X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/98f56bd39ecefc67d93931a6717ed20c2824304a..25375e8c1c8e5e3ccae47f620d5627d0c1936ff8:/article.tex?ds=sidebyside

diff --git a/article.tex b/article.tex
index 53747de..a3fb209 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]{}
@@ -89,7 +89,7 @@ $\lbrace$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
@@ -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 +173,121 @@ 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
+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~\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 for selecting  the minimum number of working sensor  nodes, in order to
+preserve  a  maximum coverage  and  extend lifetime  of  the  network. Cheng  et
+al.~\cite{cheng2014energy} have defined a  heuristic algorithm called Cover Sets
+Balance (CSB), which choose 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} focuses  on coverage-aware,
+distributed energy-efficient,  and distributed clustering  methods respectively,
+which aims to extend 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}
@@ -272,28 +376,29 @@ 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 +407,7 @@ 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
@@ -337,7 +442,7 @@ 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 +452,10 @@ 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 +492,7 @@ 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 +515,7 @@ 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 +539,16 @@ 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 +560,18 @@ 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
@@ -619,7 +733,6 @@ 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);
@@ -642,8 +755,9 @@ 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
+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 $W_{\theta}$ 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.
 
@@ -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
 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
+lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
+network  disconnection due  to node  failures.  However,  too  much subdivisions
 reduces the advantage  of the optimization. In fact, there  is a balance between
 the  benefit  from the  optimization  and the  execution  time  needed to  solve
-it. Therefore, 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
@@ -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  $E^{\scriptsize  \mbox{com}}_m$,
+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.
@@ -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 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 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 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
+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}
@@ -992,7 +1114,7 @@ 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
+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 +1122,14 @@ 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 +1149,7 @@ 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 +1176,7 @@ 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)}
@@ -1074,18 +1196,18 @@ 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
+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 bee 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 +1225,26 @@ 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  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
@@ -1148,11 +1270,12 @@ 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 +1301,7 @@ 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}
 
