X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/UIC2013.git/blobdiff_plain/856f104be1ac9636e82c13f72052ec7850f8be2b..7833340822f0dd429b4fc6a124f712684c7e2c07:/bare_conf.tex

diff --git a/bare_conf.tex b/bare_conf.tex
index 59b3d4b..72be80c 100755
--- a/bare_conf.tex
+++ b/bare_conf.tex
@@ -12,13 +12,12 @@
 
 \usepackage{float}
 \usepackage{epsfig}
-\usepackage{subfigure}
 \usepackage{calc}
  \usepackage{times,amssymb,amsmath,latexsym}
 \usepackage{graphics}
 \usepackage{graphicx}
 \usepackage{amsmath}
-\usepackage{txfonts}
+%\usepackage{txfonts}
 \usepackage{algorithmic}
 \usepackage[T1]{fontenc}
 \usepackage{tikz}
@@ -36,16 +35,15 @@
 
 \begin{document}
 
-\title{Distributed Coverage Optimization Protocol to Improve the Lifetime in Heterogeneous Energy Wireless Sensor Networks}
+\title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
 
 
 % author names and affiliations
 % use a multiple column layout for up to three different
 % affiliations
-\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon and Raphael Couturier }
-\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comte, Belfort, France \\
-Email:$\lbrace$ali.idness, karine.deschinkel, michel.salomon,raphael.couturier$\rbrace$@edu.univ-fcomte.fr 
-}
+\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raphael Couturier }
+\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comt\'e, Belfort, France \\
+Email:$\lbrace$ali.idness, karine.deschinkel, michel.salomon,raphael.couturier$\rbrace$@femto-st.fr}
 %\email{\{ali.idness, karine.deschinkel, michel.salomon, raphael.couturier\}@univ-fcomte.fr}
 %\and
 %\IEEEauthorblockN{Homer Simpson}
@@ -60,31 +58,43 @@ Email:$\lbrace$ali.idness, karine.deschinkel, michel.salomon,raphael.couturier$\
 
 
 \begin{abstract}
-%\boldmath
-One of the fundamental challenges in Wireless Sensor Networks (WSNs) is Coverage preservation and extension of network lifetime continuously and effectively during monitoring a certain geographical area.In this paper 
-a distributed coverage optimization protocol to improve the lifetime in in Heterogeneous Energy Wireless Sensor Networks is proposed. The area of interest is divided into subregions using Divide-and-conquer method and an activity scheduling for sensor nodes is planned for each subregion.Our protocol is distributed in each subregion. It divides the network lifetime into activity rounds. In each round a small
-number of active nodes is selected to ensure coverage.Each round includes four phases: INFO Exchange, Leader election, decision and sensing.Simulation results show that the proposed protocol can prolong the network
-lifetime and improve network coverage effectively.
-
-
+One of  the fundamental challenges in Wireless  Sensor Networks (WSNs)
+is  coverage   preservation, while  extending   the  network  lifetime
+continuously  and effectively  during  monitoring a  certain area  (or
+region) of interest. In this paper a coverage optimization protocol to
+improve the lifetime in  heterogeneous energy wireless sensor networks
+is proposed.   The area of  interest is first divided  into subregions
+using a  divide-and-conquer method and then scheduling  of sensor node
+activity  is  planned for  each  subregion.   The proposed  scheduling
+considers  activity  rounds during  which  a  small  number of  nodes,
+remaining  active for sensing,  is selected  to ensure  coverage. Each
+round consists  of four phases:  (i)~Information Exchange, (ii)~Leader
+Election, (iii)~Decision,  and (iv)~Sensing.  The  decision process is
+carried  out  by  a  leader  node which  solves  an  integer  program.
+Simulation  results show that  the proposed  approach can  prolong the
+network lifetime and improve the coverage performance.
 \end{abstract}
 
  %\keywords{Area Coverage, Wireless Sensor Networks, lifetime Optimization, Distributed Protocol.}
-
  
  \IEEEpeerreviewmaketitle
 
-
 \section{Introduction}
-\noindent Recent years have witnessed significant advances in wireless sensor
-networks which emerge as one of the most promising technologies for
-the 21st century~\cite{asc02}. In fact, they present huge potential in
-several domains ranging from health care applications to military
-applications. 
-A sensor network is composed of a large number of tiny sensing devices deployed in a region of interest. Each device has processing and wireless communication capabilities, which enable to sense its environment, to compute, to store information and to deliver report messages to a base station. 
+\noindent Recent years have witnessed significant advances in wireless
+communications and embedded micro-sensing MEMS technologies which have
+made  emerge wireless  ensor networks  as  one of  the most  promising
+technologies~\cite{asc02}.   In fact, they  present huge  potential in
+several  domains ranging  from  health care  applications to  military
+applications.  A sensor network is  composed of a large number of tiny
+sensing  devices deployed  in a  region of  interest. Each  device has
+processing  and wireless communication  capabilities, which  enable to
+sense its environment, to compute, to store information and to deliver
+report messages to a base station.
 %These sensor nodes run on batteries with limited capacities. To achieve a long life of the network, it is important to conserve battery power. Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
-One of the main design challenges in Wireless Sensor Networks (WSN) is to prolong the system lifetime, while achieving acceptable quality of service for applications. Indeed, sensor nodes
-have limited resources in terms of memory, energy and computational powers. 
+One of  the main design challenges  in wireless sensor  networks is to
+prolong the  network lifetime,  while achieving acceptable  quality of
+service for applications.  Indeed, sensor nodes have limited resources
+in terms of memory, energy and computational power.
 
 %\medskip
 Since sensor nodes have limited battery life and without being able to replace 
@@ -95,7 +105,7 @@ the lifetime of the network. In such a high density network, if all sensor nodes
 were to be activated at the same time, the lifetime would be reduced. Consequently, 
 future software may need to adapt appropriately to achieve acceptable quality of service for applications.  
 In this paper we concentrate on area coverage problem, with the objective of maximizing the network lifetime by using an adaptive scheduling. Area of interest is divided into subregions and an activity scheduling for sensor nodes is planned for each subregion.
-Our scheduling scheme works in period which includes a discovery phase to exchange information between sensors of the subregion, then a sensor is chosen in suitable manner to carry out a coverage strategy.  This coverage strategy involves the resolution of an integer program which provides the activation of the sensors for the $t$ next round.
+Our scheduling scheme works in round which includes a discovery phase to exchange information between sensors of the subregion, then a sensor is chosen in suitable manner to carry out a coverage strategy.  This coverage strategy involves the resolution of an integer program which provides the activation of the sensors for the next round.
 
