%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
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+\usepackage[algo2e,ruled,vlined]{algorithm2e}
\begin{document}
%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}
%\articletype{GUIDE}
-\title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}}
-
-\author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
-$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
- Belfort, France}};}
-
+\title{{\itshape Perimeter-based Coverage Optimization \\
+ to Improve Lifetime in Wireless Sensor Networks}}
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
+ $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
+ University Bourgogne Franche-Comt\'e, Belfort, France}} \\
+ $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
+}
+
\maketitle
\begin{abstract}
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
+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. We propose such an approach called Perimeter-based Coverage Optimization
-protocol (PeCO). It is a hybrid of centralized and distributed methods: the
-region of interest is first subdivided into subregions and the protocol is then
-distributed among sensor nodes in each subregion.
-The novelty of our approach lies essentially in the formulation of a new
-mathematical optimization model based on the perimeter coverage level to schedule
-sensors' activities. Extensive simulation experiments demonstrate that PeCO can
-offer longer lifetime coverage for WSNs in comparison with some other protocols.
-
-\begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
+scheduling which ensures sensing coverage while minimizing the energy cost. We
+propose such an approach called Perimeter-based Coverage Optimization protocol
+(PeCO). It is a hybrid of centralized and distributed methods: the region of
+interest is first subdivided into subregions and the protocol is then
+distributed among sensor nodes in each subregion. The novelty of our approach
+lies essentially in the formulation of a new mathematical optimization model
+based on the perimeter coverage level to schedule sensors' activities.
+Extensive simulation experiments demonstrate that PeCO can offer longer lifetime
+coverage for WSNs in comparison with some other protocols.
+
+\begin{keywords}
+ Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
\end{keywords}
\end{abstract}
-
\section{Introduction}
\label{sec:introduction}
-The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
-wireless communication hardware has given rise to the opportunity to use large
-networks of tiny sensors, called Wireless Sensor Networks
-(WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
+The continuous progress in Micro Electro-Mechanical Systems (MEMS) and wireless
+communication hardware has given rise to the opportunity to use large networks
+of tiny sensors, called Wireless Sensor Networks
+(WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
tasks. A WSN consists of small low-powered sensors working together by
communicating with one another through multi-hop radio communications. Each node
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 so on~\citep{yick2008wireless}. Typically, a sensor node contains
-three main components~\citep{anastasi2009energy}: a sensing unit able to measure
+military, and so on~\citep{yick2008wireless}. Typically, a sensor node contains
+three main components~\citep{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
communication unit for data transmission and receiving.
communication is supplied by a power supply which is a battery. This battery has
a limited energy provision and it may be unsuitable or impossible to replace or
recharge it in most applications. Therefore it is necessary to deploy WSN with
-high density in order to increase reliability and to exploit node redundancy
+high density in order to increase reliability and to exploit node redundancy
thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
of sensing areas can be exploited to schedule alternatively some sensors in a
low power sleep mode and thus save energy. Overall, the main question that must
be answered is: how to extend the lifetime coverage of a WSN as long as possible
-while ensuring a high level of coverage? These past few years many
+while ensuring a high level of coverage? These past few years many
energy-efficient mechanisms have been suggested to retain energy and extend the
-lifetime of the WSNs~\citep{rault2014energy}.\\\\
+lifetime of the WSNs~\citep{rault2014energy}.
+
This paper makes the following contributions.
\begin{enumerate}
-\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 and
- temporal subdivision. On the one hand, the area of interest is 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 have proposed a new mathematical optimization model. Instead of trying to
+\item A framework is devised 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 the proposed framework is to
+ exploit spatial and temporal subdivision. On the one hand, the area of
+ interest is 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 A new mathematical optimization model is proposed. 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. Hence, an
- optimal schedule will be obtained by minimizing a weighted sum of these
+ between the actual level of coverage and the required level. Hence, an
+ optimal schedule will be obtained by minimizing a weighted sum of these
deviations.
