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-\begin{document}
%\title{Authors' Instructions \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
-\title{Distributed Lifetime Coverage Optimization Protocol \\in Wireless Sensor Networks}
+\title{Distributed Lifetime Coverage Optimization Protocol \\
+ in Wireless Sensor Networks}
-\author{\authorname{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
-\affiliation{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e, Belfort, France}
-%\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry}
-\email{ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
-%\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu}
-}
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$,\\ Michel Salomon$^{a}$, and Rapha\"el Couturier$^{a}$\\
+$^{a}$FEMTO-ST Institute, UMR 6174 CNRS, \\ University Bourgogne Franche-Comt\'e, Belfort, France\\
+$^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}\\
+email: ali.idness@edu.univ-fcomte.fr,\\ $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
+
+%\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$,\\ Michel Salomon$^{a}$, and Rapha\"el Couturier $^{a}$ \\
+%$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University Bourgogne Franche-Comt\'e,\\ Belfort, France}} \\
+%$^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}} }
-\keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,
-Optimization, Scheduling.}
+\begin{document}
+ \maketitle
+%\keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,Optimization, Scheduling.}
\abstract{ One of the main research challenges faced in Wireless Sensor Networks
(WSNs) is to preserve continuously and effectively the coverage of an area (or
region) of interest to be monitored, while simultaneously preventing as much
as possible a network failure due to battery-depleted nodes. In this paper we
propose a protocol, called Distributed Lifetime Coverage Optimization protocol
- (DiLCO), which maintains the coverage and improves the lifetime of a wireless
+ (DiLCO), which maintains the coverage and improves the lifetime of a wireless
sensor network. First, we partition the area of interest into subregions using
a classical divide-and-conquer method. Our DiLCO protocol is then distributed
- on the sensor nodes in each subregion in a second step. To fulfill our
- objective, the proposed protocol combines two effective techniques: a leader
+ on the sensor nodes in each subregion in a second step. To fulfill our
+ objective, the proposed protocol combines two effective techniques: a leader
election in each subregion, followed by an optimization-based node activity
- scheduling performed by each elected leader. This two-step process takes
+ scheduling performed by each elected leader. This two-step process takes
place periodically, in order to choose a small set of nodes remaining active
for sensing during a time slot. Each set is built to ensure coverage at a low
- energy cost, allowing to optimize the network lifetime. More precisely, a
- period consists of four phases: (i)~Information Exchange, (ii)~Leader
- Election, (iii)~Decision, and (iv)~Sensing. The decision process, which
- results in an activity scheduling vector, is carried out by a leader node
- through the solving of an integer program. In comparison with some other
- protocols, the simulations done using the discrete event simulator OMNeT++
- show that our approach is able to increase the WSN lifetime and provides
- improved coverage performance. }
+ energy cost, allowing to optimize the network lifetime.
+%More precisely, a
+ %period consists of four phases: (i)~Information Exchange, (ii)~Leader
+ %Election, (iii)~Decision, and (iv)~Sensing. The decision process, which
+% results in an activity scheduling vector, is carried out by a leader node
+% through the solving of an integer program.
+% MODIF - BEGIN
+ Simulations are conducted using the discret event simulator
+ OMNET++. We refer to the characterictics of a Medusa II sensor for
+ the energy consumption and the computation time. In comparison with
+ two other existing methods, our approach is able to increase the WSN
+ lifetime and provides improved coverage performance. }
+% MODIF - END
-\onecolumn \maketitle \normalsize \vfill
+%\onecolumn
+
+
+%\normalsize \vfill
\section{\uppercase{Introduction}}
\label{sec:introduction}
\noindent
-Energy efficiency is a crucial issue in wireless sensor networks since sensory
+Energy efficiency is a crucial issue in wireless sensor networks since sensory
consumption, in order to maximize the network lifetime, represents 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
+coverage and connectivity~\cite{conti2014mobile}. Coverage reflects how well a
sensor field is monitored. 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 little energy as 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
+interest in the most efficient way~\cite{Nayak04}, \textcolor{blue}{which means
+ that we want to maintain the best coverage as long as possible}. On the other
+hand we want to use as little energy as 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. \textcolor{blue}{A WSN can use various types of sensors such as
+ \cite{ref17,ref19}: thermal, seismic, magnetic, visual, infrared, acoustic,
+ and radar. These sensors are capable of observing different physical
+ conditions such as: temperature, humidity, pressure, speed, direction,
+ movement, light, soil makeup, noise levels, presence or absence of certain
+ kinds of objects, and mechanical stress levels on attached objects.
