\DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
\begin{document}
-\title{Lifetime Coverage Optimization Protocol \\
- in Wireless Sensor Networks} %LiCO Protocol
+%\title{Lifetime Coverage Optimization Protocol \\
+% in Wireless Sensor Networks}
+\title{Perimeter-based Coverage Optimization to Improve \\
+ Lifetime in Wireless Sensor Networks}
\author{Ali Kadhum Idrees,~\IEEEmembership{}
Karine Deschinkel,~\IEEEmembership{}
Michel Salomon,~\IEEEmembership{}
and~Rapha\"el Couturier ~\IEEEmembership{}
- \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,
+ \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
\maketitle
\begin{abstract}
-The most important problem in Wireless Sensor Networks (WSNs) is to optimize the
+The most important problem in a Wireless Sensor Network (WSN) is to optimize the
use of its limited energy provision, so that it can fulfill its monitoring task
as long as possible. Among known available approaches that can be used to
improve power management, lifetime coverage optimization provides activity
scheduling which ensures sensing coverage while minimizing the energy cost. In
-this paper, we propose a such approach called Lifetime Coverage Optimization
+this paper, we propose such an approach called Lifetime Coverage Optimization
protocol (LiCO). It is a hybrid of centralized and distributed methods: the
region of interest is first subdivided into subregions and our protocol is then
-distributed among sensor nodes in each subregion. A sensor node which runs LiCO
-protocol repeats periodically four stages: information exchange, leader
-election, optimization decision, and sensing. More precisely, the scheduling of
-nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
-leader selected after cooperation between nodes within the same subregion. The
-novelty of approach lies essentially in the formulation of a new mathematical
-optimization model based on perimeter coverage level to schedule sensors'
-activities. Extensive simulation experiments have been performed using OMNeT++,
-the discrete event simulator, to demonstrate that LiCO is capable to offer
-longer lifetime coverage for WSNs in comparison with some other protocols.
+distributed among sensor nodes in each subregion.
+% A sensor node which runs LiCO protocol repeats periodically four stages:
+%information exchange, leader election, optimization decision, and sensing.
+%More precisely, the scheduling of nodes' activities (sleep/wake up duty cycles)
+%is achieved in each subregion by a leader selected after cooperation between
+%nodes within the same subregion.
+The novelty of our approach lies essentially in the formulation of a new
+mathematical optimization model based on perimeter coverage level to schedule
+sensors' activities. Extensive simulation experiments have been performed using
+OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to
+offer longer lifetime coverage for WSNs in comparison with some other protocols.
\end{abstract}
% Note that keywords are not normally used for peerreview papers.
can send the data it collects in its environment, thanks to its sensor, to the
user by means of sink nodes. The features of a WSN made it suitable for a wide
range of application in areas such as business, environment, health, industry,
-military, and son~\cite{yick2008wireless}. Typically, a sensor node contains
+military, and so on~\cite{yick2008wireless}. Typically, a sensor node contains
three main components~\cite{anastasi2009energy}: a sensing unit able to measure
physical, chemical, or biological phenomena observed in the environment; a
processing unit which will process and store the collected measurements; a radio
This paper makes the following contributions.
\begin{enumerate}
-\item We devise a framework to schedule nodes to be activated alternatively such
+\item We have devised a framework to schedule nodes to be activated alternatively such
that the network lifetime is prolonged while ensuring that a certain level of
- coverage is preserved. A key idea in our framework is to exploit spatial an
- temporal subdivision. On the one hand the area of interest if divided into
- several smaller subregions and on the other hand the time line is divided into
+ coverage is preserved. A key idea in our framework is to exploit spatial and
+ temporal subdivision. On the one hand, the area of interest if divided into
+ several smaller subregions and, on the other hand, the time line is divided into
periods of equal length. In each subregion the sensor nodes will cooperatively
choose a leader which will schedule nodes' activities, and this grouping of
sensors is similar to typical cluster architecture.
-\item We propose a new mathematical optimization model. Instead of trying to
+\item We have proposed a new mathematical optimization model. Instead of trying to
cover a set of specified points/targets as in most of the methods proposed in
the literature, we formulate an integer program based on perimeter coverage of
each sensor. The model involves integer variables to capture the deviations
- between the actual level of coverage and the required level. So that an
+ between the actual level of coverage and the required level. Hence, an
optimal scheduling will be obtained by minimizing a weighted sum of these
deviations.
