\section{\uppercase{Introduction}}
\label{sec:introduction}
\noindent
-Energy efficiency is a crucial issue in wireless sensor networks since sensor
-nodes drain their energy from batteries. In fact, strong constraints on energy
+Energy efficiency is a crucial issue in wireless sensor networks since sensory
consumption, in order to maximize the network lifetime, represent the major
difficulty when designing WSNs. As a consequence, one of the scientific research
challenges in WSNs, which has been addressed by a large amount of literature
during the last few years, is the design of energy efficient approaches for
-coverage and connectivity~\cite{conti2014mobile}. Coverage reflects how well a
-sensor field is monitored. The most discussed coverage problems in literature
+coverage and connectivity~\cite{conti2014mobile}. Coverage reflects how well a
+sensor field is monitored. The most discussed coverage problems in literature
can be classified into three types \cite{li2013survey}: area coverage (where
every point inside an area is to be monitored), target coverage (where the main
objective is to cover only a finite number of discrete points called targets),
and barrier coverage (to prevent intruders from entering into the region of
interest). On the one hand we want to monitor the area of interest in the most
efficient way~\cite{Nayak04}. On the other hand we want to use as less energy as
-possible. % TO BE CONTINUED
-Sensor nodes runs on batteries with limited capacities~\cite{Sudip03}
-and it is impossible, difficult or expensive to recharge and/or replace
-batteries in remote, hostile, or unpractical environments. Therefore, it is
-desired that the WSNs are deployed with high densities so as to exploit the
-overlapping sensing regions of some sensor nodes to save energy by turning off
-some of them during the sensing phase to prolong the network lifetime.
-
-In this paper we concentrate on the area coverage problem with the objective of
-maximizing the network lifetime by using DiLCO protocol to maintain the coverage
-and to improve the lifetime in WSNs. The area of interest is divided into
-subregions using divide-and-conquer method and an activity scheduling for sensor
-nodes is planned by the elected leader in each subregion. In fact, the nodes in
-a subregion can be seen as a cluster where each node sends sensing data to the
-cluster head or the sink node. Furthermore, the activities in a
-subregion/cluster can continue even if another cluster stops due to too many
-node failures. Our DiLCO protocol considers periods, where a period starts with
-a discovery phase to exchange information between sensors of the subregion, in
-order to choose in a suitable manner a sensor node (the leader) to carry out the
-coverage strategy. Our DiLCO protocol involves solving an integer program,
-which provides the activation of the sensors for the sensing phase of the
-current period.
+possible. Sensor nodes are battery-powered with no means of recharging or
+replacing, usually due to environmental (hostile or unpractical environments) or
+cost reasons. Therefore, it is desired that the WSNs are deployed with high
+densities so as to exploit the overlapping sensing regions of some sensor nodes
+to save energy by turning off some of them during the sensing phase to prolong
+the network lifetime.
+
+In this paper we design a protocol that focuses on the area coverage problem
+with the objective of maximizing the network lifetime. Our proposition, the
+DiLCO protocol, maintains the coverage and improves the lifetime in WSNs. The
+area of interest is first divided into subregions using a divide-and-conquer
+algorithm and an activity scheduling for sensor nodes is then planned by the
+elected leader in each subregion. In fact, the nodes in a subregion can be seen
+as a cluster where each node sends sensing data to the cluster head or the sink
+node. Furthermore, the activities in a subregion/cluster can continue even if
+another cluster stops due to too many node failures. Our Distributed Lifetime
+Coverage Optimization (DILCO) protocol considers periods, where a period starts
+with a discovery phase to exchange information between sensors of a same
+subregion, in order to choose in a suitable manner a sensor node (the leader) to
+carry out the coverage strategy. In each subregion the activation of the sensors
+for the sensing phase of the current period is obtained by solving an integer
+program.