 
 The remainder  of the paper is  organized as follows.
@@ -122,19 +132,19 @@ This section is dedicated to the various approaches proposed in the literature f
 
 The most discussed coverage problems in literature can be classified into two types \cite{} : area coverage and targets coverage. An area coverage problem is to find a minimum number of sensors to work such that each physical point in the area is monitored by at least a working sensor. Target coverage problem is to cover only a finite number of discrete points called targets. 
  Our work will concentrate on the area coverage by design and implement a strategy which efficiently select the active nodes that must maintain both sensing coverage and network connectivity and in the same time improve the lifetime of the wireless sensor network. But requiring that all physical points are covered may be too strict, specially where the sensor network is not dense. 
-Our approach represents an area covered by a sensor as a set of principle points and tries to maximize the total number of principles points that are covered in each round, while minimizing overcoverage (points covered by multiple active sensors simultaneously).\\
+Our approach represents an area covered by a sensor as a set of primary points and tries to maximize the total number of primary points that are covered in each round, while minimizing overcoverage (points covered by multiple active sensors simultaneously).\\
 {\bf Lifetime}\\
-Various definitions exist for the lifetime of a sensor network. Main definitions proposed in the literature are related to the remaining energy of the nodes \cite{} or to the percentage of coverage \cite{}. The lifetime of the network is mainly defined as the amount of time that the network can satisfy its coverage objective (the amount of time that the network can cover a given percentage of its area or targets of interest) . In our simulation we assume that the network is alive until all sensor nodes are died and we measure the coverage ratio during the process.
+Various definitions exist for the lifetime of a sensor network. Main definitions proposed in the literature are related to the remaining energy of the nodes \cite{} or to the percentage of coverage \cite{}. The lifetime of the network is mainly defined as the amount of time that the network can satisfy its coverage objective (the amount of time that the network can cover a given percentage of its area or targets of interest). In our simulation we assume that the network is alive until all nodes have been drained of their energy or the sensor network disconnected and we measure the coverage ratio during the process.
 
 {\bf Activity scheduling}\\
-Activity scheduling is to schedule the activation and deactivation of nodes 'sensor units. The basic objective is to decide which sensors are in which states (active or sleeping mode) and for how long a time such that the application coverage requirement can be guaranteed and network lifetime can be prolonged. Various approaches, including centralized, distributed and localized algorithms, have been proposed for activity scheduling.  In the distributed algorithms, each node in the network autonomously makes decisions on whether to turn on or turn off itself only using local neighbor information. In centralized algorithms, a central controller (node or base station) informs every sensor of the time intervals to be activated.
+Activity scheduling is to schedule the activation and deactivation of nodes 'sensor units. The basic objective is to decide which sensors are in which states (active or sleeping mode) and for how long a time such that the application coverage requirement can be guaranteed and network lifetime can be prolonged. Various approaches, including centralized, distributed and localized algorithms, have been proposed for activity scheduling.  In the distributed algorithms, each node in the network autonomously makes decisions on whether to turn on or turn off itself only using local neighbour information. In centralized algorithms, a central controller (node or base station) informs every sensor of the time intervals to be activated.
 
 {\bf Distributed approaches}
 
-Some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. Distributed algorithms typically operate in roundsf predetermined duration. At the beginning of each round, a sensor exchange information with its neighbors and makes a decision to either turn on or go to sleep for the round. This decision is basically based on simple greedy criteria like the largest uncovered area \cite{Berman05efficientenergy}, maximum uncovered targets \cite{1240799}. 
-In \cite{Tian02}, the sheduling scheme is divided into rounds, where each round has a self-scheduling phase followed by a sensing phase. Each sensor broadcasts  a message to its neighbors containing node ID and node location at the beginning of each round. 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 that nodes make conflicting decisions simultaneously and that a part of the area is no longer covered.
+Some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. Distributed algorithms typically operate in rounds for predetermined duration. At the beginning of each round, a sensor exchange information with its neighbors and makes a decision to either turn on or go to sleep for the round. This decision is basically based on simple greedy criteria like the largest uncovered area \cite{Berman05efficientenergy}, maximum uncovered targets \cite{1240799}. 
+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 to its neighbours containing node ID and node location at the beginning of each round. 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 neighbours. A back-off scheme is introduced to let each sensor delay the decision process with a random period of time, in order to avoid that nodes make conflicting decisions simultaneously and that a part of the area is no longer covered.
 \cite{Prasad:2007:DAL:1782174.1782218} propose a model for capturing the dependencies between different cover sets and propose localized heuristic based on this dependency. The algorithm consists of two phases, an initial setup phase during which each sensor calculates and prioritize 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. 
-Authors in \cite{chin2007} propose a novel distributed heuristic named distributed Energy-efficient Scheduling for k-coverage (DESK) so that the energy consumption among all the sensors is balanced, and network lifetime is maximized while the coverage requirements being maintained. This algorithm works in round, requires only 1-sensing-hop-neigbor information, and a sensor decides its status (active/sleep) based on its perimeter coverage computed through the k-Non-Unit-disk coverage algorithm  proposed in \cite{Huang:2003:CPW:941350.941367}.\\
+Authors in \cite{chin2007} propose a novel distributed heuristic named distributed Energy-efficient Scheduling for k-coverage (DESK) so that the energy consumption among all the sensors is balanced, and network lifetime is maximized while the coverage requirements being maintained. This algorithm works in round, requires only 1-sensing-hop-neighbour information, and a sensor decides its status (active/sleep) based on its perimeter coverage computed through the k-Non-Unit-disk coverage algorithm  proposed in \cite{Huang:2003:CPW:941350.941367}.\\
 
 Some others approaches  do not consider synchronized and predetermined period of time where the sensors are active or not. Each sensor maintains its own timer and its time wake-up is randomized \cite{Ye03} or regulated \cite{cardei05} over time. 
 %A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
@@ -147,6 +157,7 @@ Some others approaches  do not consider synchronized and predetermined period of
  %one way of increasing lifeteime is by turning off redundant nodes to sleep mode to conserve energy while active nodes provide essential coverage, which improves fault tolerance. 
 