-\item We have conducted extensive simulation experiments, using the discrete event
- simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
- our PeCO protocol to two approaches found in the literature:
- DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
- work published in~\citep{Idrees2} which is based on another optimization model
- for sensor scheduling.
+\item Extensive simulation experiments are conducted using the discrete event
+ simulator OMNeT++, to demonstrate the efficiency of our protocol. We have
+ compared the PeCO protocol to two approaches found in the literature:
+ DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
+ protocol DiLCO published in~\citep{Idrees2}. DiLCO uses the same framework as
+ PeCO but is based on another optimization model for sensor scheduling.
\end{enumerate}
-
-
-
-
-
-The rest of the paper is organized as follows. In the next section
-some related work in the field is reviewed. Section~\ref{sec:The PeCO Protocol Description}
+The rest of the paper is organized as follows. In the next section some related
+work in the field is reviewed. Section~\ref{sec:The PeCO Protocol Description}
is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
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 are given for future works in
+remarks are drawn and some suggestions are given for future works in
Section~\ref{sec:Conclusion and Future Works}.
\section{Related Literature}
\label{sec:Literature Review}
-In this section, some related works regarding the
-coverage problem is summarized, and specific aspects of the PeCO protocol from the works presented in
-the literature are presented.
+This section summarizes some related works regarding the coverage problem and
+presents specific aspects of the PeCO protocol common with other literature
+works.
The most discussed coverage problems in literature can be classified in three
-categories~\citep{li2013survey} according to their respective monitoring
-objective. Hence, area coverage \citep{Misra} means that every point inside a
-fixed area must be monitored, while target coverage~\citep{yang2014novel} refers
+categories~\citep{li2013survey} according to their respective monitoring
+objective. Hence, area coverage \citep{Misra} means that every point inside a
+fixed area must be monitored, while target coverage~\citep{yang2014novel} refers
to the objective of coverage for a finite number of discrete points called
-targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
+targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
preventing intruders from entering into the region of interest. In
-\citep{Deng2012} authors transform the area coverage problem into the target
+\citep{Deng2012} authors transform the area coverage problem into the target
coverage one taking into account the intersection points among disks of sensors
nodes or between disk of sensor nodes and boundaries. In
-\citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
+\citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
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. $d$ denotes the maximum number of sensors that are
-neighbors to a sensor, and $n$ is the total number of sensors in the
-network. {\it In PeCO 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.}
+each sensor. $d$ denotes the maximum number of sensors that are neighbors to a
+sensor, and $n$ is the total number of sensors in the network. {\it In PeCO
+ 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.}
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)\citep{wang2011coverage}, 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
-\citep{ling2009energy}. Active node selection is determined based on the problem
-requirements (e.g. area monitoring, connectivity, or power efficiency). For
-instance, \citet{jaggi2006} address the problem of maximizing
+non-disjoint) \citep{wang2011coverage}, 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 decided at the
+beginning of each period \citep{ling2009energy}. In fact, many authors propose
+algorithms working in such a periodic fashion
+\citep{chin2007,yan2008design,pc10}. Active node selection is determined based
+on the problem requirements (e.g. area monitoring, connectivity, or power
+efficiency). For instance, \citet{jaggi2006} address the problem of maximizing
the 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.
-\citet{chin2007}, \citet{yan2008design}, \citet{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, PeCO 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 centralized and distributed approaches, or even a mixing of these two
-concepts, have been proposed to extend the network lifetime \citep{zhou2009variable}. In distributed algorithms~\citep{Tian02,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 make a bad decision leading to a global suboptimal solution. Conversely,
-centralized
-algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always
+activated in succession to achieve the desired network lifetime. {\it Motivated
+ by these works, PeCO 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 centralized and distributed approaches, or even a mixing of these two
+concepts, have been proposed to extend the network lifetime
+\citep{zhou2009variable}. In distributed
+algorithms~\citep{ChinhVu,qu2013distributed,yangnovel} 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 make a bad decision leading to a global suboptimal solution.
