\subsection{Main Idea}
\label{ch4:sec:02:03}
-\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.
+\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
\label{FirstModel}
\end{figure}
-As shown in Figure~\ref{FirstModel}, 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 the coverage until the
-definition of a new cover set in the next period. Constraints, like 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.
+As shown in Figure~\ref{FirstModel}, 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 the coverage until the definition of a new cover set in the next period. Constraints, like 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.
+
Below, we describe each phase in more details.
\subsubsection{Leader Election Phase}
\label{ch4:sec:02:03:02}
-This step includes choosing the Wireless Sensor Node Leader (WSNL), which will be responsible for executing the coverage algorithm. Each subregion in the area of interest will select its own WSNL independently for each round. All the sensor nodes cooperate to select WSNL. The nodes in the same subregion will select the leader based on the received information from all other nodes in the same subregion. The selection criteria are, in order of importance: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Observations on previous simulations suggest to use the number of one-hop neighbors as the primary criterion to reduce energy consumption due to the communications.
+This step includes choosing the Wireless Sensor Node Leader (WSNL), which will be responsible for executing the coverage algorithm. Each subregion in the area of interest will select its own WSNL independently for each round. All the sensor nodes cooperate to select WSNL. The nodes in the same subregion will select the leader based on the received information from all other nodes in the same subregion. The selection criteria are, in order of importance: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Observations on previous simulations suggest using the number of one-hop neighbors as the primary criterion to reduce energy consumption due to the communications.
\subsubsection{Decision phase}
awake or to go to sleep for a time equal to the period of sensing until
starting a new 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{ch4:sec:03}) 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.
-
+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 $j$). In 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{ch4:sec:03}) 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.
\begin{algorithm}[h!]
\indent In this dissertation, we used an energy consumption model proposed by~\cite{DESK} and based on \cite{ref112} 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.
-\indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmels AVR ATmega103L microcontroller~\cite{ref112}. 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, the sensing subsystem that collects data, and the power supply which powers the complete sensor node \cite{ref112}. 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{table1}.
+\indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmel's AVR ATmega103L microcontroller~\cite{ref112}. 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, the sensing subsystem that collects data, and the power supply which powers the complete sensor node \cite{ref112}. 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{table1}.
\begin{table}[ht]
\caption{The Energy Consumption Model}
%We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}.
-The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36~\mbox{Joules}$, 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), and adding the energy for the pre-sensing phases. According to the interval of initial energy, a sensor may be alive during at most 20 rounds.
+The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in the active state (9.72 mW) by the time in second for one round (3600 seconds), and adding the energy for the pre-sensing phases. According to the interval of initial energy, a sensor may be alive during at most 20 rounds.
\subsection{Performance Metrics}
+ E^{a}_m+E^{s}_m \right)}{M},
\end{equation*}
-where $M$ corresponds to the number of periods. The total amount of energy
-consumed by the sensors (EC) comes through taking into consideration four main
-energy factors. The first one, denoted $E^{\scriptsize \mbox{com}}_m$,
-represents the energy consumption spent by all the nodes for wireless
-communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
-factor, corresponds to the energy consumed by the sensors in LISTENING status
-before receiving the decision to go active or sleep in period $m$.
-$E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
-nodes to solve the integer program during a period. Finally, $E^a_{m}$ and
-$E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase
+where $M$ corresponds to the number of periods. The total amount of energy consumed by the sensors (EC) comes through taking into consideration four main energy factors. The first one, denoted $E^{\scriptsize \mbox{com}}_m$, represents the energy consumption spent by all the nodes for wireless communications during the period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
+factor, corresponds to the energy consumed by the sensors in LISTENING status before receiving the decision to go active or sleep in the period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed for all the leader nodes to solve the integer program during a period. Finally, $E^a_{m}$ and $E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase
(active and sleeping nodes).
\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
\end{equation*}
Where: $A_r$ is the number of active sensors in the subregion $r$ during current period, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
-\item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power, therefore it is important that the proposed algorithm has the shortest possible execution time. The energy of a sensor node must be mainly used for the sensing phase, not for the pre-sensing ones. In this dissertation, the original execution time is computed on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6} \right)$.
+\item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power, therefore it is important that the proposed algorithm has the shortest possible execution time. The energy of a sensor node must be mainly used for the sensing phase, not for the pre-sensing ones. In this dissertation, the original execution time is computed on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmel's AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6} \right)$.
\item {{\bf Stopped simulation runs}:} A simulation ends when the sensor network becomes disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs ( in chapter 3, period consists of one round).