The remainder of the paper continues with Section~\ref{sec:Literature Review}
where a review of some related works is presented. The next section describes
the DiLCO protocol, followed in Section~\ref{cp} by the coverage model
formulation which is used to schedule the activation of
sensors. Section~\ref{sec:Simulation Results and Analysis} shows the simulation
-results. The paper ends with conclusions and some suggestions for futher work in
-Section~\ref{sec:Conclusion and Future Works}.
+results. The paper ends with conclusions and some suggestions for further work
+in Section~\ref{sec:Conclusion and Future Works}.
\section{\uppercase{Literature Review}}
\label{sec:Literature Review}
\section{ The DiLCO Protocol Description}
\label{sec:The DiLCO Protocol Description}
-\noindent In this section, we introduce a Distributed Lifetime Coverage Optimization protocol, which is called DiLCO. It is distributed on each subregion in the area of interest. It is based on two efficient techniques: network leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.
-\iffalse The main features of our DiLCO protocol:
-i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into rounds, iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi) it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative set of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our protocol.
+\noindent In this section, we introduce the DiLCO protocol which is distributed
+on each subregion in the area of interest. It is based on two efficient
+techniques: network leader election and sensor activity scheduling for coverage
+preservation and energy conservation, applied periodically to efficiently
+maximize the lifetime in the network.
+\iffalse The main features of our DiLCO protocol: i)It divides the area of
+interest into subregions by using divide-and-conquer concept, ii)It requires
+only the information of the nodes within the subregion, iii) it divides the
+network lifetime into rounds, iv)It based on the autonomous distributed decision
+by the nodes in the subregion to elect the Leader, v)It apply the activity
+scheduling based optimization on the subregion, vi) it achieves an energy
+consumption balancing among the nodes in the subregion by selecting different
+nodes as a leader during the network lifetime, vii) It uses the optimization to
+select the best representative set of sensors in the subregion by optimize the
+coverage and the lifetime over the area of interest, viii)It uses our proposed
+primary point coverage model, which represent the sensing range of the sensor as
+a set of points, which are used by the our optimization algorithm, ix) It uses a
+simple energy model that takes communication, sensing and computation energy
+consumptions into account to evaluate the performance of our protocol.
\fi
-\subsection{ Assumptions and Models}
-\noindent We consider a randomly and uniformly deployed network consisting of
-static wireless sensors. The wireless sensors are deployed in high
-density to ensure initially a high coverage ratio of the interested area. We
-assume that all nodes are homogeneous in terms of communication and
-processing capabilities and heterogeneous in term of energy provision.
-The location information is available to the sensor node either
-through hardware such as embedded GPS or through location discovery
-algorithms. We consider a boolean disk coverage model which is the most
-widely used sensor coverage model in the literature. Each sensor has a
-constant sensing range $R_s$. All space points within a disk centered
-at the sensor with the radius of the sensing range is said to be
-covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$.
-In fact, Zhang and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the
-previous hypothesis, a complete coverage of a convex area implies
-connectivity among the working nodes in the active mode.
-
-\indent Instead of working with the coverage area, we consider for each
-sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the
-sensing disk defined by a sensor is covered if all the primary points of
-this sensor are covered.
+
+\subsection{ Assumptions and models}
+
+\noindent We consider a sensor network composed of static nodes distributed
+independently and uniformly at random. A high density deployment ensures a high
+coverage ratio of the interested area at the starting. The nodes are supposed to
+have homogeneous characteristics from a communication and a processing point of
+view, whereas they have heterogeneous energy provisions. Each node has access
+to its location thanks, either to a hardware component (like a GPS unit), or a
+location discovery algorithm.
+
+\indent We consider a boolean disk coverage model which is the most widely used
+sensor coverage model in the literature. Thus, since a sensor has a constant
+sensing range $R_s$, every space points within a disk centered at a sensor with
+the radius of the sensing range is said to be covered by this sensor. We also
+assume that the communication range $R_c \geq 2R_s$. In fact, Zhang and
+Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous
+hypothesis, a complete coverage of a convex area implies connectivity among the
+working nodes in the active mode.
