Still working on sections 5 and 6

[Sensornets15.git] / Example.tex

diff --git a/Example.tex b/Example.tex
index abb42a49883b295630f4fb006bc3ebb526bf9d43..5a2a5cb009378db3ba9788d210e8f58c29bfdc99 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -64,50 +64,49 @@ Optimization, Scheduling.}
 \section{\uppercase{Introduction}}
 \label{sec:introduction}
 \noindent 
 \section{\uppercase{Introduction}}
 \label{sec:introduction}
 \noindent 

-Energy efficiency  is a crucial issue  in wireless sensor  networks since sensor
-nodes drain their  energy from batteries. In fact,  strong constraints on energy
+Energy efficiency is  a crucial issue in wireless  sensor networks since sensory

 consumption,  in order  to maximize  the network  lifetime, represent  the major
 difficulty when designing WSNs. As a consequence, one of the scientific research
 challenges in  WSNs, which has  been addressed by  a large amount  of literature
 during the  last few  years, is  the design of  energy efficient  approaches for
 consumption,  in order  to maximize  the network  lifetime, represent  the major
 difficulty when designing WSNs. As a consequence, one of the scientific research
 challenges in  WSNs, which has  been addressed by  a large amount  of literature
 during the  last few  years, is  the design of  energy efficient  approaches for

-coverage and  connectivity~\cite{conti2014mobile}. Coverage reflects  how well a
-sensor field  is monitored. The  most discussed coverage problems  in literature
+coverage and connectivity~\cite{conti2014mobile}.   Coverage reflects how well a
+sensor field is  monitored.  The most discussed coverage  problems in literature

 can  be classified into  three types  \cite{li2013survey}: area  coverage (where
 every point inside an area is  to be monitored), target coverage (where the main
 objective is to  cover only a finite number of  discrete points called targets),
 and  barrier coverage (to  prevent intruders  from entering  into the  region of
 interest). On the one  hand we want to monitor the area  of interest in the most
 efficient way~\cite{Nayak04}. On the other hand we want to use as less energy as
 can  be classified into  three types  \cite{li2013survey}: area  coverage (where
 every point inside an area is  to be monitored), target coverage (where the main
 objective is to  cover only a finite number of  discrete points called targets),
 and  barrier coverage (to  prevent intruders  from entering  into the  region of
 interest). On the one  hand we want to monitor the area  of interest in the most
 efficient way~\cite{Nayak04}. On the other hand we want to use as less energy as

-possible. % TO BE CONTINUED
-Sensor nodes runs on batteries with limited capacities~\cite{Sudip03}
-and  it  is  impossible,  difficult  or expensive  to  recharge  and/or  replace
-batteries  in remote,  hostile, or  unpractical environments.  Therefore,  it is
-desired that  the WSNs  are deployed with  high densities  so as to  exploit the
-overlapping sensing regions  of some sensor nodes to save  energy by turning off
-some of them during the sensing phase to prolong the network lifetime.
-
-In this paper we concentrate on  the area coverage problem with the objective of
-maximizing the network lifetime by using DiLCO protocol to maintain the coverage
-and  to improve  the lifetime  in WSNs.  The area  of interest  is  divided into
-subregions using divide-and-conquer method and an activity scheduling for sensor
-nodes is planned by the elected leader  in each subregion. In fact, the nodes in
-a subregion can be  seen as a cluster where each node  sends sensing data to the
-cluster   head  or   the  sink   node.    Furthermore,  the   activities  in   a
-subregion/cluster can  continue even  if another cluster  stops due to  too many
-node failures.  Our DiLCO protocol considers periods, where a period starts with
-a discovery phase  to exchange information between sensors  of the subregion, in
-order to choose in a suitable manner a sensor node (the leader) to carry out the
-coverage  strategy.  Our  DiLCO protocol  involves solving  an  integer program,
-which  provides the  activation of  the  sensors for  the sensing  phase of  the
-current period.
+possible.  Sensor nodes  are  battery-powered  with no  means  of recharging  or
+replacing, usually due to environmental (hostile or unpractical environments) or
+cost reasons.  Therefore, it  is desired  that the WSNs  are deployed  with high
+densities so as to exploit the  overlapping sensing regions of some sensor nodes
+to save energy by  turning off some of them during the  sensing phase to prolong
+the network lifetime.
+
+In this  paper we design  a protocol that  focuses on the area  coverage problem
+with  the objective  of maximizing  the network  lifetime. Our  proposition, the
+DiLCO protocol,  maintains the coverage and  improves the lifetime  in WSNs. The
+area of  interest is  first divided into  subregions using  a divide-and-conquer
+algorithm and  an activity scheduling  for sensor nodes  is then planned  by the
+elected leader in each subregion. In fact,  the nodes in a subregion can be seen
+as a cluster where each node sends  sensing data to the cluster head or the sink
+node.  Furthermore, the  activities in a subregion/cluster can  continue even if
+another cluster  stops due to too  many node failures.  Our Distributed Lifetime
+Coverage Optimization (DILCO) protocol  considers periods, where a period starts
+with  a  discovery phase  to  exchange information  between  sensors  of a  same
+subregion, in order to choose in a suitable manner a sensor node (the leader) to
+carry out the coverage strategy. In each subregion the activation of the sensors
+for the  sensing phase of the current  period is obtained by  solving an integer
+program.