+ Consequently, there is a wide range of WSN applications such as~\cite{ref22}:
+ health-care, environment, agriculture, public safety, military, transportation
+ systems, and industry applications.}
+
+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
-Distributed Lifetime Coverage Optimization (DILCO) protocol, maintains the
+Distributed Lifetime Coverage Optimization (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
+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
+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
-same subregion, in order to choose in a suitable manner a sensor node (the
+starts with a discovery phase to exchange information between sensors of the
+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 resulting activation vector is broadcast by a leader
-to every node of its subregion.
+the sensors for the sensing phase of the current period is obtained by solving
+an integer program. The resulting activation vector is broadcast by a leader to
+every node of its subregion.
+
+% MODIF - BEGIN
+Our previous paper ~\cite{idrees2014coverage} relies almost exclusively on the
+framework of the DiLCO approach and the coverage problem formulation. In this
+paper we made more realistic simulations by taking into account the
+characteristics of a Medusa II sensor ~\cite{raghunathan2002energy} to measure
+the energy consumption and the computation time. We have implemented two other
+existing \textcolor{blue}{and distributed approaches} (DESK ~\cite{ChinhVu}, and
+GAF ~\cite{xu2001geography}) in order to compare their performances with our
+approach. \textcolor{blue}{We focus on DESK and GAF protocols for two reasons.
+ First our protocol is inspired by both of them: DiLCO uses a regular division
+ of the area of interest as in GAF and a temporal division in rounds as in
+ DESK. Second, DESK and GAF are well-known protocols, easy to implement, and
+ often used as references for comparison}. We also focus on performance
+analysis based on the number of subregions.
+% MODIF - END
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
+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 a conclusion and some suggestions for further work
+sensors. Section~\ref{sec:Simulation Results and Analysis} shows the simulation
+results. The paper ends with a conclusion and some suggestions for further work
in Section~\ref{sec:Conclusion and Future Works}.
\section{\uppercase{Literature Review}}
\label{sec:Literature Review}
-\noindent In this section, we summarize some related works regarding the coverage
-problem and distinguish our DiLCO protocol from the works presented in the
-literature.
-
-The most discussed coverage problems in literature
-can be classified into three types \cite{li2013survey}: area coverage \cite{Misra} where
-every point inside an area is to be monitored, target coverage \cite{yang2014novel} where the main
-objective is to cover only a finite number of discrete points called targets,
-and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders from entering into the region of interest. In \cite{Deng2012} authors transform the area coverage problem to the target coverage problem taking into account the intersection points among disks of sensors nodes or between disk of sensor nodes and boundaries.
-{\it In DiLCO protocol, the area coverage, i.e. the coverage of every point in
- the sensing region, is transformed to the coverage of a fraction of points
- called primary points. }
-
+\noindent In this section, we summarize some related works regarding the
+coverage problem and distinguish our DiLCO protocol from the works presented in
+the literature.
+
+The most discussed coverage problems in literature can be classified into three
+types \cite{li2013survey}: area coverage \cite{Misra} where every point inside
+an area is to be monitored, target coverage \cite{yang2014novel} where the main
+objective is to cover only a finite number of discrete points called targets,
+and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders
+from entering into the region of interest. In \cite{Deng2012} authors transform
+the area coverage problem to the target coverage problem taking into account the
+intersection points among disks of sensors nodes or between disk of sensor nodes
+and boundaries. {\it In DiLCO protocol, the area coverage, i.e. the coverage of
+ every point in the sensing region, is transformed to the coverage of a
+ fraction of points called primary points. }
The major approach to extend network lifetime while preserving coverage is to
divide/organize the sensors into a suitable number of set covers (disjoint or
-non-disjoint), where each set completely covers a region of interest, and to
+non-disjoint), where each set completely covers a region of interest, and to
activate these set covers successively. The network activity can be planned in
advance and scheduled for the entire network lifetime or organized in periods,
-and the set of active sensor nodes is decided at the beginning of each period \cite{ling2009energy}.