+
+\indent For each sensor we also define a set of points called primary
+points~\cite{idrees2014coverage} to approximate the area coverage it provides,
+rather than working with a continuous coverage. Thus, a sensing disk
+corresponding to a sensor node is covered by its neighboring nodes if all its
+primary points are covered. Obviously, the approximation of coverage is more or
+less accurate according to the number of primary points.
\iffalse
By knowing the position (point center: ($p_x,p_y$)) of a wireless
\fi
-\subsection{The Main Idea}
-\noindent The area of interest can be divided using the
-divide-and-conquer strategy into smaller areas called subregions and
-then our coverage protocol will be implemented in each subregion
-simultaneously. Our DiLCO protocol works in periods fashion as shown in figure~\ref{fig2}.
+\subsection{The main idea}
+
+\noindent We start by applying a divide-and-conquer algorithm to partition the
+area of interest into smaller areas called subregions and then our protocol is
+executed simultaneously in each subregion.
+
\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{FirstModel.pdf} % 70mm
\label{fig2}
\end{figure}
-%Modifier la figure pour faire apparaitre des periodes et dans le schema en bleu, indiquer sensing round au lieu de sensing tout seul.
-
-Each period is divided into 4 phases : Information (INFO) Exchange,
-Leader Election, Decision, and Sensing. For each period there is
-exactly one set cover responsible for the sensing task. This protocol is
-more reliable against an unexpected node failure because it works
-in periods. On the one hand, if a node failure is detected before
-making the decision, the node will not participate to this phase, and,
-on the other hand, if the node failure occurs after the decision, the
-sensing task of the network will be temporarily affected: only during
-the period of sensing until a new period starts, since a new set cover
-will take charge of the sensing task in the next period. The energy
-consumption and some other constraints can easily be taken into
-account since the sensors can update and then exchange their
-information (including their residual energy) at the beginning of each
-period. However, the pre-sensing phases (INFO Exchange, Leader
-Election, Decision) are energy consuming for some nodes, even when
-they do not join the network to monitor the area.
-We define two types of packets to be used by our DiLCO protocol.
+As shown in Figure~\ref{fig2}, the proposed DiLCO protocol is a periodic
+protocol where each period is decomposed into 4~phases: Information Exchange,
+Leader Election , Decision, and Sensing. For each period there will be exactly
+one cover set in charge of the sensing task. A periodic scheduling is
+interesting because it enhances the robustness of the network against node
+failures. First, a node that has not enough energy to complete a period, or
+which fails before the decision is taken, will be excluded from the scheduling
+process. Second, if a node fails later, whereas it was supposed to sense the
+region of interest, it will only affect the quality of coverage until the
+definition of a new cover set in the next period. Constraints, like the energy
+consumption, can be easily taken into consideration since the sensors can update
+and exchange their information during the first phase. Let us notice that the
+phases before the sensing one (Information Exchange, Leader Election, and
+Decision) are energy consuming for all the nodes, even nodes that will not be
+retained by the leader to keep watch over the corresponding area.
+
+During the excution of the DiLCO protocol, two kinds of packets will be used:
%\begin{enumerate}[(a)]
\begin{itemize}
-\item INFO packet: sent by each sensor node to all the nodes inside a same subregion for information exchange.
-\item ActiveSleep packet: sent by the leader to all the nodes in its subregion to inform them to be Active or Sleep during the sensing phase.
+\item INFO packet: sent by each sensor node to all the nodes inside a same
+ subregion for information exchange.
+\item ActiveSleep packet: sent by the leader to all the nodes in its subregion
+ to inform them to be stay Active or to go Sleep during the sensing phase.
