X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/9458c6e7496a265a0e594312416aa8dd608e4296..1fe3b22ea7e88b87e651993466045645f755624d:/article.tex

diff --git a/article.tex b/article.tex
index 36c5dcf..a4752b1 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
@@ -126,14 +126,14 @@ 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,
+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
-these two objectives, the main idea  is to take advantage of overlapping sensing
+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
+we concentrate  on the area coverage problem, with the  objective of maximizing
 the network lifetime by using an optimized multirounds scheduling.
 
 % One of the major scientific research challenges in WSNs, which are addressed by a large number of literature during the last few years is to design energy efficient approaches for coverage and connectivity in WSNs~\cite{conti2014mobile}. The coverage problem is one  of the
@@ -159,6 +159,8 @@ demonstrate  the  usefulness  of   the  proposed  approach.   Finally,  we  give
 concluding    remarks   and    some    suggestions   for    future   works    in
 Section~\ref{sec:conclusion}.
 
+
+%%RC : Related works good for a phd thesis but too long for a paper. Ali you  need to learn to .... summarize :-)
 \section{Related works} % Trop proche de l'etat de l'art de l'article de Zorbas ?
 \label{rw}
 
@@ -182,6 +184,120 @@ algorithms in WSNs according to several design choices:
 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 less 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  proposed  a  linear  programming
+approach for selecting  the minimum number of working sensor  nodes, in order to
+as 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.
+
+Some        distributed       algorithms        have        been       developed
+in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02, yardibi2010distributed, prasad2007distributed,Misra}
+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}. The  authors  in  \cite{yardibi2010distributed}  have  developed  a  Distributed
+Adaptive  Sleep Scheduling  Algorithm (DASSA)  for WSNs  with  partial coverage.
+DASSA  does  not  require  location  information of  sensors  while  maintaining
+connectivity and satisfying a user defined coverage target.  In DASSA, nodes use
+the  residual  energy levels  and  feedback from  the  sink  for scheduling  the
+activity of their neighbors.  This  feedback mechanism reduces the randomness in
+scheduling  that  would   otherwise  occur  due  to  the   absence  of  location
+information.   In  \cite{ChinhVu},  the  author 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
+works in  rounds, requires  only one-hop neighbor  information, and  each sensor
+decides  its status  (active or  sleep) based  on the  perimeter  coverage model
+proposed in \cite{Huang:2003:CPW:941350.941367}.
+
+%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   proposed  an   algorithm,  called
+Geographical Adaptive Fidelity (GAF), which uses geographic location information
+to divide  the area of  interest into fixed  square grids. Within each  grid, it
+keeps only  one node  staying awake  to take the  responsibility of  sensing and
+communication.
+
+Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
+synchronized and  predetermined period of time  where the sensors  are active or
+not.   Indeed, each  sensor maintains  its  own timer  and its  wake-up time  is
+randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
+
+The MuDiLCO protocol (for 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.
+
+
+
+
+
+\iffalse
    
 \subsection{Centralized Approaches}
 %{\bf Centralized approaches}
@@ -199,25 +315,25 @@ size increases.
 
 The first algorithms proposed in the literature consider that the cover sets are
 disjoint: a sensor node appears in exactly one of the generated cover sets.  For
-instance, Slijepcevic  and Potkonjak \cite{Slijepcevic01powerefficient} proposed
-an  algorithm, which  allocates sensor  nodes  in mutually  independent sets  to
-monitor an area divided into several fields.  Their algorithm builds a cover set
-by including in  priority the sensor nodes which cover  critical fields, that is
-to say  fields that  are covered by  the smallest  number of sensors.   The time
+instance,  Slijepcevic  and  Potkonjak  \cite{Slijepcevic01powerefficient}  have
+proposed an algorithm, which allocates sensor nodes in mutually independent sets
+to monitor an area divided into  several fields.  Their algorithm builds a cover
+set by including in priority the  sensor nodes which cover critical fields, that
+is to say fields  that are covered by the smallest number  of sensors.  The time
 complexity of  their heuristic is $O(n^2)$  where $n$ is the  number of sensors.
-Abrams et al.~\cite{abrams2004set} designed three approximation algorithms for a
-variation of  the set k-cover problem,  where the objective is  to partition the
-sensors into covers such that the  number of covers that include an area, summed
-over  all   areas,  is  maximized.    Their  work  builds  upon   previous  work
+Abrams et al.~\cite{abrams2004set}  have designed three approximation algorithms
+for a variation of the set  k-cover problem, where the objective is to partition
+the sensors  into covers such  that the number  of covers that include  an area,
+summed  over all  areas, is  maximized.  Their  work builds  upon  previous work
 in~\cite{Slijepcevic01powerefficient}  and  the  generated  cover  sets  do  not
 provide complete coverage of the monitoring zone.
 