-\item We conducted extensive simulation experiments, using the discrete event
- simulator OMNeT++, to demonstrate the efficiency of our protocol. We compared
+\item We have conducted extensive simulation experiments, using the discrete event
+ simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
our LiCO protocol to two approaches found in the literature:
DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous
work published in~\cite{Idrees2} which is based on another optimization model
coverage model formulation which is used to schedule the activation of sensor
nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
results and discusses the comparison with other approaches. Finally, concluding
-remarks are drawn and some suggestions given for future works in
+remarks are drawn and some suggestions are given for future works in
Section~\ref{sec:Conclusion and Future Works}.
% that show that our protocol outperforms others protocols.
The most discussed coverage problems in literature can be classified in three
categories~\cite{li2013survey} according to their respective monitoring
objective. Hence, area coverage \cite{Misra} means that every point inside a
-fixed area must be monitored, while target coverage~\cite{yang2014novel} refer
+fixed area must be monitored, while target coverage~\cite{yang2014novel} refers
to the objective of coverage for a finite number of discrete points called
targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on
preventing intruders from entering into the region of interest. In
sensors are sufficiently covered it will be the case for the whole area. They
provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
each sensor, where $d$ denotes the maximum number of sensors that are
-neighboring to a sensor and $n$ is the total number of sensors in the
+neighbors to a sensor and $n$ is the total number of sensors in the
network. {\it In LiCO protocol, instead of determining the level of coverage of
a set of discrete points, our optimization model is based on checking the
perimeter-coverage of each sensor to activate a minimal number of sensors.}
decisions, followed by a sensing phase where one cover set is in charge of the
sensing task.}
-Various centralized and distributed approaches, or even a mixing of these two
+Various centralized and distributed approaches, or even a mixing of these two
concepts, have been proposed to extend the network lifetime. In distributed
-algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensors decides of
-its own activity scheduling after an information exchange with its neighbors.
-The main interest of a such approach is to avoid long range communications and
-thus to reduce the energy dedicated to the communications. Unfortunately, since
-each node has only information on its immediate neighbors (usually the one-hop
-ones) it may take a bad decision leading to a global suboptimal solution.
-Conversely, centralized
-algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
+algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
+own activity scheduling after an information exchange with its neighbors. The
+main interest of such an approach is to avoid long range communications and thus
+to reduce the energy dedicated to the communications. Unfortunately, since each
+node has only information on its immediate neighbors (usually the one-hop ones)
+it may take a bad decision leading to a global suboptimal solution. Conversely,
+centralized
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
provide nearly or close to optimal solution since the algorithm has a global
view of the whole network. The disadvantage of a centralized method is obviously
-its high cost in communications needed to transmit to a single node, the base
-station which will globally schedule nodes' activities, data from all the other
-sensor nodes in the area. The price in communications can be very huge since
-long range communications will be needed. In fact the larger the WNS, the higher
-the communication and thus energy cost. {\it In order to be suitable for
- large-scale networks, in the LiCO protocol the area of interest 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. Thus our
- protocol is scalable and a globally distributed method, whereas it is
- centralized in each subregion.}
+its high cost in communications needed to transmit to a single node, the base
+station which will globally schedule nodes' activities, data from all the other
+sensor nodes in the area. The price in communications can be very huge since
+long range communications will be needed. In fact the larger the WNS is, the
+higher the communication and thus the energy cost are. {\it In order to be
+ suitable for large-scale networks, in the LiCO protocol, the area of interest
+ is divided into several smaller subregions, and in each one, a node called the
+ leader is in charge of selecting the active sensors for the current
+ period. Thus our protocol is scalable and is a globally distributed method,
+ whereas it is centralized in each subregion.}
Various coverage scheduling algorithms have been developed this last years.
Many of them, dealing with the maximization of the number of cover sets, are
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 LiCO
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the LiCO
protocol, each leader, in charge of a subregion, solves an integer program
which has a twofold objective: minimize the overcoverage and the undercoverage
of the perimeter of each sensor.}
proved that if the transmission range fulfills the previous hypothesis, a
complete coverage of a convex area implies connectivity among active nodes.
