\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-Comte, Belfort, France}
+\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}
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
- sensor network. As a first step 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 election in each subregion, followed by an
- optimization-based node activity 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 result 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. }
+ 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
+ election in each subregion, followed by an optimization-based node activity
+ 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. }
\onecolumn \maketitle \normalsize \vfill
\section{\uppercase{Introduction}}
\label{sec:introduction}
+
\noindent
Energy efficiency is a crucial issue in wireless sensor networks since sensory
-consumption, in order to maximize the network lifetime, represent the major
+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
-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. 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.
+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
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.
+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
+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 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
+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 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 further work
+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 coverage lifetime maximization and scheduling, and distinguish our DiLCO protocol from the works presented in the literature. Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
+
+\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
+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.
+%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
+%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}.
+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
+ selecting the active sensors for the current period.}
+
+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.}
+
+% ***** Part which must be rewritten - Start
+
+% Start of Ali's papers catalog => there's no link between them or with our work
+% (use of subregions; optimization based method; etc.)
+\iffalse
+Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep
+scheduling algorithm for lifetime maximization in wireless sensor networks
+(ALARM). The proposed approach permits to schedule redundant nodes according to
+the weibull distribution. This work did not analyze the ALARM scheme under the
+coverage problem.
+
+Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be
+changed into a set coverage problem. By using this model, they proposed an
+Energy-Efficient central-Scheduling greedy algorithm, which can reduces energy
+consumption and increases network lifetime, by selecting a appropriate subset of
+sensor nodes to support the networks periodically.
+
+In ~\cite{chenait2013distributed}, the authors presented a coverage-guaranteed
+distributed sleep/wake scheduling scheme so ass to prolong network lifetime
+while guaranteeing network coverage. This scheme mitigates scheduling process to
+be more stable by avoiding useless transitions between states without affecting
+the coverage level required by the application.
+
+The work in~\cite{cheng2014achieving} presented a unified sensing architecture
+for duty cycled sensor networks, called uSense, which comprises three ideas:
+Asymmetric Architecture, Generic Switching and Global Scheduling. The objective
+is to provide a flexible and efficient coverage in sensor networks.
+
+In~\cite{ling2009energy}, the lifetime of a sensor node is divided into
+epochs. At each epoch, the base station deduces the current sensing coverage
+requirement from application or user request. It then applies the heuristic
+algorithm in order to produce the set of active nodes which take the mission of
+sensing during the current epoch. After that, the produced schedule is sent to
+the sensor nodes in the network.
+
+% What is the link between the previous work and this paragraph about DiLCO ?
+
+
+
+Yang et al.~\cite{yang2014energy} investigated full area coverage problem under
+the probabilistic sensing model in the sensor networks. They have studied the
+relationship between the coverage of two adjacent points mathematically and then
+convert the problem of full area coverage into point coverage problem. They
+proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select
+a subset of sensors to provide probabilistic area coverage dynamically so as to
+extend the network lifetime.
+
+The work proposed by \cite{qu2013distributed} considers the coverage problem in
+WSNs where each sensor has variable sensing radius. The final objective is to
+maximize the network coverage lifetime in WSNs.
+\fi
+% Same remark, no link with the two previous citations...
+
+
+% ***** Part which must be rewritten - End
+
+\iffalse
+
+Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
Yang et al.~\cite{yang2014energy} investigated full area coverage problem
a sensor node is divided into epochs. At each epoch, the
base station deduces the current sensing coverage requirement
from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch. After that, the produced schedule is sent to the sensor nodes in the network.
-
+\fi
\iffalse
achieve increased sensing lifetime of the network.
-\fi
+
The main contributions of our DiLCO Protocol can be summarized as follows:
(1) The distributed optimization over the subregions in the area of interest,
-(2) The distributed dynamic leader election at each round by each sensor node in the subregion,
+(2) The distributed dynamic leader election at each period by each sensor node in the subregion,
(3) The primary point coverage model to represent each sensor node in the network,
(4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion, and (5) The improved energy consumption model.
-
+\fi
\iffalse
The work presented in~\cite{luo2014parameterized,tian2014distributed} tries to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
%Je ne comprends pas la phrase ci-dessus
The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
-\fi
-\iffalse
+
+
Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to extend the network lifetime with connectivity and coverage constraints. They are included two heuristic methods within the CG framework so as to accelerate the solution process.
In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution taking into consideration frequent nodes failure.
Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
\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
+coverage ratio of the interested area at the start. 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
\fi
-\subsection{The main idea}
+\subsection{Main idea}
\label{main_idea}
\noindent We start by applying a divide-and-conquer algorithm to partition the
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
+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
+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.
-During the execution of the DiLCO protocol, two kinds of packets will be used:
+During the execution of the DiLCO protocol, two kinds of packet 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 stay Active or to go Sleep during the sensing phase.
+ to inform them to stay Active or to go Sleep during the sensing phase.