-Active node selection is determined based on the problem requirements (e.g. area
-monitoring, connectivity, power efficiency). For instance, Jaggi et al. \cite{jaggi2006}
-address the problem of maximizing network lifetime by dividing sensors into the maximum number of disjoint subsets such that each subset can ensure both coverage and connectivity. A greedy algorithm is applied once to solve this problem and the computed sets are activated in succession to achieve the desired network lifetime.
-Vu \cite{chin2007}, Padmatvathy et al. \cite{pc10}, propose algorithms working in a periodic fashion where a cover set is computed at the beginning of each period.
-{\it Motivated by these works, DiLCO protocol works in periods, where each period contains a preliminary
- phase for information exchange and decisions, followed by a sensing phase
- where one cover set is in charge of the sensing task.}
-
-Various approaches, including centralized, or distributed
-algorithms, have been proposed to extend the network lifetime.
-In distributed algorithms~\cite{yangnovel,ChinhVu,qu2013distributed},
-information is disseminated throughout the network and sensors decide
-cooperatively by communicating with their neighbors which of them will remain in
-sleep mode for a certain period of time. The centralized
+and the set of active sensor nodes is decided at the beginning of each period
+\cite{ling2009energy}. Active node selection is determined based on the problem
+requirements (e.g. area monitoring, connectivity, power efficiency). For
+instance, Jaggi et al. \cite{jaggi2006} address the problem of maximizing
+network lifetime by dividing sensors into the maximum number of disjoint subsets
+such that each subset can ensure both coverage and connectivity. A greedy
+algorithm is applied once to solve this problem and the computed sets are
+activated in succession to achieve the desired network lifetime. Vu
+\cite{chin2007}, Padmatvathy et al. \cite{pc10}, propose algorithms working in a
+periodic fashion where a cover set is computed at the beginning of each period.
+{\it Motivated by these works, DiLCO protocol works in periods, where each
+ period contains a preliminary phase for information exchange and decisions,
+ followed by a sensing phase where one cover set is in charge of the sensing
+ task.}
+
+Various approaches, including centralized, or distributed algorithms, have been
+proposed to extend the network lifetime. In distributed
+algorithms~\cite{yangnovel,ChinhVu,qu2013distributed}, information is
+disseminated throughout the network and sensors decide cooperatively by
+communicating with their neighbors which of them will remain in sleep mode for a
+certain period of time. The centralized
algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
provide nearly or close to optimal solution since the algorithm has global view
of the whole network. But such a method has the disadvantage of requiring high
communication costs, since the node (located at the base station) making the
-decision needs information from all the sensor nodes in the area and the amount of information can be huge.
-{\it In order to be suitable for large-scale network, in the DiLCO protocol, the area coverage is divided into several smaller
- subregions, and in each one, a node called the leader is in charge for
+decision needs information from all the sensor nodes in the area and the amount
+of information can be huge. {\it In order to be suitable for large-scale
+ network, in the DiLCO protocol, the area coverage is divided into several
+ smaller subregions, and in each one, a node called the leader is in charge for
selecting the active sensors for the current period.}
+% MODIF - BEGIN
+\textcolor{blue}{ Our approach to select the leader node in a subregion is quite
+ different from cluster head selection methods used in LEACH
+ \cite{DBLP:conf/hicss/HeinzelmanCB00} or its variants
+ \cite{ijcses11}. Contrary to LEACH, the division of the area of interest is
+ supposed to be performed before the leader election. Moreover, we assume that
+ the sensors are deployed almost uniformly and with high density over the area
+ of interest, such that the division is fixed and regular. As in LEACH, our
+ protocol works in round fashion. In each round, during the pre-sensing phase,
+ nodes make autonomous decisions. In LEACH, each sensor elects itself to be a
+ cluster head, and each non-cluster head will determine its cluster for the
+ round. In our protocol, nodes in the same subregion select their leader. In
+ both protocols, the amount of remaining energy in each node is taken into
+ account to promote the nodes that have the most energy to become leader.