-\indent LiCO protocol uses the same perimeter-coverage model than Huang and
+The LiCO protocol uses the same perimeter-coverage model as Huang and
Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is
said to be perimeter covered if all the points on its perimeter are covered by
at least one sensor other than itself. They proved that a network area is
-$k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
+$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
%According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model.
Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this
figure, we can see that sensor~$0$ has nine neighbors and we have reported on
\begin{figure}[ht!]
\centering
\begin{tabular}{@{}cr@{}}
- \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)}
- \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
+ \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} \\
+ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
\end{tabular}
- \caption{Perimeter coverage of sensor node 0 (a) and finding the arc of $u$'s
- perimeter covered by $v$.}
+ \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
+ $u$'s perimeter covered by $v$.}
\label{pcm2sensors}
\end{figure}
Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
locations of the left and right points of an arc on the perimeter of a sensor
-node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the
+node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
west side of sensor~$u$, with the following respective coordinates in the
sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
-obtained through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s}
-\right)$. So, the arc on the perimeter of node~$u$ defined by the angular
-interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
-node $v$.
+obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
+ - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
Every couple of intersection points is placed on the angular interval $[0,2\pi]$
in a counterclockwise manner, leading to a partitioning of the interval.
Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
-sensor $0$ and figure~\ref{expcm} gives the position of the corresponding arcs
+sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs
in the interval $[0,2\pi]$. More precisely, we can see that the points are
ordered according to the measures of the angles defined by their respective
positions. The intersection points are then visited one after another, starting
-from first intersection point after point~zero, and the maximum level of
+from the first intersection point after point~zero, and the maximum level of
coverage is determined for each interval defined by two successive points. The
maximum level of coverage is equal to the number of overlapping arcs. For
-example, between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
-(the value is highlighted in yellow at the bottom of figure~\ref{expcm}), which
-means that at most 2~neighbors can cover the perimeter in addition to node $0$.
+example,
+between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
+(the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which
+means that at most 2~neighbors can cover the perimeter in addition to node $0$.
Table~\ref{my-label} summarizes for each coverage interval the maximum level of
coverage and the sensor nodes covering the perimeter. The example discussed
above is thus given by the sixth line of the table.
%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
% to determine the level of the perimeter coverage for each left and right point of a segment.
-\begin{figure*}[ht!]
+\begin{figure*}[t!]
\centering
-\includegraphics[width=137.5mm]{expcm.pdf}
+\includegraphics[width=127.5mm]{expcm2.jpg}
\caption{Maximum coverage levels for perimeter of sensor node $0$.}
\label{expcm}
\end{figure*}
\fi
- \begin{table}[h]
+ \begin{table}[h!]
\caption{Coverage intervals and contributing sensors for sensor node 0.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
-\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in interval coverage\end{tabular}} \\ \hline
+\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline
0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
-In LiCO protocol, scheduling of sensor nodes' activities is formulated with an
+In the LiCO protocol, scheduling of sensor nodes' activities is formulated with an
integer program based on coverage intervals. The formulation of the coverage
optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
node has a part of its sensing range outside the WSN sensing field, as in
-figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
+Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
and the corresponding interval will not be taken into account by the
optimization algorithm.
-\begin{figure}[t!]
+\begin{figure}[h!]
\centering
\includegraphics[width=62.5mm]{ex4pcm.jpg}
\caption{Sensing range outside the WSN's area of interest.}
our protocol will be executed in a distributed way in each subregion
simultaneously to schedule nodes' activities for one sensing period.
-As shown in figure~\ref{fig2}, node activity scheduling is produced by our
+As shown in Figure~\ref{fig2}, node activity scheduling is produced by our
protocol in a periodic manner. Each period is divided into 4 stages: Information
(INFO) Exchange, Leader Election, Decision (the result of an optimization
problem), and Sensing. For each period there is exactly one set cover
responsible for the sensing task. Protocols based on a periodic scheme, like
LiCO, are more robust against an unexpected node failure. On the one hand, if
-node failure is discovered before taking the decision, the corresponding sensor
-node will not be considered by the optimization algorithm, and, on the other
+a node failure is discovered before taking the decision, the corresponding sensor
+node will not be considered by the optimization algorithm. On the other
hand, if the sensor failure happens 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
\begin{figure}[t!]
\centering
\includegraphics[width=80mm]{Model.pdf}
-\caption{LiCO protocol}
+\caption{LiCO protocol.}
\label{fig2}
\end{figure}
determine the activities scheduling;
\item ACTIVE: node is sensing;
\item SLEEP: node is turned off;
-\item COMMUNICATION: transmits or recevives packets.