\end{itemize}
%\end{enumerate}
-
-There are five status for each sensor node in the network :
+and each sensor node will have five possible status in the network:
%\begin{enumerate}[(a)]
\begin{itemize}
-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: sensor is waiting for a decision (to be active or not);
+\item COMPUTATION: sensor applies the optimization process as leader;
+\item ACTIVE: sensor is active;
+\item SLEEP: sensor is turned off;
+\item COMMUNICATION: sensor is transmitting or receiving packet.
\end{itemize}
%\end{enumerate}
-%Below, we describe each phase in more details.
-Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_j$ for a sensor node indexed by $j$).
-Initially, the sensor node checks its remaining energy in order to participate in the current period. After that, all the sensors collect position coordinates, remaining energy $RE_j$, sensor node id, and the number of its one-hop live neighbors during the information exchange.
-Then all the sensor nodes in the same subregion will select the leader based on the received informations. The selection criteria for the leader in order of priority are: larger number of neighbours, larger remaining energy, and then in case of equality, larger index. After that, if the sensor node is leader, it will execute the integer program algorithm (see section~\ref{cp}) which provides a set of sensors planned to be active in the sensing round. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to indicate it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing round.
-
+An outline of the protocol implementation is given by Algorithm~\ref{alg:DiLCO}
+which describes the execution of a period by a node (denoted by $s_j$ for a
+sensor node indexed by $j$). At the beginning a node checks whether it has
+enough energy to stay active during the next sensing phase. If yes, it exchanges
+information with all the other nodes belonging to the same subregion: it
+collects from each node its position coordinates, remaining energy ($RE_j$), ID,
+and the number of one-hop neighbors still alive. Once the first phase is
+completed, the nodes of a subregion choose a leader to take the decision based
+on the following criteria with decreasing importance: larger number of
+neighbors, larger remaining energy, and then in case of equality, larger index.
+After that, if the sensor node is leader, it will execute the integer program
+algorithm (see Section~\ref{cp}) which provides a set of sensors planned to be
+active in the next sensing phase. As leader, it will send an Active-Sleep packet
+to each sensor in the same subregion to indicate it if it has to be active or
+not. Alternately, if the sensor is not the leader, it will wait for the
+Active-Sleep packet to know its state for the coming sensing phase.
\iffalse
\subsubsection{Information Exchange Phase}
\iffalse
\subsection{DiLCO protocol Algorithm}
-we first show the pseudo-code of DiLCO protocol, which is executed by each sensor in the subregion and then describe it in more detail.
-\fi
+we first show the pseudo-code of DiLCO protocol, which is executed by each
+sensor in the subregion and then describe it in more detail. \fi
\begin{algorithm}[h!]
% \KwIn{all the parameters related to information exchange}
\section{Coverage problem formulation}
\label{cp}
-\indent Our model is based on the model proposed by
-\cite{pedraza2006} where the objective is to find a maximum number of
-disjoint cover sets. To accomplish this goal, authors proposed an
-integer program, which forces undercoverage and overcoverage of targets
-to become minimal at the same time. They use binary variables
-$x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
-model, we consider binary variables $X_{j}$, which determine the
-activation of sensor $j$ in the sensing round. We also
-consider primary points as targets. The set of primary points is
-denoted by $P$ and the set of sensors by $J$.
-
-\noindent For a primary point $p$, let $\alpha_{jp}$ denote the
-indicator function of whether the point $p$ is covered, that is:
+\indent Our model is based on the model proposed by \cite{pedraza2006} where the
+objective is to find a maximum number of disjoint cover sets. To accomplish
+this goal, the authors proposed an integer program which forces undercoverage
+and overcoverage of targets to become minimal at the same time. They use binary
+variables $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
+model, we consider binary variable $X_{j}$ which determine the activation of
+sensor $j$ in the sensing phase. We also consider primary points as targets.
+The set of primary points is denoted by $P$ and the set of sensors by $J$.