 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes
 the  DiLCO  protocol,  followed   in  Section~\ref{cp}  by  the  coverage  model
 formulation    which    is    used     to    schedule    the    activation    of
 sensors. Section~\ref{sec:Simulation Results  and Analysis} shows the simulation
 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes
 the  DiLCO  protocol,  followed   in  Section~\ref{cp}  by  the  coverage  model
 formulation    which    is    used     to    schedule    the    activation    of
 sensors. Section~\ref{sec:Simulation Results  and Analysis} shows the simulation

-results. The paper ends with conclusions and some suggestions for futher work in
-Section~\ref{sec:Conclusion and Future Works}.
+results. The paper  ends with conclusions and some  suggestions for further work
+in Section~\ref{sec:Conclusion and Future Works}.

 
 \section{\uppercase{Literature Review}}
 \label{sec:Literature Review}
 
 \section{\uppercase{Literature Review}}
 \label{sec:Literature Review}


@@ -204,31 +203,52 @@ The main contributions of our DiLCO Protocol can be summarized as follows:
 \section{ The DiLCO Protocol Description}
 \label{sec:The DiLCO Protocol Description}
 
 \section{ The DiLCO Protocol Description}
 \label{sec:The DiLCO Protocol Description}
 

-\noindent In this section, we introduce a Distributed Lifetime Coverage Optimization protocol, which is called DiLCO. 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.  
-\iffalse The main features of our DiLCO 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 rounds, 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 set 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.
+\noindent In this section, we  introduce the DiLCO protocol which 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,  applied  periodically  to  efficiently
+maximize the lifetime in the network.
+\iffalse  The main  features of  our DiLCO  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 rounds, 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 set 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. 

 \fi
 \fi

-\subsection{ Assumptions and Models}
-\noindent We consider  a randomly and  uniformly deployed network  consisting of
-static  wireless sensors. The  wireless sensors  are deployed  in high
-density to ensure initially a high coverage ratio of the interested area. We
-assume that  all nodes are  homogeneous in terms of  communication and
-processing capabilities and heterogeneous in term of energy provision.
-The  location  information is  available  to  the  sensor node  either
-through hardware such as embedded GPS or through location discovery
-algorithms. We consider a boolean  disk coverage model which is the most
-widely used sensor coverage model in the literature. Each sensor has a
-constant sensing range $R_s$. All space points within a disk centered
-at the sensor with the radius of the sensing range is said to be
-covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$.
-In  fact,   Zhang  and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the
-previous hypothesis, a complete coverage of a convex area implies
-connectivity among the working nodes in the active mode.
-
-\indent Instead of working with the coverage area, we consider for each
-sensor a set of points called  primary points~\cite{idrees2014coverage}. We also assume that the
-sensing disk defined  by a sensor is covered if all the primary points of
-this sensor are covered.
+
+\subsection{ Assumptions and models}
+
+\noindent  We consider  a sensor  network composed  of static  nodes distributed
+independently and uniformly at random.  A high density deployment ensures a high
+coverage ratio of the interested area at the starting. The nodes are supposed to
+have homogeneous characteristics from a  communication and a processing point of
+view, whereas they  have heterogeneous energy provisions.  Each  node has access
+to its location thanks,  either to a hardware component (like a  GPS unit), or a
+location discovery algorithm. 
+
+\indent We consider a boolean disk  coverage model which is the most widely used
+sensor coverage  model in the  literature. Thus, since  a sensor has  a constant
+sensing range $R_s$, every space points  within a disk centered at a sensor with
+the radius of  the sensing range is said  to be covered by this  sensor. We also
+assume  that  the communication  range  $R_c \geq  2R_s$.   In  fact, Zhang  and
+Zhou~\cite{Zhang05} proved that if  the transmission range fulfills the previous
+hypothesis, a complete coverage of  a convex area implies connectivity among the
+working nodes in the active mode.
+
+\indent  For  each  sensor  we  also  define a  set  of  points  called  primary
+points~\cite{idrees2014coverage} to  approximate the area  coverage it provides,
+rather  than  working  with  a   continuous  coverage.   Thus,  a  sensing  disk
+corresponding to  a sensor node is covered  by its neighboring nodes  if all its
+primary points are covered. Obviously,  the approximation of coverage is more or
+less accurate according to the number of primary points.