+ Contrary to the LEACH protocol where all sensors will be active during the
+ sensing-phase, our protocol allows to deactivate a subset of sensors through
+ an optimization process which reduces significantly the energy consumption.}
+% MODIF - END
+
A large variety of coverage scheduling algorithms has been developed. Many of
the existing algorithms, dealing with the maximization of the number of cover
sets, are heuristics. These heuristics involve the construction of a cover set
by including in priority the sensor nodes which cover critical targets, that is
-to say targets that are covered by the smallest number of sensors \cite{berman04,zorbas2010solving}. Other
-approaches are based on mathematical programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014} and dedicated
-techniques (solving with a branch-and-bound algorithms available in optimization
-solver). The problem is formulated as an optimization problem (maximization of
-the lifetime or number of cover sets) under target coverage and energy
-constraints. Column generation techniques, well-known and widely practiced
-techniques for solving linear programs with too many variables, have also been
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In DiLCO protocol, each leader, in each subregion, solves an integer
- program with a double objective consisting in minimizing the overcoverage and
- limiting the undercoverage. This program is inspired from the work of
- \cite{pedraza2006} where the objective is to maximize the number of cover
- sets.}
-
+to say targets that are covered by the smallest number of sensors
+\cite{berman04,zorbas2010solving}. Other approaches are based on mathematical
+programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
+and dedicated techniques (solving with a branch-and-bound algorithms available
+in optimization solver). The problem is formulated as an optimization problem
+(maximization of the lifetime or number of cover sets) under target coverage and
+energy constraints. Column generation techniques, well-known and widely
+practiced techniques for solving linear programs with too many variables, have
+also been
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In DiLCO
+ protocol, each leader, in each subregion, solves an integer program with a
+ double objective consisting in minimizing the overcoverage and limiting the
+ undercoverage. This program is inspired from the work of \cite{pedraza2006}
+ where the objective is to maximize the number of cover sets.}
\section{\uppercase{Description of the DiLCO protocol}}
\label{sec:The DiLCO Protocol Description}
preservation and energy conservation, applied periodically to efficiently
maximize the lifetime in the network.
-
\subsection{Assumptions and models}
\noindent We consider a sensor network composed of static nodes distributed
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
+Hou~\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.
primary points are covered. Obviously, the approximation of coverage is more or
less accurate according to the number of primary points.
-
\subsection{Main idea}
\label{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.
+executed simultaneously in each subregion. \textcolor{blue}{Sensor nodes are
+ assumed to be deployed almost uniformly over the region and the subdivision of
+ the area of interest is regular.}
\begin{figure}[ht!]
\centering
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
+interesting because it enhances the robustness of the network against node failures.
+% \textcolor{blue}{Many WSN applications have communication requirements that are periodic and known previously such as collecting temperature statistics at regular intervals. This periodic nature can be used to provide a regular schedule to sensor nodes and thus avoid a sensor failure. If the period time increases, the reliability and energy consumption are decreased and vice versa}.
+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
\end{itemize}
%\end{enumerate}
-An outline of the protocol implementation is given by Algorithm~\ref{alg:DiLCO}
+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.
-
+sensor node indexed by $j$). At the beginning a node checks whether it has
+enough energy \textcolor{blue}{(its energy should be greater than a fixed
+ treshold $E_{th}$)} 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. \textcolor{blue}{INFO
+ packet contains two parts: header and data payload. The sensor ID is included
+ in the header, where the header size is 8 bits. The data part includes
+ position coordinates (64 bits), remaining energy (32 bits), and the number of
+ one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112
+ bits.} 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 solve an integer program (see Section~\ref{cp}). \textcolor{blue}{This
+ integer program contains boolean variables $X_j$ where ($X_j=1$) means that
+ sensor $j$ will be active in the next sensing phase. Only sensors with enough
+ remaining energy are involved in the integer program ($J$ is the set of all
+ sensors involved). As the leader consumes energy (computation energy is
+ denoted by $E^{comp}$) to solve the optimization problem, it will be included
+ in the integer program only if it has enough energy to achieve the computation
+ and to stay alive during the next sensing phase, that is to say if $RE_j >
+ E^{comp}+E_{th}$. Once the optimization problem is solved, each leader will
+ send an ActiveSleep packet to each sensor in the same subregion to indicate it
+ if it has to be active or not. Otherwise, if the sensor is not the leader, it
+ will wait for the ActiveSleep packet to know its state for the coming sensing
+ phase.}
+%which provides a set of sensors planned to be
+%active in the next sensing phase.