 %In this paper we focus on centralized algorithms because distributed algorithms are outside the scope of our work. Note that centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Moreover, a recent study conducted in \cite{pc10} concludes that there is a threshold in terms of network size to switch from a localized to a centralized algorithm. Indeed the exchange of messages in large networks may consume  a considerable amount of energy in a localized approach compared to a centralized one. 
+
 {\bf Centralized approaches}\\
 Power efficient centralized schemes differ according to several criteria \cite{Cardei:2006:ECP:1646656.1646898}, such as the coverage objective (target coverage or area coverage), the node deployment method (random or deterministic) and the heterogeneity of sensor nodes (common sensing range, common battery lifetime). 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. 
 
@@ -189,16 +200,18 @@ There are three main questions which should be answered  to build a scheduling s
 \begin{itemize}
 \item {\bf How must be planned the 
 phases for information exchange, decision and sensing over time?}
-Our algorithm partitions the time line into a number of periods. Each period contains 4 phases : information Exchange, Leader Election, Decision, and Sensing. Our work further divides sensing phase into a number of rounds of predetermined length.
+Our algorithm partitions the time line into a number of rounds. Each round contains 4 phases : information Exchange, Leader Election, Decision, and Sensing. 
+
 \item {\bf What are the rules to decide which node has to turn on or off?}
-Our algorithm tends to limit the overcoverage of points of interest to avoid turning on too much sensors covering the same areas at the same time, and tries to prevent undercoverage. The decision is a good compromise between these two conflicting objectives and is made for the next $T$ rounds of sensing. In our experimentations we will check which value of $T$ is the most appropriate.
+Our algorithm tends to limit the overcoverage of points of interest to avoid turning on too much sensors covering the same areas at the same time, and tries to prevent undercoverage. The decision is a good compromise between these two conflicting objectives. 
+
 \item {\bf Which node should make such decision ?}
 As mentioned in \cite{pc10}, both centralized and distributed algorithms have their own advantages and disadvantages. Centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Distributed algorithms are very adaptable to the dynamic and scalable nature of sensors network. Authors in \cite{pc10} concludes that there is a threshold in terms of network size to switch from a localized to a centralized algorithm. Indeed the exchange of messages in large networks may consume  a considerable amount of energy in a localized approach compared to a centralized one. Our work does not consider only one leader to compute and to broadcast the schedule decision to all the sensors. When the size of network increases, the network is divided in many subregions and the decision is made by a leader in each subregion.
 \end{itemize}
 
 
 
- \section{\uppercase{Distributed coverage model}}
+ \section{\uppercase{Activity scheduling}}
 \label{pd}
 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 full coverage of the interested area. We assume that all nodes are homogeneous in terms of  communication and processing capabilities and heterogeneous in term of energy.  The location information is available to the sensor node either through hardware such as embedded GPS or through location discovery algorithms.
 The area of interest can be divided using the divide-and-conquer strategy into smaller area called subregions and then our coverage protocol will be implemented in each subregion simultaneously. Our protocol works in rounds fashion as in figure \ref{fig:4}. 
@@ -211,13 +224,11 @@ The area of interest can be divided using the divide-and-conquer strategy into s
 \label{fig:4}
 \end{figure} 
 
-Each round is divided into 4 phases : INFO Exchange, Leader Election, Decision, and Sensing. For each round there is exactly one set cover responsible for sensing task. This protocol is more reliable against the  unexpectedly node failure because it works into rounds,and if the node failure detected before taking the decision, the node will not participate in decision and if the the node failure obtain after the decision   the sensing task of the network will be affected temporarily only during the period of sensing until starting new round, since a new set cover will take charge of the sensing task in the next round. The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange the information (including their residual energy) at the beginning of each round. However, the preprocessing phase (INFO Exchange, leader Election, Decision) are energy consuming for some nodes even when they not join the network to monitor the area. We describe each phase in more detail.
+Each round is divided into 4 phases : Information (INFO) Exchange, Leader Election, Decision, and Sensing. For each round there is exactly one set cover responsible for sensing task. This protocol is more reliable against the  unexpectedly node failure because it works into rounds, and if the node failure is detected before taking the decision, the node will not participate in decision and if the node failure occurs after the decision, the sensing task of the network will be affected temporarily only during the period of sensing until starting new round, since a new set cover will take charge of the sensing task in the next round. The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange the information (including their residual energy) at the beginning of each round. However, the preprocessing phase (INFO Exchange, leader Election, Decision) are energy consuming for some nodes even when they not join the network to monitor the area. We describe each phase in more detail.
 
 \subsection{\textbf INFO Exchange Phase}
 
-Each sensor node $j$  sends its position, remaining energy $RE_j$, number of local neighbours $NBR_j$  to all wireless sensor nodes in its subregion by using INFO packet and listen to the packets sent from other nodes. After that, each node will have information about all the sensor nodes in the subregion. In our model.
-
-% the remaining energy corresponds to the time that a sensor can live in the active mode.
+Each sensor node $j$  sends its position, remaining energy $RE_j$, number of local neighbours $NBR_j$  to all wireless sensor nodes in its subregion by using INFO packet and listen to the packets sent from other nodes. After that, each node will have information about all the sensor nodes in the subregion. In our model, the remaining energy corresponds to the time that a sensor can live in the active mode.
 
 
 %\subsection{\textbf Working Phase:}
@@ -226,19 +237,16 @@ Each sensor node $j$  sends its position, remaining energy $RE_j$, number of loc
 
 \subsection{\textbf Leader Election Phase}
 This step includes choosing the Wireless Sensor Node Leader (WSNL) which will be responsible of executing coverage algorithm  to choose the list of active sensor nodes that contribute in covering the subregion.
-% The sensors in the same region are capable to communicate with each others using a routing protocol provided by the simulator OMNET++ in order to provide multi-hop communication protocol.
-The WSNL will be chosen based on the number of local neighbours $NBR_j$  of sensor node $s_j$ and it's remaining energy $RE_j$.
-If we have more than one node has the same $NBR_j$ and $RE_j$, this leads to choose WSNL based on the largest index among them. Each subregion in the area of interest will select its WSNL independently for each round. 
-
+All the sensor nodes cooperates to select WSNL. After the phase of information exchange , each sensor have all information about the other nodes in the same subregion, after that each node will execute the leader election procedure to determine who is the leader?(each node will know who is the leader) where all the nodes in the same subregion will select the same leader based on the received information from all other nodes in the same subregion.The leader will be selected as follow: It will select the node that have maximum number of neighbour  as a leader.If there are more than one node have the same maximum number of neighbours , it will take all these nodes and then select the node that have larger remaining energy. If there are more than one node have the same maximum number of neighbours and the same remaining energy then it will select the node  with larger index among them. Each subregion in the area of interest will select its own WSNL independently for each round. 
 