+
+\noindent Let $\alpha_{jp}$ denote the indicator function of whether the primary
+point $p$ is covered, that is:
\begin{equation}
\alpha_{jp} = \left \{
\begin{array}{l l}
\end{array} \right.
%\label{eq12}
\end{equation}
-The number of active sensors that cover the primary point $p$ is equal
-to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+The number of active sensors that cover the primary point $p$ can then be
+computed by $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
\begin{equation}
X_{j} = \left \{
\begin{array}{l l}
\label{eq14}
\end{equation}
-\noindent Our coverage optimization problem can then be formulated as follows
+\noindent Our coverage optimization problem can then be formulated as follows:
\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
\right.
\end{equation}
-
-
\begin{itemize}
-\item $X_{j}$ : indicates whether or not the sensor $j$ is actively
- sensing in the round (1 if yes and 0 if not);
-\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
- one that are covering the primary point $p$;
-\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
+\item $X_{j}$ : indicates whether or not the sensor $j$ is actively sensing (1
+ if yes and 0 if not);
+\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that
+ are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
$p$ is being covered (1 if not covered and 0 if covered).
\end{itemize}
-The first group of constraints indicates that some primary point $p$
-should be covered by at least one sensor and, if it is not always the
-case, overcoverage and undercoverage variables help balancing the
-restriction equations by taking positive values. There are two main
-objectives. First, we limit the overcoverage of primary points in order to
-activate a minimum number of sensors. Second we prevent the absence of monitoring on
- some parts of the subregion by minimizing the undercoverage. The
-weights $w_\theta$ and $w_U$ must be properly chosen so as to
-guarantee that the maximum number of points are covered during each
-round.
-
-
-
-
-\section{\uppercase{Simulation Results and Analysis}}
+The first group of constraints indicates that some primary point $p$ should be
+covered by at least one sensor and, if it is not always the case, overcoverage
+and undercoverage variables help balancing the restriction equations by taking
+positive values. Two objectives can be noticed in our model. First, we limit the
+overcoverage of primary points to activate as few sensors as possible. Second,
+to avoid a lack of area monitoring in a subregion we minimize the
+undercoverage. Both weights $w_\theta$ and $w_U$ must be carefully chosen in
+order to guarantee that the maximum number of points are covered during each
+period.
+
+\section{\uppercase{Protocol evaluation}}
\label{sec:Simulation Results and Analysis}
-\noindent \subsection{Simulation Framework}
-In this subsection, we conducted a series of simulations to evaluate the
-efficiency and the relevance of our DiLCO protocol, using the discrete event
-simulator OMNeT++ \cite{varga}. The simulation parameters are summarized in
-Table~\ref{table3}.
+\noindent \subsection{Simulation framework}
+
+To assess the performance of our DiLCO protocol, we have used the discrete
+event simulator OMNeT++ \cite{varga} to run different series of simulations.
+Table~\ref{table3} gives the chosen parameters setting.
\begin{table}[ht]
\caption{Relevant parameters for network initializing.}
% is used to refer this table in the text
\end{table}
-We performed simulations for five different densities varying from 50 to 250~nodes. Experimental results are the average obtained from 25 randomly generated networks (25 for each network density) in which nodes are deployed over a $(50 \times 25)~m^2 $ sensing field. More precisely, the deployment is controlled at a coarse scale in order to ensure that the deployed nodes can cover the sensing field with a high coverage ratio.\\
-
-We first concentrate on the required number of subregions making effective our protocol. Thus our DiLCO protocol is declined into five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$ or $32$ subregions (leaders).
-
-We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
-The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
-% We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node.
-%The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU.
-%revoir la phrase
-
-For our energy consumption model, we refer to the sensor node Medusa II which uses Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The typical architecture of a sensor is composed of four subsystems : the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for
-transmitting/receiving messages, sensing subsystem that collects data, and the power supply which powers the complete sensor node ~\cite{raghunathan2002energy}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table4}.
