X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/98f56bd39ecefc67d93931a6717ed20c2824304a..4e0783212d2ef38d47c78e94e3053b88999aef79:/article.tex?ds=sidebyside

diff --git a/article.tex b/article.tex
index 53747de..6707012 100644
--- a/article.tex
+++ b/article.tex
@@ -67,7 +67,7 @@
 %% \address{Address\fnref{label3}}
 %% \fntext[label3]{}
 
-\title{Multiperiod Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
+\title{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
 
 %% use optional labels to link authors explicitly to addresses:
 %% \author[label1,label2]{}
@@ -89,11 +89,11 @@ $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcom
 %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
+(WSNs). In this paper, a method called Multiround 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
+sensor nodes in each subregion. The proposed MuDiLCO protocol works in 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
@@ -117,24 +117,24 @@ Optimization, Scheduling, Distributed Computation.
  
 \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
+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
+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
+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
+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.
+the network lifetime by using an optimized multiround 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
@@ -173,17 +173,122 @@ algorithms in WSNs according to several design choices:
 \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.
+  to minimize the number of sensors during a sensing round.
 \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  Additional  requirements  for  energy-efficient  coverage  and  connected
-  coverage.
+\item  Additional  requirements  for  energy-efficient and  connected coverage.
 \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 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}
+
+The major approach  is to divide/organize the sensors into  a suitable number of
+cover sets where  each set completely covers an interest  region and to activate
+these cover sets 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 make 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~\cite{abrams2004set,cardei2005improving,Slijepcevic01powerefficient}.     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  reliable because  a sensor  may be
+involved in more than one cover sets.
+%For instance, the proposed work in ~\cite{cardei2005energy, berman04}    
+
+In~\cite{yang2014maximum},  the  authors have  considered  a linear  programming
+approach  to select  the minimum  number of  working sensor  nodes, in  order to
+preserve a  maximum coverage  and to  extend lifetime of  the network.  Cheng et
+al.~\cite{cheng2014energy} have defined a  heuristic algorithm called Cover Sets
+Balance  (CSB), which  chooses  a set  of  active nodes  using  the tuple  (data
+coverage range, residual  energy).  Then, they have introduced  a new Correlated
+Node Set Computing (CNSC) algorithm to  find the correlated node set for a given
+node.   After that,  they  proposed a  High  Residual Energy  First (HREF)  node
+selection algorithm to minimize the number  of active nodes so as to prolong the
+network  lifetime.  Various  centralized  methods  based  on  column  generation
+approaches                    have                   also                   been
+proposed~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+
+\subsection{Distributed approaches}
+%{\bf Distributed approaches}
+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.
+
+Many distributed algorithms have been  developed to perform the scheduling so as
+to          preserve         coverage,          see          for         example
+\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02,       yardibi2010distributed,
+  prasad2007distributed,Misra}.   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}.   The  Distributed  Adaptive Sleep  Scheduling  Algorithm
+(DASSA) \cite{yardibi2010distributed}  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 have designed 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 from~\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. 
+
+The  works presented  in  \cite{Bang, Zhixin,  Zhang}  focus on  coverage-aware,
+distributed energy-efficient,  and distributed clustering  methods respectively,
+which  aim at extending  the network  lifetime, while  the coverage  is ensured.
+More recently, Shibo et al.  \cite{Shibo} have 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.  have  described 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 time-slot 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  Multiround 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. In fact, in this paper we make a multiround optimization, while it was
+a single round optimization in our previous work.
+
+\iffalse
    
 \subsection{Centralized Approaches}
 %{\bf Centralized approaches}
@@ -231,7 +336,7 @@ 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
+Also, they require  a smaller number of participating nodes  in order to achieve
 these results.
 