\label{ch4:sec:04:05}
In this subsection, we are studied the performance of our DiLCO protocol for a 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 did not take the DiLCO-1 protocol in our simulation results because it need high execution time to give the decision leading to consume all it's energy before producing the solution for optimization problem.
+The DiLCO-1 protocol is a centralized approach to 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 did not take the DiLCO-1 protocol in our simulation results because it needs a high execution time to give the decision leading to consume all its energy before producing the solution for the optimization problem.
\begin{enumerate}[i)]
\item {{\bf Coverage Ratio}}
\end{figure}
It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty rounds.
DiLCO-2 protocol gives near similar coverage ratio with other ones for first 10 rounds and then decreased until the died of the network in the round $18^{th}$ because it consumes more energy with the effect of the network disconnection.
-As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases, the coverage preservation for area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to DiLCO-8, DiLCO-16 and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16 and DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
+As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases, the coverage preservation for the area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to DiLCO-8, DiLCO-16, and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16, and DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
\item {{\bf Active Sensors Ratio}}
%\subsubsection{Active Sensors Ratio}
\caption{Active sensors ratio for 150 deployed nodes }
\label{Figures/ch4/R1/ASR}
\end{figure}
-The results presented in figure~\ref{Figures/ch4/R1/ASR} show the increase in the number of subregions led to increase in the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes but it preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.
+
+The results presented in figure~\ref{Figures/ch4/R1/ASR} show the increase in the number of subregions led to increasing in the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but it preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.
\item {{\bf The percentage of stopped simulation runs}}
%\subsubsection{The percentage of stopped simulation runs}
The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view but as the network size increase the energy consumption increase compared with DiLCO-2, DiLCO-4, and DiLCO-8. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.\\
-As shown in Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50}, DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.
+As shown in Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50}, DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem, as well as the higher energy consumed during the communication.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf}
\label{Figures/ch4/R1/T}
\end{figure}
-We can see from figure~\ref{Figures/ch4/R1/T}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions, because it distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.
+We can see from figure~\ref{Figures/ch4/R1/T}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions because it distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.
-The DiLCO-32 protocol has more suitable times at the same time it turn on redundant nodes more. We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
+The DiLCO-32 protocol has more suitable times at the same time it turns on redundant nodes more. We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
\item {{\bf The Network Lifetime}}
%\subsubsection{The Network Lifetime}
\caption{Network Lifetime for $Lifetime95$}
\label{Figures/ch4/R1/LT95}
\end{figure}
-We see that DiLCO-2 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumed during the communication seems to be huge because it is distributed over only two subregions.
+We see that DiLCO-2 protocol results in execution times that quickly become unsuitable for a sensor network, as well as the energy consumed during the communication, seems to be huge because it is distributed over only two subregions.
-As highlighted by figures~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol that leads to the larger lifetime improvement. By choosing the best suited nodes, for each round, to cover the area of interest and by
-letting the other ones sleep in order to be used later in next rounds, DiLCO-16 protocol efficiently extends the network lifetime because the benefit from the optimization with 16 subregions is better than DiLCO-32 protocol with 32 subregion. DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.
+As highlighted by figures~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol that leads to the larger lifetime improvement. By choosing the best-suited nodes, for each round, to cover the area of interest and by
+letting the other ones sleep in order to be used later in next rounds, DiLCO-16 protocol efficiently extends the network lifetime because the benefit from the optimization with 16 subregions is better than DiLCO-32 protocol with 32 subregions. DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.
Comparison shows that DiLCO-16 protocol, which uses 16 leaders, is the best one because it is used less number of active nodes during the network lifetime compared with DiLCO-32 protocol. It also means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+
\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}
\caption{Coverage ratio for 150 deployed nodes}
\label{Figures/ch4/R2/CR}
\end{figure}
+
It is shown that all models provide a very near coverage ratios during the network lifetime, with very small superiority for the models with higher number of primary points. Moreover, when the number of rounds increases, coverage ratio produced by Model~3, Model~4, and Model~5 decreases in comparison with Model~1 and Model~2 due to the high energy consumption during the listening to take the decision after finishing optimization process for larger number of primary points. As shown in figure ~\ref{Figures/ch4/R2/CR}, Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead,
thanks to Model~2, which is slightly more efficient than other Models, because it is balanced between the number of rounds and the better coverage ratio in comparison with other Models.