\end{itemize}
%\end{enumerate}
and each sensor node will have five possible status in the network:
\end{algorithm}
\iffalse
-The DiLCO protocol work in rounds and executed at each sensor node in the network , each sensor node can still sense data while being in
+The DiLCO protocol work in rounds and executed at each sensor node in the network, each sensor node can still sense data while being in
LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow:
Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
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
+model, we consider that the binary variable $X_{j}$ determines 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 $J$.
\end{array} \right.
\label{eq13}
\end{equation}
-\noindent More precisely, $\Theta_{p}$ represents the number of active
-sensor nodes minus one that cover the primary point $p$.\\
-The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
-by:
+\noindent More precisely, $\Theta_{p}$ represents the number of active sensor
+nodes minus one that cover the primary point~$p$. The Undercoverage variable
+$U_{p}$ of the primary point $p$ is defined by:
\begin{equation}
U_{p} = \left \{
\begin{array}{l l}
%\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\\
+\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}
ATmega103L in case of Medusa II, to perform the computations; a communication
(radio) 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
+all the other unit can 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.
receive such packets, we use the equation giving the energy spent to send a
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 is equal to $0.2575 mW$.
+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 it's energy provision reaches a value below
-$E_{th}=36$~Joules, the minimum energy needed for a node to stay active during
-one period, it will no more participate in the coverage task. 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 active during at most 20 rounds.
+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.
+According to the interval of initial energy, a sensor may be active 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}
+\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
+ the coverage ratio drops below a predefined threshold. We denote by
+ $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
+ the network can satisfy an area coverage greater than $95\%$ (respectively
+ $50\%$). We assume that the sensor network can fulfill its task until all its
+ nodes have been drained of their energy or it becomes disconnected. Network
+ connectivity is crucial because an active sensor node without connectivity
+ towards a base station cannot transmit any information regarding an observed
+ event in the area that it monitors.
+
\item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to
observe the area of interest. In our case, we discretized the sensor field
as a regular grid, which yields the following equation to compute the
\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
\end{equation*}
where $n$ is the number of covered grid points by active sensors of every
-subregions during the current sensing phase and $N$ is total number of grid
+subregions during the current sensing phase and $N$ is the total number of grid
points in the sensing field. In our simulations, we have a layout of $N = 51
\times 26 = 1326$ grid points.
%The accuracy of this method depends on the distance between grids. In our
\fi
\item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
- total energy consumed by the sensors during $Lifetime_{95}$ or
+ 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*}
+ E^{a}_m+E^{s}_m \right)}{M},
\end{equation*}
-where $M$ corresponds to the number of periods. The total energy consumed by
+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 $E^{\scriptsize \mbox{com}}_m$, represent the
+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
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 Network Lifetime}:} we define the network lifetime as the time until
- the coverage ratio drops below a predefined threshold. We denote by
- $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
- the network can satisfy an area coverage greater than $95\%$ (respectively
- $50\%$). We assume that the sensor network can fulfill its task until all its
- nodes have been drained of their energy or it becomes disconnected. Network
- connectivity is crucial because an active sensor node without connectivity
- towards a base station cannot transmit any information regarding an observed
- event in the area that it monitors.
\iffalse
-\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.
+\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.
-\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.
+\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.
\fi
different numbers of subregions. We consider partitions of the WSN area into
$2$, $4$, $8$, $16$, and $32$ subregions. Thus the DiLCO protocol is declined in
five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32. Simulations
-without partitioning the area of interest, case which corresponds to a
+without partitioning the area of interest, cases which correspond to a
centralized approach, are not presented because they require high execution
times to solve the integer program and therefore consume too much energy.
\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 little better coverage ratio
+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 {\bf
- X} (respectively {\bf Y}), 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.
+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
(except in the first periods where DESK and GAF slightly outperform them) for a
greater number of periods. In fact, when our protocol is applied with a large
number of subregions (from 8 to 32~regions), it activates a restricted number of
-nodes, and thus allow to extend the network lifetime.
+nodes, and thus enables the extension of the network lifetime.
\parskip 0pt
\begin{figure}[t!]
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 excessive subdivision of the area of interest
-prevents to ensure 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.
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 same 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 case of our protocol, the subdivision
+the larger level of coverage ($95\%$) in the case of our protocol, the subdivision
in $16$~subregions seems to be the most appropriate.
% with our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
\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 longest
+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
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 to elect a leader node
+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
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
-study the impact of the number of subregions chosen to subdivide the area of
+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 allows to improves the lifetime. The more
-there are subregions, the more the network is robust 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.
\iffalse
\noindent In this paper, we have addressed the problem of the coverage and the lifetime
\section*{\uppercase{Acknowledgements}}
-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
+\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
acknowledge the University of Babylon - IRAQ for the financial support and
-Campus France for the received support.
+Campus France for the received support. This paper is also partially funded by
+the Labex ACTION program (contract ANR-11-LABX-01-01).
%\vfill
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