-\cite{cardei2005improving} proposed a method  to efficiently compute the maximum
-number of disjoint  set covers such that each set can  monitor all targets. They
-first transform the problem into a  maximum flow problem, which is formulated as
-a mixed integer  programming (MIP). Then their heuristic uses  the output of the
-MIP to compute disjoint set covers.  Results show that this heuristic provides a
-number      of     set      covers     slightly      larger      compared     to
+In \cite{cardei2005improving}, the authors have proposed a method to efficiently
+compute the maximum number of disjoint set covers such that each set can monitor
+all targets. They first transform the problem into a maximum flow problem, which
+is formulated  as a mixed integer  programming (MIP). Then  their heuristic uses
+the output  of the MIP to compute  disjoint set covers.  Results  show that this
+heuristic  provides  a  number  of   set  covers  slightly  larger  compared  to
 \cite{Slijepcevic01powerefficient}, but with a  larger execution time due to the
 complexity of the mixed integer programming resolution.
 
@@ -261,6 +377,8 @@ 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
@@ -286,27 +404,27 @@ its status by a  rule named off-duty eligible rule, which tells  him to turn off
 if its sensing area is covered by its neighbors. A back-off scheme is introduced
 to let each sensor  delay the decision process with a random  period of time, in
 order  to avoid  simultaneous conflicting  decisions between  nodes and  lack of
-coverage  on  any  area.    \cite{prasad2007distributed}  defines  a  model  for
-capturing the  dependencies between different cover sets  and proposes localized
+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}  developed a  Distributed Adaptive
-Sleep Scheduling Algorithm  (DASSA) for WSNs with partial  coverage.  DASSA does
-not require  location information of sensors while  maintaining connectivity and
-satisfying a  user defined  coverage target.  In  DASSA, nodes use  the residual
-energy levels  and feedback from the  sink for scheduling the  activity of their
-neighbors.  This  feedback mechanism reduces  the randomness in  scheduling that
-would  otherwise  occur  due  to   the  absence  of  location  information.   In
-\cite{ChinhVu},  the  author  proposed  a novel  distributed  heuristic,  called
-Distributed  Energy-efficient Scheduling  for k-coverage  (DESK),  which ensures
-that  the energy  consumption among  the sensors  is balanced  and  the lifetime
-maximized while the coverage requirement is maintained.  This heuristic works in
-rounds, requires only one-hop neighbor  information, and each sensor decides its
-status  (active or  sleep) based  on the  perimeter coverage  model  proposed in
-\cite{Huang:2003:CPW:941350.941367}.
+The  authors  in  \cite{yardibi2010distributed}  have  developed  a  Distributed
+Adaptive  Sleep Scheduling  Algorithm (DASSA)  for WSNs  with  partial coverage.
+DASSA  does  not  require  location  information of  sensors  while  maintaining
+connectivity and satisfying a user defined coverage target.  In DASSA, nodes use
+the  residual  energy levels  and  feedback from  the  sink  for scheduling  the
+activity of their neighbors.  This  feedback mechanism reduces the randomness in
+scheduling  that  would   otherwise  occur  due  to  the   absence  of  location
+information.   In  \cite{ChinhVu},  the  author 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
+works in  rounds, requires  only one-hop neighbor  information, and  each sensor
+decides  its status  (active or  sleep) based  on the  perimeter  coverage model
+proposed in \cite{Huang:2003:CPW:941350.941367}.
 