+Conversely, centralized
+algorithms~\citep{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, and data from all the other
-sensor nodes in the area. The price in communications can be 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 PeCO 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 these past few years.
+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 huge since long
+range communications will be needed. In fact the larger the WSN, the higher the
+communication energy cost. {\it In order to be suitable for large-scale
+ networks, in PeCO 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 PeCO protocol is
+ scalable and a globally distributed method, whereas it is centralized in each
+ subregion.}
+
+Various coverage scheduling algorithms have been developed these past few years.
Many of them, 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
-\citep{berman04,zorbas2010solving}. Other approaches are based on mathematical
-programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014}
-and dedicated techniques (solving with a branch-and-bound algorithm available in
+\citep{berman04,zorbas2010solving}. Other approaches are based on mathematical
+programming
+formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014} and
+dedicated techniques (solving with a branch-and-bound algorithm 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~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it In the PeCO
- 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.}
-
-
-
-The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. It is an improved version
-of a research work they presented in~\citep{idrees2014coverage}. First, they partition the area of interest into subregions using a divide-and-conquer method. DiLCO protocol is then distributed on the sensor nodes in each subregion in a second step. DiLCO protocol combines two techniques: a leader election in each subregion, followed by an optimization-based node activity scheduling performed by each elected leader. The proposed DiLCO protocol is a periodic protocol where each period is decomposed into 4 phases: information exchange, leader election, decision, and sensing. The simulations show that DiLCO is able to increase the WSN lifetime and provides improved coverage performance. {\it In the PeCO
- protocol, We have proposed a new mathematical optimization model. Instead of trying to
-cover a set of specified points/targets as in DiLCO protocol, 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. The idea is that an optimal scheduling will be obtained by minimizing a weighted sum of these deviations.}
-
-
+used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
+{\it In the PeCO 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.}
+
+The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage
+Optimization (DiLCO) protocol, which maintains the coverage and improves the
+lifetime in WSNs. It is an improved version of a research work presented
+in~\citep{idrees2014coverage}. First, the area of interest is partitioned into
+subregions using a divide-and-conquer method. DiLCO protocol is then distributed
+on the sensor nodes in each subregion in a second step. Hence this protocol
+combines two techniques: a leader election in each subregion, followed by an
+optimization-based node activity scheduling performed by each elected
+leader. The proposed DiLCO protocol is a periodic protocol where each period is
+decomposed into 4 phases: information exchange, leader election, decision, and
+sensing. The simulations show that DiLCO is able to increase the WSN lifetime
+and provides improved coverage performance. {\it In the PeCO protocol, a new
+ mathematical optimization model is proposed. Instead of trying to cover a set
+ of specified points/targets as in DiLCO protocol, 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. The idea is that an optimal scheduling will be obtained by
+ minimizing a weighted sum of these deviations.}
-
\section{ The P{\scshape e}CO Protocol Description}
\label{sec:The PeCO Protocol Description}
-In this section, the Perimeter-based Coverage
-Optimization protocol is decribed in details. First we present the assumptions we made and the models
-we considered (in particular the perimeter coverage one), second we describe the
-background idea of our protocol, and third we give the outline of the algorithm
-executed by each node.
+%In this section, the Perimeter-based Coverage
+%Optimization protocol is decribed in details. First we present the assumptions we made and the models
+%we considered (in particular the perimeter coverage one), second we describe the
+%background idea of our protocol, and third we give the outline of the algorithm
+%executed by each node.
\subsection{Assumptions and Models}
\label{CI}
-A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
+A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
distributed in a bounded sensor field is considered. The wireless sensors are
deployed in high density to ensure initially a high coverage ratio of the area
-of interest. We assume that all the sensor nodes are homogeneous in terms of
-communication, sensing, and processing capabilities and heterogeneous from
-the energy provision point of view. The location information is available to a
+of interest. All the sensor nodes are supposed to be homogeneous in terms of
+communication, sensing, and processing capabilities and heterogeneous from the
+energy provision point of view. The location information is available to a
sensor node either through hardware such as embedded GPS or location discovery
-algorithms. We consider a Boolean disk coverage model,
-which is the most widely used sensor coverage model in the literature, and all
-sensor nodes have a constant sensing range $R_s$. Thus, all the space points
-within a disk centered at a sensor with a radius equal to the sensing range are
-said to be covered by this sensor. We also assume that the communication range
-$R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, \citet{Zhang05}
-proved that if the transmission range fulfills the previous hypothesis, the
-complete coverage of a convex area implies connectivity among active nodes.