 \subsection{\textbf Decision Phase}
-The WSNL will execute the GLPK algorithm to select which sensors will be activated in the next rounds to cover the subregion. WSNL will send Active-Sleep packet to each sensor in the subregion based on algorithm's results. 
+The WSNL will solve an integer program (see section \ref{cp}) to select which sensors will be activated in the next round to cover the subregion. WSNL will send Active-Sleep packet to each sensor in the subregion based on algorithm's results. 
 %The main goal in this step after choosing the WSNL is to produce the best representative active nodes set that will take the responsibility of covering the whole region $A^k$ with minimum number of sensor nodes to prolong the lifetime in the wireless sensor network. For our problem, in each round we need to select the minimum set of sensor nodes to improve the lifetime of the network and in the same time taking into account covering the region $A^k$ . We need an optimal solution with tradeoff between our two conflicting objectives.
 %The above region coverage problem can be formulated as a Multi-objective optimization problem and we can use the Binary Particle Swarm Optimization technique to solve it. 
 \\
 
 \subsection{\textbf Sensing Phase}
- 	The algorithm will produce the best representative set of the active nodes that will take the mission of coverage preservation in the subregion during the Sensing phase. Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake (or sleep) for sensing task is the same for all wireless sensor nodes in the network.  
+ 	Active sensors in the round will execute their sensing task to preserve maximal coverage  in the region of interest. We will assume that the cost of keeping a node awake (or sleep) for sensing task is the same for all wireless sensor nodes in the network. Each sensor received Active-Sleep packet will go to awake or sleep for a time equal to the period of sensing until starting new round.  
 
 
 
@@ -247,7 +255,7 @@ The WSNL will execute the GLPK algorithm to select which sensors will be activat
 
 %\noindent We try to produce an adaptive scheduling which allows sensors to operate alternatively so as to prolong the network lifetime. For convenience, the notations and assumptions are described first.
 %The wireless sensor node use the  binary disk sensing model by which each sensor node will has a certain sensing range is reserved within a circular disk called radius $R_s$.
-\noindent 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 is at least twice of the sening range. In fact, Zhang and Zhou ~\cite{Zhang05} prove that if the tranmission range is at least twice of the sensing range, a complete coverage of a convex area implies connectivity amnong the working nodes in the active mode.
+\noindent 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 is at least twice of the sensing range. In fact, Zhang and Zhou ~\cite{Zhang05} prove that if the transmission range is at least twice of the sensing range, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
 %To calculate the coverage ratio for the area of interest, we can propose the following coverage model which is called Wireless Sensor Node Area Coverage Model to ensure that all the area within each node sensing range are covered. We can calculate the positions of the points in the circle disc of the sensing range of wireless sensor node based on the Unit Circle in figure~\ref{fig:cluster1}:
 
 %\begin{figure}[h!]
@@ -261,10 +269,10 @@ The WSNL will execute the GLPK algorithm to select which sensors will be activat
 %\end{figure}
 
 %By using the Unit Circle in figure~\ref{fig:cluster1}, 
-%We choose to representEach wireless sensor node will be represented into a selected number of principle points by which we can know if the sensor node is covered or not.
-% Figure ~\ref{fig:cluster2} shows the selected principle points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
+%We choose to representEach wireless sensor node will be represented into a selected number of primary points by which we can know if the sensor node is covered or not.
+% Figure ~\ref{fig:cluster2} shows the selected primary points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
 
-\noindent Instead of working with area coverage, we consider for each sensor a set of points called principal points. And we assume the sensing disk defined by a sensor is covered  if all principal points of this sensor are covered.
+\noindent Instead of working with area coverage, we consider for each sensor a set of points called primary points. And we assume the sensing disk defined by a sensor is covered  if all primary points of this sensor are covered.
 
 %\begin{figure}[h!]
 %\centering
@@ -278,7 +286,7 @@ The WSNL will execute the GLPK algorithm to select which sensors will be activat
 
 
 
-\noindent By knowing the position (point center :($p_x,p_y$) of the Wireless sensor node and its $R_s$ , we calculate the principle points directly based on proposed model. We use these principle points (that can be increased or decreased as if it is necessary) as references to ensure that the monitoring area of the region is covered by the selected set of sensors instead of using the all points in the area.
+\noindent By knowing the position (point center :($p_x,p_y$) of the wireless sensor node and its $R_s$ , we calculate the primary points directly based on proposed model. We use these primary points (that can be increased or decreased as if it is necessary) as references to ensure that the monitoring area of the region is covered by the selected set of sensors instead of using the all points in the area.
 
  \begin{figure}[h!]
 %\centering
@@ -291,11 +299,11 @@ The WSNL will execute the GLPK algorithm to select which sensors will be activat
 %\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
 %\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
 %\end{multicols} 
-\caption{Wireless Sensor node represented by 13 principle points }
+\caption{Wireless Sensor node represented by 13 primary points }
 \label{fig3}
 \end{figure}
 
-\noindent We can calculate the positions of the selected principle points in the circle disk of the sensing range of wireless sensor node in figure ~\ref{fig3} as follow:\\
+\noindent We can calculate the positions of the selected primary points in the circle disk of the sensing range of wireless sensor node in figure ~\ref{fig3} as follow:\\
 $p_x,p_y$ = point center of wireless sensor node. \\  
 $X_1=(p_x,p_y)$ \\ 
 $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\           
@@ -322,47 +330,46 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
 %To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$  that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
 