 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
 %heterogeneous energy wireless sensor networks. 
@@ -315,26 +433,27 @@ status  (active or  sleep) based  on the  perimeter coverage  model  proposed in
 The  works presented in  \cite{Bang, Zhixin,  Zhang} focuses  on coverage-aware,
 distributed energy-efficient,  and distributed clustering  methods respectively,
 which aims  to extend the network  lifetime, while the coverage  is ensured.  S.
-Misra et al.  \cite{Misra} proposed a localized algorithm for coverage in sensor
-networks. The algorithm conserve the  energy while ensuring the network coverage
-by activating the subset of sensors  with the minimum overlap area. The proposed
-method preserves the network connectivity  by formation of the network backbone.
-More recently,  Shibo et  al. \cite{Shibo} expressed  the coverage problem  as a
-minimum weight submodular set cover problem and proposed a Distributed Truncated
-Greedy Algorithm (DTGA) to solve it.  They take advantage from both temporal and
-spatial  correlations between  data sensed  by different  sensors,  and leverage
-prediction,  to   improve  the  lifetime.   In   \cite{xu2001geography},  Xu  et
-al. proposed  an algorithm, called  Geographical Adaptive Fidelity  (GAF), which
-uses geographic location  information to divide the area  of interest into fixed
-square grids. Within each grid, it keeps only one node staying awake to take the
-responsibility of sensing and communication.
+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
+proposed method preserves  the network connectivity by formation  of the network
+backbone.  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   proposed  an   algorithm,  called
+Geographical Adaptive Fidelity (GAF), which uses geographic location information
+to divide  the area of  interest into fixed  square grids. Within each  grid, it
+keeps only  one node  staying awake  to take the  responsibility of  sensing and
+communication.
 
 Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
 synchronized and  predetermined period of time  where the sensors  are active or
 not.   Indeed, each  sensor maintains  its  own timer  and its  wake-up time  is
 randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
 
-The MuDiLCO protocol (for Multiperiod Distributed Lifetime Coverage Optimization
+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
@@ -344,6 +463,10 @@ 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}
@@ -380,7 +503,7 @@ 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.
@@ -425,16 +548,16 @@ is the subject of another study not presented here.
 %The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader after the decision to apply multi-round activity scheduling during the sensing phase. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will produce the cover sets of sensor nodes to take the mission of coverage during the sensing phase for $T$ rounds. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's schedule for $T$ rounds during the period of sensing, either Active or sleep until the starting of next period. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep based on it's schedule for $T$ rounds during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, which are includes $T$ rounds, all the sensor nodes in the same subregion will start new period by executing the MuDiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
 
 \subsection{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  (said a cover set) is  responsible for the
+sensing task. A multiround optimization process executed in each period after information exchange and leader election in order to produce a $T$ cover sets of sensors to 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}
@@ -446,12 +569,15 @@ sensing task.
 % set cover responsible for the sensing task.  
 %For each round a set of sensors (said a cover set) is responsible for the sensing task.
 
-This protocol is  reliable against an unexpected node  failure, because it works
-in periods.  On the one hand,  if a node  failure is detected before  making the
-decision, the node  will not participate to this phase, and,  on the other hand,
-if the node  failure occurs after the decision, the sensing  task of the network
-will be  temporarily affected:  only during  the period of  sensing until  a new
+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
 period starts.
+%%RC so if there are at least one failure per period, the coverage is bad...
 
 The  energy consumption  and some  other constraints  can easily  be  taken into
 account,  since the  sensors  can  update and  then  exchange their  information
@@ -464,7 +590,7 @@ monitor the area.
 
 We define two types of packets that will be used by the proposed protocol:
 \begin{enumerate}[(a)] 
-\item INFO  packet: a such packet  will be sent by  each sensor node  to all the
+\item INFO  packet: such a  packet  will be sent by  each sensor node  to all the
   nodes inside a subregion for information exchange.
 \item  Active-Sleep  packet: sent  by  the  leader to  all  the  nodes inside  a
   subregion to  inform them to remain Active  or to go Sleep  during the sensing
@@ -522,17 +648,17 @@ activated in  the following  sensing phase  to cover the  subregion to  which it
 belongs.  The integer  program will produce $T$ cover sets,  one for each round.
 The WSNL will send an Active-Sleep  packet to each sensor in the subregion based
 on the algorithm's results, indicating if  the sensor should be active or not in
-each  round of the  sensing phase.  The integer  program is  based on  the model
-proposed by \cite{pedraza2006} with some modification, where the objective is to
-find a maximum number of disjoint cover sets.  To fulfill this goal, the authors
-proposed  an integer  program  which forces  undercoverage  and overcoverage  of
-targets to become minimal at the  same time.  They use binary variables $x_{jl}$
-to indicate if sensor  $j$ belongs to cover set $l$.  In  our model, we consider
-binary variables $X_{t,j}$ to determine  the possibility of activation of sensor
-$j$ during  the round $t$  of a given  sensing phase.  We also  consider primary
-points as targets.  The  set of primary points is denoted by  $P$ and the set of
-sensors by  $J$. Only sensors  able to  be alive during  at least one  round are
-involved in the integer program.
+each round  of the  sensing phase.  The  integer program  is based on  the model
+proposed by  \cite{pedraza2006} with some modifications, where  the objective is
+to find  a maximum  number of disjoint  cover sets.   To fulfill this  goal, the
+authors proposed an integer  program which forces undercoverage and overcoverage
+of  targets to  become minimal  at  the same  time.  They  use binary  variables
+$x_{jl}$ to indicate if  sensor $j$ belongs to cover set $l$.   In our model, we
+consider binary  variables $X_{t,j}$ to determine the  possibility of activation
+of sensor $j$ during  the round $t$ of a given sensing  phase.  We also consider
+primary points as targets.  The set of  primary points is denoted by $P$ and the
+set of sensors by  $J$. Only sensors able to be alive  during at least one round
+are involved in the integer program.
 