\label{Figures/ch4/R2/ASR}
\end{figure}
-The results presented in figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed Model 1, in comparison with the other Models. The
-model with less number of primary points uses less active nodes than the other models, which uses a more number of primary points to represent the area of the sensor. According to the results that presented in figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model~1 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model~2 approach is to use less number of active nodes for each round compared with Model~3, Model~4, and Model~5; and this led to continue for a larger number of rounds with extending the network lifetime. Model~2 has a better coverage ratio compared to Model~1 and acceptable number of rounds.
+The results presented in figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed Model 1, in comparison with the other Models. The model with fewer number of primary points uses fewer active nodes than the other models, which uses larger number of primary points to represent the area of the sensor. According to the results that presented in figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model~1 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model~2 approach is to use fewer number of active nodes for each round compared with Model~3, Model~4, and Model~5. This led to continuing for a larger number of rounds with extending the network lifetime. Model~2 has a better coverage ratio compared to Model~1 and acceptable number of rounds.
\item {{\bf he percentage of stopped simulation runs}}
\label{Figures/ch4/R2/SR}
\end{figure}
-As shown in Figure~\ref{Figures/ch4/R2/SR}, when the number of primary points are increased, the percentage of the stopped simulation runs per round is increased. The reason behind the increase is the increase in the sensors dead when the primary points increases. We are observed that the Model~1 is a better than other models because it conserve more energy by turn on less number of sensors during the sensing phase, but in the same time it preserve the coverage with a less coverage ratio in comparison with other models. Model~2 seems to be more suitable to be used in wireless sensor networks.
+As shown in Figure~\ref{Figures/ch4/R2/SR}, when the number of primary points is increased, the percentage of the stopped simulation runs per round is increased. The reason behind the increase is the increase in the sensors dead when the primary points increase. We are observed that the Model~1 is a better than other models because it conserve more energy by turn on less number of sensors during the sensing phase, but in the same time it preserve the coverage with a less coverage ratio in comparison with other models. Model~2 seems to be more suitable to be used in wireless sensor networks.
\item {{\bf The Energy Consumption}}
\label{Figures/ch4/R2/EC50}
\end{figure}
-We see from the results presented in Figures~\ref{Figures/ch4/R2/EC95} and \ref{Figures/ch4/R2/EC50}, The energy consumed by the network for each round increases when the primary points increases, because the decision for optimization process will takes more time leads to consume more energy during the listening mode. The results show that Model~1 is the most competitive from the energy consumption point of view but the worst one from coverage ratio point of view. The other Models have a high energy consumption due to the increase in the primary points, which are led to increase the energy consumption during the listening mode before producing the solution by solving the optimization process. In fact, we see that Model~2 is a good candidate to be used by wireless sensor network because it preserve a good coverage ratio and a suitable energy consumption in comparison with other models.
+ We see from the results presented in Figures~\ref{Figures/ch4/R2/EC95} and \ref{Figures/ch4/R2/EC50}, The energy consumed by the network for each round increases when the primary points increases, because the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model~1 is the most competitive from the energy consumption point of view, but the worst one from coverage ratio point of view. The other Models have a high energy consumption due to the increase in the primary points, which are led to increase the energy consumption during the listening mode before producing the solution by solving the optimization process. In fact, we see that Model~2 is a good candidate to be used by wireless sensor network because it preserves a good coverage ratio with a suitable energy consumption in comparison with other models.
\item {{\bf Execution Time}}
%\subsubsection{Execution Time}
\label{Figures/ch4/R2/T}
\end{figure}
-They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model~1 has lower execution time in comparison with other Models, because it used smaller number of primary points to represent the area of the sensor. Conversely, the other primary point models have been presented a higher execution times.
+They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model~1 has lower execution time in comparison with other Models because it used smaller number of primary points to represent the area of the sensor. Conversely, the other primary point models have been presented a higher execution times.
Moreover, Model~2 has more suitable times and coverage ratio that lead to continue for a larger number of rounds extending the network lifetime. We think that a good primary point model, this one that balances between the coverage ratio and the number of rounds during the lifetime of the network.
\item {{\bf The Network Lifetime}}
\subsection{Performance Comparison with other Approaches}
\label{ch4:sec:04:07}
-Based on the results, which are conducted from previous two subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are the best candidates to be compared with other two approaches. The first approach, called DESK that proposed by ~\cite{DESK}, which is a full distributed coverage algorithm. The second approach, called GAF~\cite{GAF}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time.
+Based on the results, which are conducted from previous two subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are the best candidates to be compared with other two approaches. The first approach is called DESK~\cite{DESK}, which is a fully distributed coverage algorithm. The second approach is called GAF~\cite{GAF}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time.
\begin{enumerate}[i)]