+\item COMMUNICATION: transmits or receives packets.
\end{itemize}
%\end{enumerate}
%Below, we describe each phase in more details.
}
\emph{$s_k.status$ = COMMUNICATION}\;
- \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \;
+ \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;
\emph{Update $RE_k $}\;
}
\Else{
}
}
\Else { Exclude $s_k$ from entering in the current sensing stage}
-
-
\caption{LiCO($s_k$)}
\label{alg:LiCO}
-
\end{algorithm}
-In this algorithm, K.CurrentSize and K.PreviousSize refer to the current size
-and the previous size of the subnetwork in the subregion respectively. That
-means the number of sensor nodes which are still alive. Initially, the sensor
-node checks its remaining energy $RE_k$, which must be greater than a threshold
-$E_{th}$ in order to participate in the current period. Each sensor node
-determines its position and its subregion using an embedded GPS or a location
-discovery algorithm. After that, all the sensors collect position coordinates,
-remaining energy, sensor node ID, and the number of its one-hop live neighbors
-during the information exchange. The sensors inside a same region cooperate to
-elect a leader. The selection criteria for the leader, in order of priority,
-are: larger number of neighbors, larger remaining energy, and then in case of
-equality, larger index. Once chosen, the leader collects information to
-formulate and solve the integer program which allows to construct the set of
-active sensors in the sensing stage.
+In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
+current number and the previous number of alive nodes in the subnetwork of the
+subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
+must be greater than a threshold $E_{th}$ in order to participate in the current
+period. Each sensor node determines its position and its subregion using an
+embedded GPS or a location discovery algorithm. After that, all the sensors
+collect position coordinates, remaining energy, sensor node ID, and the number
+of their one-hop live neighbors during the information exchange. The sensors
+inside a same region cooperate to elect a leader. The selection criteria for the
+leader, in order of priority, are: larger number of neighbors, larger remaining
+energy, and then in case of equality, larger index. Once chosen, the leader
+collects information to formulate and solve the integer program which allows to
+construct the set of active sensors in the sensing stage.
%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
\end{itemize}
$I_j$ refers to the set of coverage intervals which have been defined according
to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
-let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved
+let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
in coverage interval~$i$ of sensor~$j$, that is:
\begin{equation}
a^j_{ik} = \left \{
lifetime, the objective is to activate a minimal number of sensors in each
period to ensure the desired coverage level. As the number of alive sensors
decreases, it becomes impossible to reach the desired level of coverage for all
-coverage intervals. Therefore we uses variables $M^j_i$ and $V^j_i$ as a measure
+coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure
of the deviation between the desired number of active sensors in a coverage
interval and the effective number. And we try to minimize these deviations,
first to force the activation of a minimal number of sensors to ensure the
$\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
relative importance of satisfying the associated level of coverage. For example,
weights associated with coverage intervals of a specified part of a region may
-be given a relatively larger magnitude than weights associated with another
+be given by a relatively larger magnitude than weights associated with another
region. This kind of integer program is inspired from the model developed for
brachytherapy treatment planning for optimizing dose distribution
\cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
network coverage and a longer WSN lifetime. We have given a higher priority for
the undercoverage (by setting the $\alpha^j_i$ with a larger value than
-$\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor
-j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so
-as to minimize the number of active sensor nodes which contribute in covering
-the interval.
+$\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
+sensor~$j$. On the other hand, we have given a little bit lower value for
+$\beta^j_i$ so as to minimize the number of active sensor nodes which contribute
+in covering the interval.
We introduce the following performance metrics to evaluate the efficiency of our
approach.
$Lifetime_{50}$ denote, respectively, the amount of time during which is
guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
fulfill the expected monitoring task until all its nodes have depleted their
- energy or if the network is not more connected. This last condition is crucial
+ energy or if the network is no more connected. This last condition is crucial
because without network connectivity a sensor may not be able to send to a
base station an event it has sensed.
-\item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to
+\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:
\begin{equation*}
\scriptsize
- \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
+ \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
- points in the sensing field. In our simulations we have set a layout of
+ points in the sensing field. In our simulations we have set a layout of
$N~=~51~\times~26~=~1326$~grid points.