 
-\noindent 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 propose a integer program  which forces undercoverage and overcoverage of targets to become minimal at the same time. They use variables $x_{s,l}$ to indicate if the sensor $s$ belongs to cover set $l$. In our model, we consider binary variables $X_{j,t}$ which determine the activation of sensor $j$ in round $t$. We replace the constraint guarantying that each sensor is a member of only one cover of the entire set of disjoint covers by a constraint specifying that the sum of energy consumed by the activation of sensor during several rounds is less than or equal to the remaining energy of the sensor. We also consider principle points as targets.  \\
-\noindent For a principle point $p$, let $\alpha_{jp}$ denote the indicator function of whether the point $p$ is covered, that is, \\
+\noindent 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 propose a integer program  which forces undercoverage and overcoverage of targets to become minimal at the same time. They use binary variables $x_{s,l}$ to indicate if the sensor $s$ belongs to cover set $l$.  In our model, we consider binary variables $X_{j}$ which determine the activation of sensor $j$ in the 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, \\
 \begin{equation}
 \alpha_{jp} = \left \{ 
 \begin{array}{l l}
-  1 & \mbox{if the principal point $p$ is covered} \\
+  1 & \mbox{if the primary point $p$ is covered} \\
  & \mbox{by active sensor node $j$} \\
   0 & \mbox{Otherwise}\\
 \end{array} \right.
 %\label{eq12} 
 \end{equation}
-The number of sensors that are covering point $p$ during a round $t$ is equal to $\sum_{j \in J} \alpha_{jp} * X_{j,t}$ where :
+The number of sensors that are covering point $p$ is equal to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where :
 \begin{equation}
-X_{j,t} = \left \{ 
+X_{j} = \left \{ 
 \begin{array}{l l}
-  1& \mbox{if sensor $s_j$  is active during round } t\\
-  0 &  \mbox{Otherwise}\\
+  1& \mbox{if sensor $j$  is active} \\
+  0 &  \mbox{otherwise}\\
 \end{array} \right.
 %\label{eq11} 
 \end{equation}
-We define the Overcoverage variable $\Theta_{p,t}$ .\\
+We define the Overcoverage variable $\Theta_{p}$ .\\
 
 \begin{equation}
- \Theta_{p,t} = \left \{ 
+ \Theta_{p} = \left \{ 
 \begin{array}{l l}
-  0            & \mbox{if point p is not }\\
-&\mbox{covered during round } t\\
-  \left( \sum_{j \in J} \alpha_{jp} * X_{j,t} \right)- 1 & \mbox{Otherwise}\\
+  0            & \mbox{if point p is not covered}\\
+  \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise}\\
 \end{array} \right.
 \label{eq13} 
 \end{equation}
 
 
-\noindent$\Theta_{p}$ represents the number of active sensor nodes minus one that cover the principle point $p$.\\
-The Undercoverage variable $U_{p,t}$ of the principle point $p$ is defined as follow :\\
+\noindent$\Theta_{p}$ represents the number of active sensor nodes minus one that cover the primary point $p$.\\
+The Undercoverage variable $U_{p}$ of the primary point $p$ is defined as follow :\\
 
 \begin{equation}
-U_{p,t} = \left \{ 
+U_{p} = \left \{ 
 \begin{array}{l l}
-  1 &\mbox{if point } $p$ \mbox{ is not covered during round } $t$\\
-  0 & \mbox{Otherwise}\\
+  1 &\mbox{if point } $p$ \mbox{ is not covered} \\
+  0 & \mbox{otherwise}\\
 \end{array} \right.
 \label{eq14} 
 \end{equation}
@@ -371,27 +378,27 @@ U_{p,t} = \left \{
 \begin{equation} \label{eq:ip2r}
 \left \{
 \begin{array}{ll}
-\min \sum_{p \in P} (w_{\theta,t} \Theta_{p,t} + w_{u,t} U_{p,t})&\\
+\min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
 \textrm{subject to :}&\\
-\sum_{j \in J}  \alpha_{jp} X_{j,t} - \Theta_{p,t}+ U_{p,t} =1, &\forall p \in P, \forall t \in T\\
+\sum_{j \in J}  \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
 %\label{c1} 
-\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
+%\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
 %\label{c2}
-\Theta_{p,t}\in \mathbb{N} , &\forall p \in P, \forall t \in T\\
-U_{p,t} \in \{0,1\}, &\forall p \in P, \forall t \in T \\
-X_{j,t} \in \{0,1\}, &\forall j \in J, \forall t \in T
+\Theta_{p}\in \mathbb{N} , &\forall p \in P\\
+U_{p} \in \{0,1\}, &\forall p \in P \\
+X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}
 \right.
 \end{equation}
 \begin{itemize}
-\item $X_{j,t}$ : indicating whether or not sensor $j$ is active in round $t$(1 if yes and 0 if not)
-\item $\Theta_{p,t}$ : {\it overcoverage}, the number of sensors minus one that are covering point $p$ in round $t$
-\item $U_{p,t}$ : {\it undercoverage}, indicating whether or not point $p$ is being covered (1 if not covered and 0 if covered) in round $t$
+\item $X_{j}$ : indicating whether or not sensor $j$ is active in the round (1 if yes and 0 if not)
+\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that are covering point $p$
+\item $U_{p}$ : {\it undercoverage}, indicating whether or not point $p$ is being covered (1 if not covered and 0 if covered) 
 \end{itemize}
-The first group of constraints indicates that some point $p$ should be covered by at least one sensor in every round $t$ and, if it is not always the case, overcoverage and undercoverage variables help balance the restriction equation by taking positive values. Second group of contraints ensures for each sensor that the amount of energy consumed during its activation periods will be less than or equal to its remaining energy.
-There are two main objectives. We limit overcoverage of principle points in order to activate a minimum number of sensors and we prevent that parts of the subregion are not monitored by minimizing undercoverage. The weights $w_{\theta,t}$ and $w_{u,t}$ must be properly chosen so as to guarantee that the maximum number of points are covered during each round. 
+The first group of constraints indicates that some point $p$ should be covered by at least one sensor and, if it is not always the case, overcoverage and undercoverage variables help balance the restriction equation by taking positive values. Second group of contraints ensures for each sensor that the amount of energy consumed during its activation periods will be less than or equal to its remaining energy.
+There are two main objectives. We limit overcoverage of primary points in order to activate a minimum number of sensors and we prevent that parts of the subregion are not monitored by minimizing 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 equation \eqref{eq15}, there are two main objectives: the first one using  the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the  Undercoverage parameter  to maximize the coverage in the region by means of covering each principle point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each principle point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
+%In equation \eqref{eq15}, there are two main objectives: the first one using  the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the  Undercoverage parameter  to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
 %at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.
 %\subsection{Notations and assumptions}
 