\begin{algorithm}[h!]
\section{\uppercase{Coverage problem formulation}}
\label{cp}
+% MODIF - BEGIN
+We formulate the coverage optimization problem with an integer program.
+The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}.
+The area coverage problem is expressed as the coverage of a fraction of points called primary points.
+Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
+and the set of alive sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of active sensors that cover the primary point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :
+\begin{equation}
+ \Theta_{p} = \left \{
+\begin{array}{l l}
+ 0 & \mbox{if the primary point}\\
+ & \mbox{$p$ is not covered,}\\
+ \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq13}
+\end{equation}
+More precisely, $\Theta_{p}$ represents the number of active sensor
+nodes minus one that cover the primary point~$p$.
+In the same way, we define the undercoverage variable
+$U_{p}$ of the primary point $p$ as:
+\begin{equation}
+U_{p} = \left \{
+\begin{array}{l l}
+ 1 &\mbox{if the primary point $p$ is not covered,} \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq14}
+\end{equation}
+There is, of course, a relationship between the three variables $X_j$, $\Theta_p$, and $U_p$ which can be formulated as follows :
+\begin{equation}
+\sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, \forall p \in P
+\end{equation}
+If the point $p$ is not covered, $U_p=1$, $\sum_{j \in J} \alpha_{jp} X_{j}=0$ and $\Theta_{p}=0$ by definition, so the equality is satisfied.
+On the contrary, if the point $p$ is covered, $U_p=0$, and $\Theta_{p}=\left( \sum_{j \in J} \alpha_{jp} X_{j} \right)- 1$.
+\noindent Our coverage optimization problem can then be formulated as follows:
+\begin{equation} \label{eq:ip2r}
+\left \{
+\begin{array}{ll}
+\min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
+\textrm{subject to :}&\\
+\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 \\
+%\label{c2}
+\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}
+The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage. \textcolor{blue}{ By
+ choosing $w_{U}$ much larger than $w_{\theta}$, the coverage of a
+ maximum of primary points is ensured. Then for the same number of covered
+ primary points, the solution with a minimal number of active sensors is
+ preferred. }
+%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.
+% MODIF - END
+
+\iffalse
+
\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
order to guarantee that the maximum number of points are covered during each
period.
+\fi
+
\section{\uppercase{Protocol evaluation}}
\label{sec:Simulation Results and Analysis}
\noindent \subsection{Simulation framework}
1-bit-content message defined in~\cite{raghunathan2002energy} (we assume
symmetric communication costs), and we set their respective size to 112 and
24~bits. The energy required to send or receive a 1-bit-content message is thus
- equal to 0.2575 mW.
-
-Each node has an initial energy level, in Joules, which is randomly drawn in the
-interval $[500-700]$. If its energy provision reaches a value below the
-threshold $E_{th}=36$~Joules, the minimum energy needed for a node to stay
-active during one period, it will no longer take part in the coverage task. This
-value corresponds to the energy needed by the sensing phase, obtained by
-multiplying the energy consumed in active state (9.72 mW) by the time in seconds
-for one period (3,600 seconds), and adding the energy for the pre-sensing phases.
+ equal to 0.2575~mW.
+
+Each node has an initial energy level, in Joules, which is randomly drawn in
+$[500-700]$. If its energy provision reaches a value below the threshold
+$E_{th}=36$~Joules, the minimum energy needed for a node to stay active during
+one period, it will no longer take part in the coverage task. This value
+corresponds to the energy needed by the sensing phase, obtained by multiplying
+the energy consumed in active state (9.72 mW) by the time in seconds for one
+period (3,600 seconds), and adding the energy for the pre-sensing phases.