-
- % MICHEL TO BE CONTINUED FROM HERE
-
-\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
-in order to minimize the communication overhead and maximize the
-network lifetime. The Active Sensors Ratio is defined as follows:
-\begin{equation*}
-\scriptsize
-\mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$S$}} \times 100 .
-\end{equation*}
-Where: $A_r^t$ is the number of active sensors in the subregion $r$ in the current sensing stage, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
-
-
-
-\item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
- total 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:
+\item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
+ activate nodes as few as possible, in order to minimize the communication
+ overhead and maximize the WSN lifetime. The active sensors ratio is defined as
+ follows:
\begin{equation*}
\scriptsize
- \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m
- + E^{a}_m+E^{s}_m \right)}{M},
+ \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
\end{equation*}
-
-where $M$ corresponds to the number of periods. The total 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
-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 $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
+ current sensing period~$p$, $|S|$ is the number of sensors in the network, and
+ $R$ is the number of subregions.
+\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
+ energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
+ divided by the number of periods. The value of EC is computed according to
+ this formula:
+ \begin{equation*}
+ \scriptsize
+ \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
+ + E^{a}_p+E^{s}_p \right)}{P},
+ \end{equation*}
+ where $P$ corresponds to the number of periods. The total energy consumed by
+ the sensors comes through taking into consideration four main energy
+ factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
+ energy consumption spent by all the nodes for wireless communications during
+ period $p$. $E^{\scriptsize \mbox{list}}_p$, 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 $p$. $E^{\scriptsize \mbox{comp}}_p$
+ refers to the energy needed by all the leader nodes to solve the integer
+ program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
+ consumed by the WSN during the sensing phase (active and sleeping nodes).
\end{itemize}
%\end{enumerate}
\subsection{Simulation Results}
-In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
-
-We compared LiCO protocol to three other approaches: the first, called DESK and proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm; the second, called GAF ~\cite{xu2001geography}, consists in dividing the region
-into fixed squares. During the decision phase, in each square, one sensor is
-chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
-\subsubsection{\textbf{Coverage Ratio}}
-Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
-
+In order to assess and analyze the performance of our protocol we have
+implemented LiCO protocol in OMNeT++~\cite{varga} simulator. Besides LiCO, two
+other protocols, described in the next paragraph, will be evaluated for
+comparison purposes. The simulations were run on a laptop DELL with an Intel
+Core~i3~2370~M (2.4~GHz) processor (2 cores) whose MIPS (Million Instructions
+Per Second) rate is equal to 35330. To be consistent with the use of a sensor
+node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate
+equal to 6, the original execution time on the laptop is multiplied by 2944.2
+$\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for
+Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer
+program instance in a standard format, which is then read and solved by the
+optimization solver GLPK (GNU linear Programming Kit available in the public
+domain) \cite{glpk} through a Branch-and-Bound method.
+
+As said previously, the LiCO is compared with three other approaches. The first
+one, called DESK, is a fully distributed coverage algorithm proposed by
+\cite{ChinhVu}. The second one, called GAF~\cite{xu2001geography}, consists in
+dividing the monitoring area into fixed squares. Then, during the decision
+phase, in each square, one sensor is chosen to remain active during the sensing
+phase. The last one, the DiLCO protocol~\cite{Idrees2}, is an improved version
+of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
+LiCO and DiLCO protocols are based on the same framework. In particular, the
+choice for the simulations of a partitioning in 16~subregions was chosen because
+it corresponds to the configuration producing the better results for DiLCO. The
+protocols are distinguished from one another by the formulation of the integer
+program providing the set of sensors which have to be activated in each sensing
+phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
+whereas LiCO protocol objective is to reach a desired level of coverage for each
+sensor perimeter. In our experimentations, we chose a level of coverage equal to
+one ($l=1$).
+
+\subsubsection{\bf Coverage Ratio}
+
+Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes
+obtained with the four protocols. DESK, GAF, and DiLCO provide a little better
+coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, against 98.76\%
+produced by LiCO for the first periods. This is due to the fact that at the
+beginning DiLCO protocol puts in sleep status more redundant sensors (which
+slightly decreases the coverage ratio), while the three other protocols activate
+more sensor nodes. Later, when the number of periods is beyond~70, it clearly
+appears that LiCO provides a better coverage ratio and keeps a coverage ratio
+greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
+compared to DESK). The energy saved by LiCO in the early periods allows later a
+substantial increase of the coverage performance.