+Simulations with five different node densities going from 50 to 250~nodes were
+performed considering each time 25~randomly generated networks, to obtain
+experimental results which are relevant. The nodes are deployed on a field of
+interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
+high coverage ratio.
+
+We chose as energy consumption model the one proposed proposed by~\cite{ChinhVu}
+and based on ~\cite{raghunathan2002energy} with slight modifications. The energy
+consumed by the communications is added and the part relative to a variable
+sensing range is removed. We also assume that the nodes have the characteristics
+of the Medusa II sensor node platform \cite{raghunathan2002energy}. A sensor
+node typically consists of four units: a MicroController Unit, an Atmels AVR
+ATmega103L in case of Medusa II, to perform the computations; a communication
+(adio) unit able to send and receive messages; a sensing unit to collect data; a
+power supply which provides the energy consumed by node. Except the battery, all
+the other unit can be be switched off to save energy according to the node
+status. Table~\ref{table4} summarizes the energy consumed (in milliWatt per
+second) by a node for each of its possible status.
\begin{table}[ht]
-\caption{The Energy Consumption Model}
+\caption{Energy consumption model}
% title of Table
\centering
% used for centering table
+{\scriptsize
\begin{tabular}{|c|c|c|c|c|}
% centered columns (4 columns)
\hline
%inserts double horizontal lines
-Sensor mode & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
+Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
\hline
% inserts single horizontal line
Listening & ON & ON & ON & 20.05 \\
%\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
\hline
\end{tabular}
+}
\label{table4}
% is used to refer this table in the text
\end{table}
-For the sake of simplicity we ignore the energy needed to turn on the
-radio, to start up the sensor node, the transition from one status to another, etc.
-%We also do not consider the need of collecting sensing data. PAS COMPRIS
-Thus, when a sensor becomes active (i.e., it already decides its status), it can turn its radio off to save battery. DiLCO protocol uses two types of packets for communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24 bits respectively.
-The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets.
-The energy needed to send or receive a 1-bit is equal to $0.2575 mW$.
+% MICHEL - TO BE CONTINUED
-The initial energy of each node is randomly set in the interval $[500-700]$. Each sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mW) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.\\
-
-
-In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach:
+For the sake of simplicity we ignore the energy needed to turn on the radio, to
+start up the sensor node, the transition from one status to another, etc.
+%We also do not consider the need of collecting sensing data. PAS COMPRIS
+Thus, when a sensor becomes active (i.e., it already decides its status), it can
+turn its radio off to save battery. DiLCO protocol uses two types of packets for
+communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24
+bits respectively. The value of energy spent to send a 1-bit-content message is
+obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the
+energy cost for transmitting messages and we propose the same value for
+receiving the packets. The energy needed to send or receive a 1-bit is equal to
+$0.2575 mW$.
+
+The initial energy of each node is randomly set in the interval $[500-700]$.
+Each sensor node will not participate in the next round if its remaining energy
+is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay
+alive during one round. This value has been computed by multiplying the energy
+consumed in active state (9.72 mW) by the time in second for one round (3600
+seconds). According to the interval of initial energy, a sensor may be alive
+during at most 20 rounds.\\
+
+In the simulations, we introduce the following performance metrics to evaluate
+the efficiency of our approach:
%\begin{enumerate}[i)]
\begin{itemize}
%\subsection{Performance Analysis for differnet subregions}
\subsection{Performance Analysis}
\label{sub1}
+
+We first concentrate on the required number of subregions making effective our
+protocol. Thus our DiLCO protocol is declined into five versions: DiLCO-2,
+DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$
+or $32$ subregions (leaders).
+
In this subsection, we study the performance of our DiLCO protocol for different number of subregions (Leaders).
The DiLCO-1 protocol is a centralized approach on all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLC0-1 protocol in our simulation results because it requires high execution time to solve the integer program and thus it is too costly in term of energy.