@@ -418,59 +425,190 @@ There are two main objectives. We limit overcoverage of principle points in orde
 \section{\uppercase{Simulation Results}}
 \label{exp}
 In this section, we conducted a series of simulations to evaluate the efficiency of our approach
-based on the discrete event simulator OMNeT++ (http://www.omnetpp.org/).we conduct simulations for six
-different densities varying from 50 to 300 nodes. Experimental results were obtained from randomly generated
-networks in which nodes are deployed over a $ 50\times25(m2) $sensing field. For each network deployment, we
-assume that the deployed nodes can fully cover the sensing field with the given sensing range. 100 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 100 runs.Simulation ends when there is at least one active node has no connectivity with the network.Our proposed coverage protocol use the Radio energy dissipation model that defined by~\cite{HeinzelmanCB02} as energy consumption model by each wireless sensor node for transmitting and receiving the packets in the network.The energy of each node in the network is initialized randomly within the range 24-60 joules, and each sensor will consumes 0.2 watts during the period of sensing which it is 60 seconds.Each active node will consumes 12 joules during sensing phase and each sleep node will consumes 0.002 joules.Each sensor node will not participate in the next round if it's remaining energy less than 12 joules. In all experiments the parameters are given by $R_s = 5m $ , $ W_{\Theta} =1$ and $W_{\Psi} = P^2$.
-We evaluate the efficiency of our approach using some performance metrics such as:coverage ratio, number of
-active nodes ratio, energy saving ratio, number of rounds, network lifetime and execution time of our approach.Coverage ratio measures how much area of a sensor field is covered. In our case, the coverage ratio is regarded as the number of principle points covered among the set of all principle points within the field.In our simulation the sensing field is sub divided into two subregions each one equal to $ 25\times25(m2)  $ of the sensing field.
+based on the discrete event simulator OMNeT++ (http://www.omnetpp.org/). We conduct simulations for five
+different densities varying from 50 to 250 nodes. Experimental results were obtained from randomly generated
+networks in which nodes are deployed over a $ 50\times25(m^2) $sensing field. For each network deployment, we
+assume that the deployed nodes can fully cover the sensing field with the given sensing range. 10 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 10 runs. Simulation ends when there all the nodes are dead or the sensor network becomes disconnected (some nodes may not be able to sent to a base station an event they sense) . Our proposed coverage protocol use the Radio energy dissipation model that defined by~\cite{HeinzelmanCB02} as energy consumption model by each wireless sensor node for transmitting and receiving the packets in the network. The energy of each node in the network is initialized randomly within the range 24-60 joules, and each sensor will consumes 0.2 watts during the sensing period  of 60 seconds. Each active node will consumes 12 joules during sensing phase and each sleep node will consume 0.002 joules. Each sensor node will not participate in the next round if it's remaining energy less than 12 joules. In all experiments the parameters are given by $R_s = 5m $ , $ w_{\Theta} =1$ and $w_{U} = |P^2|$.
+We evaluate the efficiency of our approach using some performance metrics such as : coverage ratio, number of
+active nodes ratio, energy saving ratio, Energy Consumption,network lifetime, execution time and the number of stopped simulation runs.
+Our approach is called Strategy (with Two Leaders) will be compared with two approaches: The first one called Strategy (with One Leader) that use the same our approach method but it implemented in $ 50\times25(m^2) $sensing field with one leader. The second method called Simple Heuristic which consists in dividing uniformly the region into squares $(5 * 5)m^2$ . During the  pre-sensing phase, in each square, a sensor is  chosen randomly,  and will be turned on for the next round.
+In our simulation the sensing field is subdivided into two subregions each one equal to $ 25\times25)m^2 $ of the sensing field.
 
 \subsection{The impact of the Number of Rounds on Coverage Ratio:} 
-In this experiment, we study the impact of the number of rounds on the coverage ratio and for different sizes for sensor network.For each Sensor network size we will take the average of coverage ratio per round and for 100 simulation.Fig. 3 show the impact of the number of rounds on coverage ratio for different network sizes and for two subregions.
+In this experiment,the Coverage ratio measures how much area of a sensor field is covered. In our case, the coverage ratio is regarded as the number of primary points covered among the set of all primary points within the field. Fig. \ref{fig3} shows the impact of the number of rounds on the average coverage ratio for 150 deployed nodes for the three approaches.
+The comparison shows that the Strategy (with One Leader) gives the same or better than the Strategy (with Two Leaders) for rounds from 1 to 14. after that the Strategy (with One Leader) will suffer from the sensor network becomes disconnected more than Strategy (with Two Leaders) leads to give the advantage for Strategy (with Two Leaders) that will give better coverage and more network lifetime for the rest last rounds because the Strategy (with Two Leaders) subdivide the region into 2 subregions and if on of the two subregion becomes disconnected, it not leads to stop the the responsibility of coverage optimization in the other subregion.
+\parskip 0pt 
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.5]{TheCoverageRatio150.pdf} %\\~ ~ ~(a)
 
- \begin{figure}[h!]
+\caption{The impact of the Number of Rounds on Coverage Ratio for 150 deployed nodes }
+\label{fig3}
+\end{figure} 
+
+\begin{figure}[h!]
 %\centering
 % \begin{multicols}{6}
 \centering
 %\includegraphics[scale=0.10]{fig21.pdf}\\~ ~ ~(a)
 %\includegraphics[scale=0.10]{fig22.pdf}\\~ ~ ~(b)
-\includegraphics[scale=0.5]{CR2R2L_1.eps}\\~ ~ ~(a)
-\includegraphics[scale=0.5]{CR2R2L_2.eps}\\~ ~ ~(b)
+\includegraphics[scale=0.5]{TheCoverageRatio250.pdf} %\\~ ~ ~(a)
+%\includegraphics[scale=0.5]{CR2R2L_2.eps} %\\~ ~ ~(b)
 %\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
 %\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
 %\end{multicols} 
-\caption{The impact of the Number of Rounds on Coverage Ratio.(a):subregion 1. (b): subregion 2 }
-\label{fig3}
+\caption{The impact of the Number of Rounds on Coverage Ratio for 250 deployed nodes }
+\label{fig4}
+\end{figure}
+
+Fig. \ref{fig4} represents the average coverage ratio provided by
+Strategy (with Two Leaders),Strategy (with One Leader) and Simple Heuristic for 250 deployed nodes while
+varying the number of rounds. We made the same observation as in Fig. \ref{fig3}, i.e.  Strategy (with One Leader) guarantee a good coverage in the beginning the same or equal to Strategy (with Two Leaders) then when the number of rounds increases, the coverage ratio decreases due to network becomes disconnected. Meanwhile,the Strategy (with Two Leaders) ensures better coverage despite the variation in rounds number.\\
+\parskip 0pt 
+As shown in Fig. \ref{fig3} and Fig. \ref{fig4},the Strategy (with Two Leaders) gives a full average coverage ratio or more than 90\% in the first rounds and then it decreases when the number of rounds increases due to dead nodes.Although some nodes are dead, sensor activity scheduling in each subregion choose other nodes to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the full coverage for larger number of rounds.\\
+
+\subsection{The impact of the Number of Rounds on Active Sensor Ratio:} 
+It is important to have as few active nodes as possible in each round in order to minimize the communication
+overhead and maximize the network lifetime. The Active Sensor Ratio(\%) = ((the no. of active sensor during this round) /  (Total number of sensors in the network for the subregion)) * 100. Fig. \ref{fig5} and \ref{fig6} shows the average number of active nodes ratio versus rounds for 150 and 250 deployed nodes respectively.
+
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.5]{TheActiveSensorRatio150.pdf} %\\~ ~ ~(a)
+\caption{The impact of the Number of Rounds on Active Sensor Ratio for 150 deployed nodes }
+\label{fig5}
+\end{figure} 
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.46]{TheActiveSensorRatio250.pdf} %\\~ ~ ~(a)
+\caption{The impact of the Number of Rounds on Active Sensor Ratio for 250 deployed nodes }
+\label{fig6}
 \end{figure} 
 