According to the interval of initial energy, a sensor may be active during at
most 20 periods.
\times 26 = 1326$ grid points.
\item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
- total amount of energy consumed by the sensors during $Lifetime_{95}$ or
- $Lifetime_{50}$, divided by the number of periods. Formally, the computation
+ total amount of energy consumed by the sensors during $Lifetime_{95}$
+ or $Lifetime_{50}$, divided by the number of periods. Formally, the computation
of EC can be expressed as follows:
\begin{equation*}
\scriptsize
+ 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 (active and sleeping nodes).
-
+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
+(active and sleeping nodes).
\end{itemize}
%\end{enumerate}
-
%\subsection{Performance Analysis for different subregions}
\subsection{Performance analysis}
\label{sub1}
\subsubsection{Coverage ratio}
Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. It
-can be seen that both DESK and GAF provide a coverage ratio which is slightly better
-compared to DiLCO in the first thirty periods. This can be easily explained by
-the number of active nodes: the optimization process of our protocol activates
-less nodes than DESK or GAF, resulting in a slight decrease of the coverage
-ratio. In case of DiLCO-2 (respectively DiLCO-4), the coverage ratio exhibits a
-fast decrease with the number of periods and reaches zero value in period~18
-(respectively 46), whereas the other versions of DiLCO, DESK, and GAF ensure a
-coverage ratio above 50\% for subsequent periods. We believe that the results
-obtained with these two methods can be explained by a high consumption of energy
-and we will check this assumption in the next subsection.
+can be seen that both DESK and GAF provide a coverage ratio which is slightly
+better compared to DiLCO in the first thirty periods. This can be easily
+explained by the number of active nodes: the optimization process of our
+protocol activates less nodes than DESK or GAF, resulting in a slight decrease
+of the coverage ratio. In case of DiLCO-2 (respectively DiLCO-4), the coverage
+ratio exhibits a fast decrease with the number of periods and reaches zero value
+in period~18 (respectively 46), whereas the other versions of DiLCO, DESK, and
+GAF ensure a coverage ratio above 50\% for subsequent periods. We believe that
+the results obtained with these two methods can be explained by a high
+consumption of energy and we will check this assumption in the next subsection.
Concerning DiLCO-8, DiLCO-16, and DiLCO-32, these methods seem to be more
efficient than DESK and GAF, since they can provide the same level of coverage
\parskip 0pt
\begin{figure}[t!]
\centering
- \includegraphics[scale=0.45] {R/CR.pdf}
+ \includegraphics[scale=0.475] {CR.pdf}
\caption{Coverage ratio}
\label{fig3}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/EC.pdf}
+\includegraphics[scale=0.475]{EC.pdf}
\caption{Energy consumption per period}
\label{fig95}
\end{figure}
protocol. Indeed, the protocols DiLCO-16/50, DiLCO-32/50, DiLCO-16/95, and
DiLCO-32/95 consume less energy than their DESK and GAF counterparts for a
similar level of area coverage. This observation reflects the larger number of
-nodes set active by DESK and GAF.
+nodes set active by DESK and GAF.
+
+Now, if we consider a same protocol, we can notice that the average consumption
+per period increases slightly for our protocol when increasing the level of
+coverage and the number of node, whereas it increases more largely for DESK and
+GAF. In case of DiLCO, it means that even if a larger network allows to improve
+the number of periods with a minimum coverage level value, this improvement has
+a higher energy cost per period due to communication overhead and a more
+difficult optimization problem. However, in comparison with DESK and GAF, our
+approach has a reasonable energy overcost.