 
 \iffalse
 By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless
 
 \iffalse
 By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless


@@ -274,11 +294,12 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 
 \fi
 
 
 \fi
 

-\subsection{The Main Idea}
-\noindent The   area  of  interest   can  be  divided using the
-divide-and-conquer strategy into smaller areas  called subregions and
-then  our coverage  protocol  will be  implemented  in each  subregion
-simultaneously. Our DiLCO protocol works in periods fashion as shown in figure~\ref{fig2}.
+\subsection{The main idea}
+
+\noindent We start  by applying a divide-and-conquer algorithm  to partition the
+area of interest  into smaller areas called subregions and  then our protocol is
+executed   simultaneously  in   each   subregion.
+

 \begin{figure}[ht!]
 \centering
 \includegraphics[width=75mm]{FirstModel.pdf} % 70mm
 \begin{figure}[ht!]
 \centering
 \includegraphics[width=75mm]{FirstModel.pdf} % 70mm


@@ -286,48 +307,58 @@ simultaneously. Our DiLCO protocol works in periods fashion as shown in figure~\
 \label{fig2}
 \end{figure} 
 
 \label{fig2}
 \end{figure} 
 

-%Modifier la figure pour faire apparaitre des periodes et dans le schema en bleu, indiquer sensing round au lieu de sensing tout seul.
-
-Each period  is divided  into 4 phases  : Information  (INFO) Exchange,
-Leader  Election, Decision,  and  Sensing.  For  each  period there  is
-exactly one set cover responsible for the sensing task. This protocol is
-more reliable  against an unexpected node failure  because it works
-in periods. On the  one hand,  if a node failure is detected before
-making the decision, the node will not participate to this phase, and,
-on the other hand, if the  node failure occurs after the decision, the
-sensing task of the network  will be temporarily affected: only during
-the period of sensing until a new period starts, since a new set cover
-will take charge of the sensing task in the next period.  The energy
-consumption and some other constraints can easily be taken into
-account since the sensors can update and then exchange  their
-information (including their residual energy) at the beginning of each
-period.  However,   the  pre-sensing  phases   (INFO  Exchange,  Leader
-Election,  Decision) are energy  consuming for  some nodes,  even when
-they do not  join the network to monitor the  area. 
-We define two types of packets to be used by our DiLCO protocol.
+As  shown  in Figure~\ref{fig2},  the  proposed  DiLCO  protocol is  a  periodic
+protocol where  each period is  decomposed into 4~phases:  Information Exchange,
+Leader Election ,  Decision, and Sensing. For each period  there will be exactly
+one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
+interesting  because it  enhances the  robustness  of the  network against  node
+failures. First,  a node  that has not  enough energy  to complete a  period, or
+which fails before  the decision is taken, will be  excluded from the scheduling
+process. Second,  if a node  fails later, whereas  it was supposed to  sense the
+region  of interest,  it will  only  affect the  quality of  coverage until  the
+definition of a new cover set  in the next period.  Constraints, like the energy
+consumption, can be easily taken into consideration since the sensors can update
+and exchange their  information during the first phase.  Let  us notice that the
+phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
+Decision) are  energy consuming for all the  nodes, even nodes that  will not be
+retained by the leader to keep watch over the corresponding area.
+
+During the excution of the DiLCO protocol, two kinds of packets will be used:

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

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

 \end{itemize}
 %\end{enumerate}
 \end{itemize}
 %\end{enumerate}

-
-There are five status for each sensor node in the network :
+and each sensor node will have five possible status in the network:

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

-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: sensor is waiting for a decision (to be active or not);
+\item COMPUTATION: sensor applies the optimization process as leader;
+\item ACTIVE: sensor is active;
+\item SLEEP: sensor is turned off;
+\item COMMUNICATION: sensor is transmitting or receiving packet.