-As shown Fig. 3 (a) and (b) our protocol can give a full average coverage ratio in the first rounds and then it decreases when the number of rounds increases due to dead nodes.Although some nodes are dead, sensor activity scheduling choose other nodes to ensure the coverage of interest area. Moreover, when we have a dense sensor network, it leads to maintain the full coverage for larger number of rounds.
+The results in Fig. \ref{fig5} shows the superior of the Strategy (with Two Leaders) and the Strategy (with One Leader) on Simple Heuristic. The Strategy (with One Leader) uses minimum number of active nodes than the Strategy (with Two Leaders) until the last rounds because it uses central control on all the sensing field , the advantage of the Strategy (with Two Leaders) approach is that even if a network is disconnected in a one subregion the other one usually continues the optimization and this leads to extend the lifetime of the network.
+In Fig. \ref{fig6}, we see the same observation that we saw on fig. \ref{fig5} but in the last rounds the Strategy (with Two Leaders) will be the better because the effect of disconnected network increases and it becomes near or equal to the Strategy (with One Leader) leads to give minimum average of active nodes.
 
 \subsection{The impact of the Number of Rounds on Energy Saving Ratio:} 
 
-\subsection{The impact of the Number of Rounds on Active Sensor Ratio:} 
+In this experiment, the Energy saving ratio ESR(\%) =( (No. of alive sensors in the network during this round) / (total number  of sensors in the network for the subregion)) * 100. Fig. \ref{fig5} and \ref{fig6} shows the average number of active nodes ratio versus rounds for all three approach and for 150 and 250 deployed nodes respectively.
+
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.5]{TheEnergySavingRatio150.pdf} %\\~ ~ ~(a)
+\caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes }
+\label{fig5}
+\end{figure} 
 
-\subsection{The impact of Number of Sensors on Number of Rounds:} 
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.46]{TheEnergySavingRatio250.pdf} %\\~ ~ ~(a)
+\caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes }
+\label{fig6}
+\end{figure} 
+
+Simulation results explain the efficiency of the Strategy (with Two Leaders) to save the energy during larger number of rounds that seems to be very near the central approach (Strategy (with One Leader))which it be better in general.
 
-\subsection{The impact of Number of Sensors on Network Lifetime:} 
+\subsection{The Network Lifetime:} 
+we can define the network lifetime as the time until all nodes have been drained of their energy or the sensor network disconnected. In Fig. \ref{fig7}, the network lifetime for different network sizes and for the three approaches is illustrated. 
+
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.46]{TheNetworkLifetime.pdf} %\\~ ~ ~(a)
+\caption{The Network Lifetime }
+\label{fig7}
+\end{figure} 
+
+As shown in fig. \ref{fig7}, the network lifetime increase when the size of the network increase because the efficient of our approach in choosing the best representative nodes that will cover all the subregion and let the others nodes to sleep to be used later in the next rounds. Comparison shows that our approach is better than the other two methods in improving the network lifetime and this shows us by distributing the algorithm in each node in the network and subdivide the sensing field into many subregions to be managed independently and simultaneously can be more powerful against the sensor network disconnected in some subregions leads to maximize the lifetime of the network obviously.
+
+\subsection{The Energy Consumption:} 
+In this experiment, we study the effect of the multi-hop communication protocol on the performance of our approach and compare it with other two approaches. The average energy consumption calculated based only on the energy consumed by transmitting and receiving packets by all sensor nodes in the network and during the lifetime of the network for 10 simulation runs divided by the average number of rounds and for different sizes of the network.We took the total energy consumption in both subregions for Strategy (with Two Leaders) and Simple heuristic. Fig. \ref{fig8} illustrates the Energy Consumption for different network sizes and for the three approaches. 
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.46]{TheEnergyConsumption.pdf} 
+\caption{The Energy Consumption  }
+\label{fig8}
+\end{figure} 
+
+The results show that our approach consume less energy during the lifetime of the network by using multi-hop communication protocol in comparison with other two approaches especially Strategy (with One Leader) in spite of our approach make the network live for a longer time.
 
 \subsection{The impact of Number of Sensors on Execution Time:}
+It is important to have time efficient algorithm to be executed in sensor node because the limited resources in the sensor node. We took the total Execution Time of algorithms in both subregions for Strategy (with Two Leaders) and Simple heuristic. Table \ref{table1} exhibits the execution time for three approaches using different number of sensors.
 
-\subsection{Performance Comparison:}
-\label{Simulation Results}
+\begin{table}[ht]
+\caption{The Execution Time(s) vs The Number of Sensors }
+% title of Table
+\centering
+
+% used for centering table
+\begin{tabular}{|c| c| c| c |}
+% centered columns (4 columns)
+\hline\hline
+%inserts double horizontal lines
+Sensors Number & Strategy & Strategy  & Simple Heuristic \\ [0.5ex]
+ & (with Two Leaders) & (with One Leader)  \\ [0.5ex]
+%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
+% inserts table
+%heading
+\hline
+% inserts single horizontal line
+50 & 0.097 & 0.189 & 0.001 \\
+% inserting body of the table
+\hline
+100 & 0.419 & 1.972 & 0.0032 \\
+\hline
+150 & 1.295 & 13.098 & 0.0032 \\
+\hline
+200 & 4.54 & 169.469 & 0.0046 \\
+\hline
+250 & 12.252 & 1581.163 & 0.0056 \\ [1ex]   
+
+% [1ex] adds vertical space
+\hline
+%inserts single line
+\end{tabular}
+\label{table1}
+% is used to refer this table in the text
+\end{table}
+
+Table  \ref{table1} shows the efficiency of our algorithm to produce the solution with good execution time though the Simple Heuristic gives the solution in less time but our approach ensure a better coverage for the region with energy saving and less energy consumption led to extend the lifetime of the network.
+
+\subsection{The Number of Stopped Simulation Runs :}
+In this study, we will shows the number of stopped simulation runs (the disconnected network) per round for 150 and 250 deployed nodes and for three approaches. Fig. \ref{fig9} and \ref{fig10} illustrate the number of stopped simulation runs per round for 150 and 250 deployed nodes respectively.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.50]{TheNumberofStoppedSimulationRuns150.pdf} 
+\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
+\label{fig9}
+\end{figure} 
 