 In  the  case  of  non-disjoint algorithms  \cite{pujari2011high},  sensors  may
@@ -272,28 +377,29 @@ 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.  In \cite{prasad2007distributed} a model for capturing the
-dependencies between different  cover sets is defined and  it 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.
+Many distributed algorithms have been  developed to perform the scheduling so as
+to          preserve         coverage,          see          for         example
+\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02,yardibi2010distributed}.
+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.   In \cite{prasad2007distributed}  a model  for
+capturing  the dependencies  between  different  cover sets  is  defined and  it
+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}  have  developed  a  Distributed
 Adaptive  Sleep Scheduling  Algorithm (DASSA)  for WSNs  with  partial coverage.
@@ -302,7 +408,7 @@ 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 have proposed  a  novel  distributed
+information.  In  \cite{ChinhVu}, the author  have 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
@@ -314,9 +420,9 @@ proposed in \cite{Huang:2003:CPW:941350.941367}.
 %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 coverage-aware,
+The  works presented in  \cite{Bang, Zhixin,  Zhang} focus  on coverage-aware,
 distributed energy-efficient,  and distributed clustering  methods respectively,
-which aims  to extend the network  lifetime, while the coverage  is ensured.  S.
+which aim  to extend the network  lifetime, while the coverage  is ensured.  S.
 Misra et al.   \cite{Misra} have 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
@@ -337,7 +443,7 @@ 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
+The MuDiLCO protocol (for Multiround 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
@@ -347,6 +453,10 @@ 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.
 
+
+
+
+\fi
 %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}
@@ -383,7 +493,7 @@ approach.
 %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
+%In this section, we introduce a Multiround 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.
@@ -406,7 +516,7 @@ 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.
+active nodes.
 
 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,
@@ -430,14 +540,16 @@ is the subject of another study not presented here.
 \subsection{Background idea}
 %%RC : we need to clarify the difference between round and period. Currently it seems to be the same (for me at least).
 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
+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.
+and for each round a set of sensors (a cover set) is responsible for the sensing
+task. In  this way  a multiround optimization  process is performed  during each
+period  after  Information~Exchange  and  Leader~Election phases,  in  order  to
+produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
 \begin{figure}[ht!]
 \centering \includegraphics[width=100mm]{Modelgeneral.pdf} % 70mm
 \caption{The MuDiLCO protocol scheme executed on each node}
@@ -449,15 +561,18 @@ 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. 
+This protocol minimizes the impact of unexpected node failure (not due to batteries
+running out of energy), because it works in periods. 
+%This protocol is reliable against an unexpected node failure, because it works in periods. 
 %%RC : why? I am not convinced
- 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
+ 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.
 %%RC so if there are at least one failure per period, the coverage is bad...
+%%MS if we want to be reliable against many node failures we need to have an
+%% overcoverage...  
 
 The  energy consumption  and some  other constraints  can easily  be  taken into
 account,  since the  sensors  can  update and  then  exchange their  information
@@ -482,7 +597,7 @@ There are five status for each sensor node in the network:
 \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 ACTIVE: sensor node is taking part in 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}
@@ -509,7 +624,7 @@ 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 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
+will select the  leader based on the received information  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
@@ -534,11 +649,11 @@ 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.
+consider binary  variables $X_{t,j}$ to determine the  possibility of activating
+sensor $j$ during 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
 
@@ -574,7 +689,7 @@ We define the Overcoverage variable $\Theta_{t,p}$ as:
 \label{eq13} 
 \end{equation}
 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
+minus  one  that  cover  the  primary  point $p$  during  round  $t$.   The
 Undercoverage variable  $U_{t,p}$ of the primary  point $p$ during  round $t$ is
 defined by:
 \begin{equation}
@@ -619,14 +734,13 @@ U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T  \la
 
 %%RC why W_{\theta} is not defined (only one sentence)? How to define in practice Wtheta and Wu?
 
-
 \begin{itemize}
 \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);
+  during round $t$ (1 if yes and 0 if not);
 \item $\Theta_{t,p}$ - {\it overcoverage}:  the number of sensors minus one that
-  are covering the primary point $p$ during the round $t$;
+  are covering the primary point $p$ during 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
+  point $p$  is being covered during round $t$ (1  if not covered  and 0 if
   covered).
 \end{itemize}
 
@@ -642,9 +756,10 @@ 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 $W_U$.
+to guarantee that the maximum number of points are covered during each round. 
+%% MS W_theta is smaller than W_u => problem with the following sentence
+In our simulations priority is given  to the coverage by choosing $W_{U}$ very
+large compared to $W_{\theta}$.
 %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}
@@ -709,8 +824,7 @@ 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
+250~nodes 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.
@@ -745,10 +859,10 @@ Sensing time for one round & 60 Minutes \\
 $E_{R}$ & 36 Joules\\
 $R_s$ & 5~m   \\     
 %\hline
-$w_{\Theta}$ & 1   \\
+$W_{\Theta}$ & 1   \\
 % [1ex] adds vertical space
 %\hline
-$w_{U}$ & $|P^2|$
+$W_{U}$ & $|P|^2$
 %inserts single line
 \end{tabular}
 \label{table3}
@@ -757,24 +871,23 @@ $w_{U}$ & $|P^2|$
   
 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 and we will  make comparisons 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.
+rounds in one sensing period).  In  the following, we will make comparisons 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.
 