 %parler de la limite en energie Et pour un round
 
@@ -611,6 +737,9 @@ U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T  \la
 %(W_{\theta}+W_{\psi} = P)    \label{eq19} 
 %\end{equation}
 
+%%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);
@@ -706,6 +835,9 @@ 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.
 
+%%RC these parameters are realistic?
+%% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
+
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}
 % title of Table
@@ -814,11 +946,11 @@ COMPUTATION & on & on & on & 26.83 \\
 % is used to refer this table in the text
 \end{table}
 
-For sake  of simplicity we  ignore the  energy needed to  turn on the  radio, to
+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  it's status), it
-can turn its  radio off to save  battery. MuDiLCO uses two types  of packets for
+Thus, when a sensor becomes active (i.e., it already decides 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
@@ -857,7 +989,7 @@ of grid points  in the sensing field of  the network. In our simulations $N = 51
 % Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
 
 \item{{\bf Number  of Active Sensors Ratio  (ASR)}:} it is important  to have as
-  few  active  nodes  as  possible  in  each  round,in  order  to  minimize  the
+  few  active  nodes  as  possible  in  each  round, in  order  to  minimize  the
   communication overhead  and maximize the network lifetime.  The Active Sensors
   Ratio is defined as follows:
 \begin{equation*}
@@ -920,7 +1052,6 @@ network in round $t$.
 
 \end{enumerate}
 
-%%%%%%%%%%%%%%%%%%%%%%%%VU JUSQU ICI**************************************************
 
 \section{Results and analysis}
 
@@ -928,8 +1059,13 @@ network in round $t$.
 
 Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. We
 can notice that for the first thirty rounds both DESK and GAF provide a coverage
-which is a little bit better than the  one of MuDiLCO-T. This is due to the fact
-that in  comparison with MuDiLCO that  uses optimization to put  in SLEEP status
+which is a little bit better than the one of MuDiLCO-T.  
+%%RC : need to uniformize MuDiLCO or MuDiLCO-T?
+
+%%RC maybe increase the size of the figure for the reviewers, no?
+
+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
@@ -1017,8 +1153,8 @@ due  to activating a  larger number  of redundant  nodes as  well as  the energy
 consumed during  the different  status of the  sensor node. Among  the different
 versions of our protocol, the MuDiLCO-7  one consumes more energy than the other
 versions. This is  easy to understand since the bigger the  number of rounds and
-the  number of  sensors involved  in the  integer program,  the larger  the time
-computation to  solve the optimization  problem. To improve the  performances of
+the number of  sensors involved in the integer program are,  the larger the time
+computation to solve the optimization problem is. To improve the performances of
 MuDiLCO-7, we  should increase the  number of subregions  in order to  have less
 sensors to consider in the integer program.
 
@@ -1104,7 +1240,7 @@ 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
+protocol,   called   MuDiLCO    (Multiround  Distributed   Lifetime   Coverage
 Optimization)  combines two  efficient techniques:  network leader  election and
 sensor activity scheduling.
 %,  where the challenges
@@ -1132,11 +1268,14 @@ 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.
+student   services,  and   international  mobility).%,   and  the   University  ofFranche-Comt\'e - France for all the support in France. 
+
+
+
 
 %% \linenumbers
 
@@ -1160,7 +1299,7 @@ Franche-Comt\'e - France for all the support in France.
 %% TeX file.
 
 \bibliographystyle{elsarticle-num} 
-\bibliography{biblio}
+\bibliography{article}
   
 \end{document}
 