+
\parskip 0pt
\begin{figure}[h!]
\centering
\includegraphics[scale=0.5] {R/CR.eps}
-\caption{The coverage ratio for 200 deployed nodes}
+\caption{Coverage ratio for 200 deployed nodes.}
\label{fig333}
\end{figure}
-DESK, GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
-
%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
%because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
-\subsubsection{\textbf{Active Sensors Ratio}}
-Having active nodes as few as possible in each period is essential in order to minimize the energy consumption and so maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 200 deployed nodes.
+\subsubsection{\bf Active Sensors Ratio}
+
+Having the less active sensor nodes in each period is essential to minimize the
+energy consumption and so maximize the network lifetime. Figure~\ref{fig444}
+shows the average active nodes ratio for 200 deployed nodes. We observe that
+DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
+rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and
+20.16 \% active nodes during the same time interval. As the number of periods
+increases, LiCO protocol has a lower number of active nodes in comparison with
+the three other approaches, while keeping a greater coverage ratio as shown in
+Figure \ref{fig333}.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/ASR.eps}
-\caption{The active sensors ratio for 200 deployed nodes }
+\caption{Active sensors ratio for 200 deployed nodes.}
\label{fig444}
\end{figure}
-We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, LiCO protocol has a lower number of active nodes in comparison with the three other approaches, while keeping of greater coverage ratio as shown in figure \ref{fig333}.
-
-\subsubsection{\textbf{The Energy Consumption}}
-We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it for the four approaches. Figures~\ref{fig3EC95} and \ref{fig3EC50} illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$.
+\subsubsection{\bf Energy Consumption}
+
+We study the effect of the energy consumed by the WSN during the communication,
+computation, listening, active, and sleep status for different network densities
+and compare it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
+illustrate the energy consumption for different network sizes and for
+$Lifetime95$ and $Lifetime50$. The results show that our LiCO protocol is the
+most competitive from the energy consumption point of view. As shown in both
+figures, LiCO consumes much less energy than the three other methods. One might
+think that the resolution of the integer program is too costly in energy, but
+the results show that it is very beneficial to lose a bit of time in the
+selection of sensors to activate. Indeed the optimization program allows to
+reduce significantly the number of active sensors and so the energy consumption
+while keeping a good coverage level.
\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/EC95.eps}
-\caption{The Energy Consumption per period with $Lifetime_{95}$}
-\label{fig3EC95}
-\end{figure}
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/EC50.eps}
-\caption{The Energy Consumption per period with $Lifetime_{50}$}
-\label{fig3EC50}
+ \centering
+ \begin{tabular}{@{}cr@{}}
+ \includegraphics[scale=0.475]{R/EC95.eps} & \raisebox{2.75cm}{(a)} \\
+ \includegraphics[scale=0.475]{R/EC50.eps} & \raisebox{2.75cm}{(b)}
+ \end{tabular}
+ \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+ \label{fig3EC}
\end{figure}
-The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures~\ref{fig3EC95} and \ref{fig3EC50}, LiCO consumes much less energy than the three other methods. One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed this optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.
%The optimization algorithm, which used by LiCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
%The other approaches have a high energy consumption due to activating a larger number of sensors. In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
%\subsubsection{Execution Time}
-\subsubsection{\textbf{The Network Lifetime}}
-We observe the superiority of LiCO and DiLCO protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/LT95.eps}
-\caption{The Network Lifetime for $Lifetime_{95}$}
-\label{fig3LT95}
-\end{figure}
-
+\subsubsection{\bf Network Lifetime}
+
+We observe the superiority of LiCO and DiLCO protocols in comparison against the
+two other approaches in prolonging the network lifetime. In
+Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
+different network sizes. As highlighted by these figures, the lifetime
+increases with the size of the network, and it is clearly the larger for DiLCO
+and LiCO protocols. For instance, for a network of 300~sensors and coverage
+ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime
+is about two times longer with LiCO compared to DESK protocol. The performance
+difference is more obvious in Figure~\ref{fig3LT}(b) than in
+Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
+the time, and the lifetime with a coverage of 50\% is far more longer than with
+95\%.