 \end{itemize}
 %\end{enumerate}
 \end{itemize}
 %\end{enumerate}

-%Below, we describe each phase in more details.
-Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_j$ for a sensor node indexed by $j$).
-Initially, the sensor node checks its remaining energy in order to participate in the current period. After that, all the sensors collect position coordinates, remaining energy $RE_j$, sensor node id, and the number of its one-hop live neighbors during the information exchange. 
-Then all the sensor nodes in the same subregion will select the leader based on the received informations. The selection criteria for the leader in order  of priority  are: larger number  of neighbours,  larger remaining  energy, and  then in  case of equality, larger index. After that, if the sensor node is leader, it will execute the integer program algorithm (see section~\ref{cp}) which provides a set of sensors planned to be active in the sensing round. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to indicate it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing round.
-

 
 

+An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO}
+which describes  the execution of  a period  by a node  (denoted by $s_j$  for a
+sensor  node indexed by  $j$). At  the beginning  a node  checks whether  it has
+enough energy to stay active during the next sensing phase. If yes, it exchanges
+information  with  all the  other  nodes belonging  to  the  same subregion:  it
+collects from each node its position coordinates, remaining energy ($RE_j$), ID,
+and  the number  of  one-hop neighbors  still  alive. Once  the  first phase  is
+completed, the nodes  of a subregion choose a leader to  take the decision based
+on  the  following  criteria   with  decreasing  importance:  larger  number  of
+neighbors, larger remaining energy, and  then in case of equality, larger index.
+After that,  if the sensor node is  leader, it will execute  the integer program
+algorithm (see Section~\ref{cp})  which provides a set of  sensors planned to be
+active in the next sensing phase. As leader, it will send an Active-Sleep packet
+to each sensor  in the same subregion to  indicate it if it has to  be active or
+not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
+Active-Sleep packet to know its state for the coming sensing phase.

 
 \iffalse
 \subsubsection{Information Exchange Phase}
 
 \iffalse
 \subsubsection{Information Exchange Phase}


@@ -374,8 +405,8 @@ Active-Sleep packet is obtained.
 
 \iffalse
 \subsection{DiLCO protocol Algorithm}
 
 \iffalse
 \subsection{DiLCO protocol Algorithm}

-we first show the pseudo-code of DiLCO protocol, which is executed by each sensor in the subregion and then describe it in more detail. 
-\fi
+we  first show  the pseudo-code  of DiLCO  protocol, which  is executed  by each
+sensor in the subregion and then describe it in more detail.  \fi

 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}
 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}


@@ -428,19 +459,17 @@ The sensor node enter in listening mode waiting to receive ActiveSleep packet fr
 \section{Coverage problem formulation}
 \label{cp}
 
 \section{Coverage problem formulation}
 \label{cp}
 

-\indent   Our   model   is   based   on  the   model   proposed   by
-\cite{pedraza2006} where the objective is  to find a maximum number of
-disjoint  cover sets.   To accomplish  this goal,  authors  proposed an
-integer program, which forces undercoverage and overcoverage of targets
-to  become  minimal at  the  same  time.   They use  binary  variables
-$x_{jl}$ to indicate  if sensor $j$ belongs to cover  set $l$.  In our
-model,  we  consider  binary  variables $X_{j}$,  which  determine  the
-activation of  sensor $j$ in the  sensing round. We also
-consider  primary points  as targets.   The set  of primary  points is
-denoted by $P$ and the set of sensors by $J$.
-
-\noindent  For  a primary  point  $p$,  let  $\alpha_{jp}$ denote  the
-indicator function of whether the point $p$ is covered, that is:
+\indent Our model is based on the model proposed by \cite{pedraza2006} where the
+objective is  to find a  maximum number of  disjoint cover sets.   To accomplish
+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  variable $X_{j}$ which  determine the  activation of
+sensor $j$  in the sensing  phase. We also  consider primary points  as targets.
+The set of primary points is denoted by $P$ and the set of sensors by $J$.
+
+\noindent Let $\alpha_{jp}$ denote the indicator function of whether the primary
+point $p$ is covered, that is:

 \begin{equation}
 \alpha_{jp} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 \alpha_{jp} = \left \{ 
 \begin{array}{l l}


@@ -450,8 +479,8 @@ indicator function of whether the point $p$ is covered, that is:
 \end{array} \right.
 %\label{eq12} 
 \end{equation}
 \end{array} \right.
 %\label{eq12} 
 \end{equation}