 Some preliminary experiments were performed to study the choice of the number of
-subregions  which subdivide  the  sensing field,  considering different  network
+subregions  which subdivides  the  sensing field,  considering different  network
 sizes. They show that as the number of subregions increases, so does the network
-lifetime. Moreover, it  makes the MuDiLCO-T protocol more  robust against random
-network  disconnection due  to  node failures.  However,  too much  subdivisions
-reduces the advantage  of the optimization. In fact, there  is a balance between
+lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
+network  disconnection due  to node  failures.  However,  too  many subdivisions
+reduce the advantage  of the optimization. In fact, there  is a balance between
 the  benefit  from the  optimization  and the  execution  time  needed to  solve
-it. Therefore, we  have set the number  of subregions to 16 rather  than 32. 
+it. Therefore, we have set the number of subregions to 16 rather than 32.
 
-\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
@@ -789,13 +902,12 @@ 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
+is responsible  for transmitting/receiving messages, the  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 $0.2575~mW$.
+summarized in Table~\ref{table4}.
 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}
@@ -829,13 +941,14 @@ COMPUTATION & on & on & on & 26.83 \\
 For the 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
-Thus, when a sensor becomes active (i.e., it already decides its status), it can
+Thus, when a sensor becomes active (i.e., it has already chosen its 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.
+value for receiving the packets. The energy  needed to send or receive a 1-bit
+packet is equal to $0.2575~mW$.
 
 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
@@ -851,16 +964,16 @@ To evaluate our approach we consider the following performance metrics:
 
 \begin{enumerate}[i]
   
-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area
+\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of 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:
+  a connected grid  of points and we use  each grid point as a  sample point to
+  compute the coverage. The coverage ratio can be calculated by:
 \begin{equation*}
 \scriptsize
 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
 \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
+subregions during round $t$ in the current sensing phase and $N$ is the total number
 of grid points  in the sensing field of  the network. In our simulations $N = 51
 \times 26 = 1326$ grid points.
 %The accuracy of this method depends on the distance between grids. In our
@@ -878,11 +991,11 @@ of grid points  in the sensing field of  the network. In our simulations $N = 51
 \end{equation*}
 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.
+network, and $R$ is the total number of 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
+  $Lifetime_{95}$ (respectively  $Lifetime_{50}$) the amount of  time during
   which  the  network   can  satisfy  an  area  coverage   greater  than  $95\%$
   (respectively $50\%$). We assume that the network is alive until all nodes have
   been   drained    of   their   energy   or   the    sensor   network   becomes
@@ -894,28 +1007,40 @@ network, and $R$ is the total number of the subregions in the network.
   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
-\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*}
 
+  % New version with global loops on period
+  \begin{equation*}
+    \scriptsize
+    \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
+  \end{equation*}
+
+
+% Old version with loop on round outside the loop on period
+%  \begin{equation*}
+%    \scriptsize
+%    \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*}
+
+% Ali version 
 %\begin{equation*}
 %\scriptsize
 %\mbox{EC} =  \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
 %\end{equation*}
 
-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 $t$.
+% Old version -> where $M_L$ and  $T_L$ are respectively the number of  periods and rounds during
+%$Lifetime_{95}$ or  $Lifetime_{50}$. 
+% New version
+where  $M_L$ is  the number  of periods  and  $T_m$ the  number of  rounds in  a
+period~$m$, both  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  $E^{\scriptsize  \mbox{com}}_m$,
+represents  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.
@@ -932,31 +1057,28 @@ network in round $t$.
 
 \end{enumerate}
 
-
 \section{Results and analysis}
 
 \subsection{Coverage ratio} 
 
 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.  
-%%RC : need to uniformize MuDiLCO or MuDiLCO-T?
-
+which is a little bit better than the one of MuDiLCO.  
+%%RC : need to uniformize MuDiLCO or MuDiLCO-T? 
+%%MS : MuDiLCO everywhere
 %%RC maybe increase the size of the figure for the reviewers, no?
+This is due  to the fact that, in comparison with  MuDiLCO which 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 node 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 saves more energy,  with less dead nodes, at most for several
+rounds, and thus should extend the network lifetime.
 