\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/LT50.eps}
-\caption{The Network Lifetime for $Lifetime_{50}$}
-\label{fig3LT50}
+ \centering
+ \begin{tabular}{@{}cr@{}}
+ \includegraphics[scale=0.475]{R/LT95.eps} & \raisebox{2.75cm}{(a)} \\
+ \includegraphics[scale=0.475]{R/LT50.eps} & \raisebox{2.75cm}{(b)}
+ \end{tabular}
+ \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
+ and (b)~$Lifetime_{50}$.}
+ \label{fig3LT}
\end{figure}
-As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously increases when the size of the network increases, and it is clearly larger with DiLCO and LiCO protocols compared with the two other methods. For instance, for a network of 300 sensors, the coverage ratio is greater than 50\% about two times longer with LiCO compared to DESK method.
+%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
-%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
-Figure~\ref{figLTALL} introduces the comparisons of the lifetime coverage for different coverage ratios for LiCO and DiLCO protocols.
-We denote by Protocol/50, Protocol/80, Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ respectively. Indeed there are applications that do not require a 100\% coverage of the surveillance region. LiCO might be an interesting method since it achieves a good balance between a high level coverage ratio and network lifetime.
+Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for
+different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
+Protocol/90, and Protocol/95 the amount of time during which the network can
+satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
+respectively, where Protocol is DiLCO or LiCO. Indeed there are applications
+that do not require a 100\% coverage of the area to be monitored. LiCO might be
+an interesting method since it achieves a good balance between a high level
+coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three
+lower coverage ratios, moreover the improvements grow with the network
+size. DiLCO is better for coverage ratios near 100\%, but in that case LiCO is
+not so bad for the smallest network sizes.
\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/LTa.eps}
-\caption{The Network Lifetime for different coverage ratios}
+\centering \includegraphics[scale=0.5]{R/LTa.eps}
+\caption{Network lifetime for different coverage ratios.}
\label{figLTALL}
\end{figure}
-
%Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
-\section{\uppercase{Conclusion and Future Works}}
+\section{Conclusion and Future Works}
\label{sec:Conclusion and Future Works}
-In this paper we have studied the problem of lifetime coverage optimization in
-WSNs. We designed a protocol LiCO that schedules node' activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.
-
-
+In this paper we have studied the problem of lifetime coverage optimization in
+WSNs. We designed a new protocol, called Lifetime Coverage Optimization, which
+schedules nodes' activities (wake up and sleep stages) with the objective of
+maintaining a good coverage ratio while maximizing the network lifetime. This
+protocol is applied in a distributed way in regular subregions obtained after
+partitioning the area of interest in a preliminary step. It works in periods and
+is based on the resolution of an integer program to select the subset of sensors
+operating in active status for each period. Our work is original in so far as it
+proposes for the first time an integer program scheduling the activation of
+sensors based on their perimeter coverage level, instead of using a set of
+targets/points to be covered.
%To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques: network
%leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
%periods, each period consists of four stages: (i) Information Exchange,
%(ii) Leader Election, (iii) a Decision based new optimization model in order to
%select the nodes remaining active for the last stage, and (iv) Sensing.
-We carried out severals simulations to evaluate the proposed protocol. The simulation results show that LiCO is is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption.
-%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily.
-
-We have identified different research directions that arise out of the work presented here.
-We plan to extend our framework such that the schedules are planned for multiple periods in advance.
+We carried out several simulations to evaluate the proposed protocol. The
+simulation results show that LiCO is more energy-efficient than other
+approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
+energy consumption.
+%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have identified different research directions that arise out of the work presented here.
+We plan to extend our framework such that the schedules are planned for multiple
+sensing periods.
%in order to compute all active sensor schedules in only one step for many periods;
-We also want to improve our integer program to take into account the heterogeneous sensors, which do not have the same energy, processing, sensing and communication capabilities;
+We also want to improve our integer program to take into account heterogeneous
+sensors from both energy and node characteristics point of views.
%the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
-Finally, our final goal is to implement our protocol using a sensor-testbed to evaluate their performance in real world applications.
+Finally, it would be interesting to implement our protocol using a
+sensor-testbed to evaluate it in real world applications.
-\section*{\uppercase{Acknowledgements}}
-\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.
-
-
+\section*{Acknowledgments}
+\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
+acknowledge the University of Babylon - IRAQ for financial support and Campus
+France for the received support. This work has also been supported by the Labex
+ACTION.
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