\subsubsection{Execution time}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/T.pdf}
+\includegraphics[scale=0.475]{T.pdf}
\caption{Execution time in seconds}
\label{fig8}
\end{figure}
Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison
-with other DiLCO versions, because the activity scheduling is tackled by a
+with other DiLCO versions, because the activity scheduling is tackled by a
larger number of leaders and each leader solves an integer problem with a
limited number of variables and constraints. Conversely, DiLCO-2 requires to
solve an optimization problem with half of the network nodes and thus presents a
high execution time. Nevertheless if we refer to Figure~\ref{fig3}, we observe
that DiLCO-32 is slightly less efficient than DilCO-16 to maintain as long as
-possible high coverage. In fact an excessive subdivision of the area of interest
-prevents it to ensure a good coverage especially on the borders of the
+possible high coverage. In fact an excessive subdivision of the area of interest
+prevents it to ensure a good coverage especially on the borders of the
subregions. Thus, the optimal number of subregions can be seen as a trade-off
between execution time and coverage performance.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/LT.pdf}
+\includegraphics[scale=0.475]{LT.pdf}
\caption{Network lifetime}
\label{figLT95}
\end{figure}
As highlighted by Figure~\ref{figLT95}, when the coverage level is relaxed
($50\%$) the network lifetime also improves. This observation reflects the fact
that the higher the coverage performance, the more nodes must be active to
-ensure the wider monitoring. For a similar level of coverage, DiLCO outperforms
+ensure the wider monitoring. For a similar level of coverage, DiLCO outperforms
DESK and GAF for the lifetime of the network. More specifically, if we focus on
-the larger level of coverage ($95\%$) in the case of our protocol, the subdivision
-in $16$~subregions seems to be the most appropriate.
+the larger level of coverage ($95\%$) in the case of our protocol, the
+subdivision in $16$~subregions seems to be the most appropriate.
\section{\uppercase{Conclusion and future work}}
\label{sec:Conclusion and Future Works}
-A crucial problem in WSN is to schedule the sensing activities of the different
-nodes in order to ensure both coverage of the area of interest and longer
+A crucial problem in WSN is to schedule the sensing activities of the different
+nodes in order to ensure both coverage of the area of interest and longer
network lifetime. The inherent limitations of sensor nodes, in energy provision,
-communication and computing capacities, require protocols that optimize the use
-of the available resources to fulfill the sensing task. To address this
-problem, this paper proposes a two-step approach. Firstly, the field of sensing
+communication and computing capacities, require protocols that optimize the use
+of the available resources to fulfill the sensing task. To address this
+problem, this paper proposes a two-step approach. Firstly, the field of sensing
is divided into smaller subregions using the concept of divide-and-conquer
method. Secondly, a distributed protocol called Distributed Lifetime Coverage
-Optimization is applied in each subregion to optimize the coverage and lifetime
-performances. In a subregion, our protocol consists in electing a leader node
+Optimization is applied in each subregion to optimize the coverage and lifetime
+performances. In a subregion, our protocol consists in electing a leader node
which will then perform a sensor activity scheduling. The challenges include how
-to select the most efficient leader in each subregion and the best
+to select the most efficient leader in each subregion and the best
representative set of active nodes to ensure a high level of coverage. To assess
the performance of our approach, we compared it with two other approaches using
-many performance metrics like coverage ratio or network lifetime. We have also
-studied the impact of the number of subregions chosen to subdivide the area of
+many performance metrics like coverage ratio or network lifetime. We have also
+studied the impact of the number of subregions chosen to subdivide the area of
interest, considering different network sizes. The experiments show that
-increasing the number of subregions improves the lifetime. The more subregions there are, the more robust the network is against random disconnection
-resulting from dead nodes. However, for a given sensing field and network size
-there is an optimal number of subregions. Therefore, in case of our simulation
-context a subdivision in $16$~subregions seems to be the most relevant. The
-optimal number of subregions will be investigated in the future.
+increasing the number of subregions improves the lifetime. The more subregions
+there are, the more robust the network is against random disconnection resulting
+from dead nodes. However, for a given sensing field and network size there is
+an optimal number of subregions. Therefore, in case of our simulation context a
+subdivision in $16$~subregions seems to be the most relevant. The optimal number
+of subregions will be investigated in the future.
\section*{\uppercase{Acknowledgements}}
the Labex ACTION program (contract ANR-11-LABX-01-01).
%\vfill
-\bibliographystyle{apalike}
+\bibliographystyle{plain}
{\small
\bibliography{Example}}