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.50]{TheNumberofStoppedSimulationRuns250.pdf} 
+\caption{The Number of Stopped Simulation Runs against Rounds for 250 deployed nodes }
+\label{fig10}
+\end{figure} 
 
-\section{\uppercase{Conclusions}}
-\label{sec:conclusion}
-In this paper, we have addressed the problem of lifetime optimization in wireless sensor networks. This is a very 
-natural and important problem, as sensor nodes
-have limited resources in terms of memory, energy and computational power.
-%energy-efficiency is crucial in power-limited wireless sensor network. 
-To cope with this problem, 
-%an efficient centralized energy-aware algorithm is presented and analyzed. Our algorithm seeks to 
-%Energy-efficiency is crucial in power-limited wireless sensor network, since sensors have significant power constraints (battery life). In this paper we have investigated the problem of 
+The results explain the powerful of our approach against the Stopped Simulation Runs in comparison with other two approaches especially in the last rounds from the network lifetime and this will participate in extending the life time of the network.
 
+\label{Simulation Results}
 
 
+\section{\uppercase{Conclusions and Future Works}}
+\label{sec:conclusion}
+In this paper, we have addressed the problem of lifetime optimization in wireless sensor networks. This is a very natural and important problem, as sensor nodes have limited resources in terms of memory, energy and computational power. To cope with this problem, The field of sensing divided into smaller subregion using the concept of divide-and-conquer method and then multi-rounds coverage protocol will optimize the lifetime in each subregion.The suggested protocol joins 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 representative active nodes that will optimize the lifetime and take the responsibility of covering the subregion. The network lifetime in each subregion is divided into rounds, each round consists of four phases information exchange, Leader Election, Decision with optimization, and sensing.Our simulation results show that the proposed protocol outperforms or very near some other methods in terms of lifetime, coverage ratio, Active sensor Ratio, energy saving , energy consumption,  execution time, and the number of stopped simulation runs. In future, we will study and prepare the one round coverage protocol by which all active sensor schedules will be prepared in one round using intelligent optimization methods such as swarms optimization or Evolutionary algorithms.
 
 
 % use section* for acknowledgement
@@ -481,14 +619,14 @@ To cope with this problem,
 
 \begin{thebibliography}{1}
 
-
-\bibitem{wns07}
-  J. Wang, C. Niu, and R. Shen,~\emph{Randomized approach for target coverage scheduling in directional sensor network},~ICESS2007,~pp. 379-390,~2007.
+%1
+%\bibitem{wns07}
+ % J. Wang, C. Niu, and R. Shen,~\emph{Randomized approach for target coverage scheduling in directional sensor network},~ICESS2007,~pp. 379-390,~2007.
   
 
-
-\bibitem{dw60}
-  G.~B. Dantzig and P.~ Wolfe,~\emph {Decomposition principle for linear programs},~Operations Research,~pp. 101-111,~ 1960.
+%2
+%\bibitem{dw60}
+ % G.~B. Dantzig and P.~ Wolfe,~\emph {Decomposition principle for linear programs},~Operations Research,~pp. 101-111,~ 1960.
  
 
 \bibitem{asc02}
@@ -509,13 +647,13 @@ To cope with this problem,
  Wireless Networks,~ vol.~11,~ issue~3,~pp.~333--340,~May~2005.
  
  
+%7
+%\bibitem{Cardei05energy-efficienttarget}
+% M.~ Cardei ,~ M.~ T.~ Thai,~ Y.~ Li and W.~ Wu,~ emph{Energy-efficient target coverage in wireless sensor networks},IEEE Infocom,~pp.~1976--1984,~2005.
 
-\bibitem{Cardei05energy-efficienttarget}
- M.~ Cardei ,~ M.~ T.~ Thai,~ Y.~ Li and W.~ Wu,~ emph{Energy-efficient target coverage in wireless sensor networks},IEEE Infocom,~pp.~1976--1984,~2005.
-
-
-\bibitem{b04}
- P.~ Berman,~ G.~ Calinescu ,~ C.~ Shah and A.~ Zelikovsky,~emph{Power efficient monitoring management in sensor networks},~Wireless Communications and Networking Conference,~ WCNC. ~2004,~2004.
+%8
+%\bibitem{b04}
+% P.~ Berman,~ G.~ Calinescu ,~ C.~ Shah and A.~ Zelikovsky,~emph{Power efficient monitoring management in sensor networks},~Wireless Communications and Networking Conference,~ WCNC. ~2004,~2004.
 
 \bibitem{Berman05efficientenergy}
    P.~ Berman ,~ G.~ Calinescu ,~ C.~ Shah and A. Zelikovsky,~emph {Efficient energy management in sensor networks},~ Ad Hoc and Sensor Networks. Nova Science Publishers,~Nova Science Publisher,~2005.
@@ -528,41 +666,42 @@ To cope with this problem,
  S.~K.~Prasad, and A.~Dhawan,~emph{Distributed algorithms for lifetime of wireless sensor networks based on dependencies among cover sets},~Proceedings of the 14th international conference on High performance computing ,~HiPC'07,pp.~381--392,~2007.
  
 
-
-\bibitem{Zorbas:2010:SCP:1715927.1715956}
- D.~ Zorbas ,~ D. Glynos ,~ P.~ Kotzanikolaou and C.~ Douligeris,~emph {Solving coverage problems in wireless sensor networks using cover sets},~ Ad Hoc Netw.,~ vol.~8,issue~4,~pp.~400--415,June~ 2010.
+%12
+%\bibitem{Zorbas:2010:SCP:1715927.1715956}
+% D.~ Zorbas ,~ D. Glynos ,~ P.~ Kotzanikolaou and C.~ Douligeris,~emph {Solving coverage problems in wireless sensor networks using cover sets},~ Ad Hoc Netw.,~ vol.~8,issue~4,~pp.~400--415,June~ 2010.
  
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