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

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


@@ -483,7 +512,7 @@ U_{p} = \left \{
 \label{eq14} 
 \end{equation}
 
 \label{eq14} 
 \end{equation}
 

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

 \begin{equation} \label{eq:ip2r}
 \left \{
 \begin{array}{ll}
 \begin{equation} \label{eq:ip2r}
 \left \{
 \begin{array}{ll}


@@ -500,38 +529,32 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \right.
 \end{equation}
 
 \right.
 \end{equation}
 

-
-

 \begin{itemize}
 \begin{itemize}

-\item $X_{j}$  : indicates whether or  not the sensor  $j$ is actively
-  sensing in the round (1 if yes and 0 if not);
-\item $\Theta_{p}$  : {\it overcoverage}, the number  of sensors minus
-  one that are covering the primary point $p$;
-\item $U_{p}$  : {\it undercoverage},  indicates whether or  not the primary point
+\item $X_{j}$ :  indicates whether or not the sensor $j$  is actively sensing (1
+  if yes and 0 if not);
+\item $\Theta_{p}$  : {\it overcoverage}, the  number of sensors  minus one that
+  are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage},  indicates whether or not the primary point

   $p$ is being covered (1 if not covered and 0 if covered).
 \end{itemize}
 
   $p$ is being covered (1 if not covered and 0 if covered).
 \end{itemize}
 

-The first group  of constraints indicates that some  primary point $p$
-should be covered by at least one  sensor and, if it is not always the
-case,  overcoverage  and  undercoverage  variables  help  balancing  the
-restriction  equations by taking  positive values.  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.
-
-
-
-
-\section{\uppercase{Simulation Results and Analysis}}  
+The first group  of constraints indicates that some primary  point $p$ should be
+covered by at least  one sensor and, if it is not  always the case, overcoverage
+and undercoverage  variables help balancing the restriction  equations by taking
+positive values. Two objectives can be noticed in our model. First, we limit the
+overcoverage of primary  points to activate as few  sensors as possible. Second,
+to  avoid   a  lack  of  area   monitoring  in  a  subregion   we  minimize  the
+undercoverage. Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
+order to  guarantee that the  maximum number of  points are covered  during each
+period.
+
+\section{\uppercase{Protocol evaluation}}  

 \label{sec:Simulation Results and Analysis}
 \label{sec:Simulation Results and Analysis}

-\noindent \subsection{Simulation Framework}
-In this subsection, we conducted a series of simulations to evaluate the
-efficiency and the relevance of our DiLCO protocol, using the discrete event
-simulator OMNeT++  \cite{varga}. The simulation parameters are summarized in
-Table~\ref{table3}.
+\noindent \subsection{Simulation framework}
+
+To assess the performance of our DiLCO protocol, we have used the discrete
+event simulator OMNeT++ \cite{varga} to run different series of simulations.
+Table~\ref{table3} gives the chosen parameters setting.

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


@@ -570,29 +593,36 @@ $w_{U}$ & $|P|^2$
 % is used to refer this table in the text
 \end{table}
 
 % is used to refer this table in the text
 \end{table}
 

-We  performed  simulations for five different densities varying from 50 to 250~nodes. Experimental results are the average obtained from 25 randomly generated networks (25 for each network density) in which nodes are deployed over a $(50 \times 25)~m^2 $ sensing field. More precisely, the deployment is controlled at a coarse scale in order to ensure that the deployed nodes can cover the sensing field with a high coverage ratio.\\
-
-We first concentrate on the required number of subregions making effective our protocol. Thus our DiLCO protocol is declined into five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$ or $32$ subregions (leaders).  
-
-We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
-The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
-% We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node. 
-%The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU. 
-%revoir la phrase
-
-For our energy consumption model, we refer to the sensor node Medusa II which uses Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The typical architecture of a sensor is composed of four subsystems : the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for
-transmitting/receiving messages, sensing subsystem that collects data, and the power supply which  powers the complete sensor node ~\cite{raghunathan2002energy}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second)  for the different status of the sensor is summarized in Table~\ref{table4}. 
+Simulations with five  different node densities going from  50 to 250~nodes were
+performed  considering  each  time  25~randomly generated  networks,  to  obtain
+experimental results  which are relevant. The  nodes are deployed on  a field of
+interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
+high coverage ratio.
+
+We chose as energy consumption model the one proposed proposed by~\cite{ChinhVu}
+and based on ~\cite{raghunathan2002energy} with slight modifications. The energy
+consumed by  the communications  is added  and the part  relative to  a variable
+sensing range is removed. We also assume that the nodes have the characteristics
+of  the Medusa II  sensor node  platform \cite{raghunathan2002energy}.  A sensor
+node typically  consists of  four units: a  MicroController Unit, an  Atmels AVR
+ATmega103L in  case of Medusa II,  to perform the  computations; a communication
+(adio) unit able to send and receive messages; a sensing unit to collect data; a
+power supply which provides the energy consumed by node. Except the battery, all
+the other  unit can  be be  switched off to  save energy  according to  the node
+status.  Table~\ref{table4} summarizes  the  energy consumed  (in milliWatt  per
+second) by a node for each of its possible status.