-This is due to the fact
-that in comparison with MuDiLCO-T 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  node
-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
-saves more  energy, with less dead nodes,  at most for several  rounds, and thus
-should extend the network lifetime.
-
-\begin{figure}[t!]
+\begin{figure}[ht!]
 \centering
  \includegraphics[scale=0.5] {R1/CR.pdf} 
 \caption{Average coverage ratio for 150 deployed nodes}
@@ -970,14 +1092,14 @@ 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.
+MuDiLCO clearly  outperforms them  with only 24.8\%  of active nodes.  After the
+thirty-fifth round, MuDiLCO exhibits larger numbers 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
+activated many nodes  at the beginning. Anyway, MuDiLCO  activates the available
 nodes in a more efficient manner.
 
-\begin{figure}[t!]
+\begin{figure}[ht!]
 \centering
 \includegraphics[scale=0.5]{R1/ASR.pdf}  
 \caption{Active sensors ratio for 150 deployed nodes}
@@ -989,10 +1111,9 @@ nodes in a more efficient manner.
 %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.  DESK stops first,  after around 45~rounds, because it consumes the
+per round for  150 deployed nodes. This figure gives the  breakpoint for each method.  DESK stops first,  after approximately 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
+phase. GAF  stops secondly for the  same reason than  DESK.  MuDiLCO 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
@@ -1000,14 +1121,14 @@ still connected.
 
 %%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{figure}[t!]
+\begin{figure}[ht!]
 \centering
 \includegraphics[scale=0.5]{R1/SR.pdf} 
 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
 
-\subsection{Energy Consumption} \label{subsec:EC}
+\subsection{Energy consumption} \label{subsec:EC}
 
 We  measure  the  energy  consumed  by the  sensors  during  the  communication,
 listening, computation, active, and sleep status for different network densities
@@ -1027,7 +1148,7 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
   \label{fig7}
 \end{figure} 
 
-The  results  show  that MuDiLCO-T  is  the  most  competitive from  the  energy
+The  results  show  that  MuDiLCO  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
@@ -1054,7 +1175,7 @@ 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}[t!]
+\begin{figure}[ht!]
 \centering
 \includegraphics[scale=0.5]{R1/T.pdf}  
 \caption{Execution Time (in seconds)}
@@ -1062,11 +1183,11 @@ for different network sizes.
 \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
+into account to schedule the sensing phase. The times obtained for $T=1,3$
+or $5$ seem 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
+we need to choose a relevant number of subregions 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
@@ -1074,18 +1195,18 @@ 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}
 
 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
+node  density  which  results in  more  and  more  redundant  nodes that  can  be
+deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
+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 be observed  for MuDiLCO-7 in case
+of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  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
@@ -1103,26 +1224,26 @@ linked.
   \label{fig8}
 \end{figure} 
 
-% 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. 
+% 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 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.
+%In Figure~\ref{fig8}, Comparison shows that our MuDiLCO 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.
 
 
-\section{Conclusion and Future Works}
+\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  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.
+We have addressed  the problem of the coverage and of 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 (Multiround  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
@@ -1130,17 +1251,17 @@ sensor activity scheduling.
 %subregion using more than one cover set during the sensing phase. 
 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
+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
+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
+the resulting optimization problem leads to too high resolution times 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
@@ -1148,11 +1269,12 @@ an excessive energy consumption.
 % use section* for acknowledgement
 
 \section*{Acknowledgment}
-As a Ph.D.  student, Ali Kadhum IDREES would like  to gratefully acknowledge the
+This work is  partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
+As a Ph.D.  student, Ali Kadhum IDREES would like to gratefully acknowledge the
 University  of Babylon  - Iraq  for the  financial support,  Campus  France (The
 French  national agency  for the  promotion of  higher  education, international
-student   services,  and   international  mobility),   and  the   University  of
-Franche-Comt\'e - France for all the support in France. This work is  partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
+student   services,  and   international  mobility).%,   and  the   University  ofFranche-Comt\'e - France for all the support in France. 
+
 
 
 
@@ -1178,7 +1300,7 @@ Franche-Comt\'e - France for all the support in France. This work is  partially
 %% TeX file.
 
 \bibliographystyle{elsarticle-num} 
-\bibliography{biblio}
+\bibliography{article}
   
 \end{document}
 
