367,
  }
  
 @ARTICLE{Huang:2003:CPW:941350.941367,

- author = "C.-F. HUANG and Y.-C. TSENG",
+ author = "C.-F. Huang and Y.-C. Tseng",

  title = "The Coverage Problem in a Wireless Sensor Network",
  JOURNAL = {Mobile Networks and Applications},
  VOLUME = {10},
  title = "The Coverage Problem in a Wireless Sensor Network",
  JOURNAL = {Mobile Networks and Applications},
  VOLUME = {10},


@@ -188,7 +188,7 @@ year = {2003},
   title={Distributed energy-efficient solutions for area coverage problems in wireless sensor networks},
   author={Vu, Chinh Trung},
   year={2009},
   title={Distributed energy-efficient solutions for area coverage problems in wireless sensor networks},
   author={Vu, Chinh Trung},
   year={2009},

-  school={GEORGIA STATE UNIVERSITY}
+  school={Georgia State University}

 }
 
 
 }