 
 \begin{table}[ht]
 
 \begin{table}[ht]

-\caption{The Energy Consumption Model}
+\caption{Energy consumption model}

 % title of Table
 \centering
 % used for centering table
 % title of Table
 \centering
 % used for centering table

+{\scriptsize

 \begin{tabular}{|c|c|c|c|c|}
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines
 \begin{tabular}{|c|c|c|c|c|}
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines

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

 \hline
 % inserts single horizontal line
 Listening & ON & ON & ON & 20.05 \\
 \hline
 % inserts single horizontal line
 Listening & ON & ON & ON & 20.05 \\


@@ -607,22 +637,36 @@ Computation & ON & ON & ON & 26.83 \\
 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
  \hline
 \end{tabular}
 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
  \hline
 \end{tabular}

+}

 
 \label{table4}
 % is used to refer this table in the text
 \end{table}
 
 
 \label{table4}
 % is used to refer this table in the text
 \end{table}
 

-For the sake of simplicity we ignore the energy needed to turn on the
-radio, to start up the sensor node, the transition 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 turn its radio off to save battery. DiLCO protocol uses two types of packets for communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24 bits respectively. 
-The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets.
-The energy needed to send or receive a 1-bit is equal to $0.2575 mW$.
+% MICHEL - TO BE CONTINUED

 
 

-The initial energy of each node is randomly set in the interval $[500-700]$.  Each  sensor  node will  not participate in the next round if its remaining energy is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mW) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.\\ 
-
-
-In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach: 
+For the sake of simplicity we ignore  the energy needed to turn on the radio, to
+start up the sensor node, the transition 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
+turn its radio off to save battery. DiLCO protocol uses two types of packets for
+communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24
+bits respectively.  The value of energy spent to send a 1-bit-content message is
+obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the
+energy  cost  for  transmitting messages  and  we  propose  the same  value  for
+receiving the packets.  The energy needed to send or receive a 1-bit is equal to
+$0.2575 mW$.
+
+The initial  energy of each  node is randomly  set in the  interval $[500-700]$.
+Each sensor node will not participate  in the next round if its remaining energy
+is less than $E_{th}=36 Joules$, the  minimum energy needed for the node to stay
+alive during one  round. This value has been computed  by multiplying the energy
+consumed in  active state (9.72 mW)  by the time  in second for one  round (3600
+seconds). According  to the interval  of initial energy,  a sensor may  be alive
+during at most 20 rounds.\\
+
+In the simulations,  we introduce the following performance  metrics to evaluate
+the efficiency of our approach:

 
 %\begin{enumerate}[i)]
 \begin{itemize}
 
 %\begin{enumerate}[i)]
 \begin{itemize}


@@ -701,6 +745,12 @@ disconnected (some nodes are dead and are not able to send information to the ba
 %\subsection{Performance Analysis for differnet subregions}
 \subsection{Performance Analysis}
 \label{sub1}
 %\subsection{Performance Analysis for differnet subregions}
 \subsection{Performance Analysis}
 \label{sub1}

+
+We first concentrate  on the required number of  subregions making effective our
+protocol.  Thus our  DiLCO protocol  is  declined into  five versions:  DiLCO-2,
+DiLCO-4, DiLCO-8, DiLCO-16,  and DiLCO-32, corresponding to $2$,  $4$, $8$, $16$
+or $32$ subregions (leaders).
+

 In this subsection, we study the performance of our DiLCO protocol for  different number of subregions (Leaders).
 The DiLCO-1 protocol is a centralized approach on all the area of the interest, while  DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLC0-1 protocol in our simulation results because it requires  high execution time to solve the integer program and thus it is too costly in term of energy.
 
 In this subsection, we study the performance of our DiLCO protocol for  different number of subregions (Leaders).
 The DiLCO-1 protocol is a centralized approach on all the area of the interest, while  DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLC0-1 protocol in our simulation results because it requires  high execution time to solve the integer program and thus it is too costly in term of energy.