-
-The PeCO protocol uses the same perimeter-coverage model as \citet{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. Authors \citet{huang2005coverage} proved that a network area is
-$k$-covered (every point in the area covered by at least k sensors) if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
+algorithms. A Boolean disk coverage model, which is the most widely used sensor
+coverage model in the literature, is considered and all sensor nodes have a
+constant sensing range $R_s$. Thus, all the space points within a disk centered
+at a sensor with a radius equal to the sensing range are said to be covered by
+this sensor. We also assume that the communication range $R_c$ satisfies $R_c
+\geq 2 \cdot R_s$. In fact, \citet{Zhang05} proved that if the transmission
+range fulfills the previous hypothesis, the complete coverage of a convex area
+implies connectivity among active nodes.
+
+The PeCO protocol uses the same perimeter-coverage model as
+\citet{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. Authors \citet{huang2005coverage} proved that a
+network area is $k$-covered (every point in the area is covered by at least
+$k$~sensors) if and only if each sensor in the network is $k$-perimeter-covered
+(perimeter covered by at least $k$ sensors).
-Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this
-figure, sensor~$0$ has nine neighbors and we have reported on
-its perimeter (the perimeter of the disk covered by the sensor) for each
-neighbor the two points resulting from the intersection of the two sensing
-areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
-for left and right from a neighboing point of view. The resulting couples of
-intersection points subdivide the perimeter of sensor~$0$ into portions called
-arcs.
+Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this figure,
+sensor~$0$ has nine neighbors and we have reported on its perimeter (the
+perimeter of the disk covered by the sensor) for each neighbor the two points
+resulting from the intersection of the two sensing areas. These points are
+denoted for neighbor~$i$ by $iL$ and $iR$, respectively for left and right from
+a neighboring point of view. The resulting couples of intersection points
+subdivide the perimeter of sensor~$0$ into portions called arcs.
\begin{figure}[ht!]
\centering
\label{figure1}
\end{figure}
-Figure~\ref{figure1}(b) describes the geometric information used to find the
+Figure~\ref{figure1}(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~$v$ 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
-the euclidean distance between nodes~$u$ and $v$ is computed: $Dist(u,v)=\sqrt{\vert
- u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
-obtained through the formula:
+sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates the
+euclidean distance between nodes~$u$ and $v$ is computed as follows:
+$$
+ Dist(u,v)=\sqrt{\vert u_x - v_x \vert^2 + \vert u_y-v_y \vert^2},
+$$
+while the angle~$\alpha$ is obtained through the formula:
\[
-\alpha = \arccos \left(\frac{Dist(u,v)}{2R_s}
-\right).
+\alpha = \arccos \left(\frac{Dist(u,v)}{2R_s} \right).
\]
-The arc on the perimeter of~$u$ defined by the angular interval $[\pi
- - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
+The arc on the perimeter of~$u$ defined by the angular interval $[\pi -
+ \alpha,\pi + \alpha]$ is then 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{figure1}(a) illustrates the arcs for the nine neighbors of
-sensor $0$ and Figure~\ref{figure2} gives the position of the corresponding arcs
+sensor $0$ and Table~\ref{my-label} gives the position of the corresponding arcs
in the interval $[0,2\pi)$. More precisely, 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 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 $3$
+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{figure2}), 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.
-
\begin{figure*}[t!]
\centering
-\includegraphics[width=127.5mm]{figure2.eps}
+\includegraphics[width=0.95\linewidth]{figure2.eps}
\caption{Maximum coverage levels for perimeter of sensor node $0$.}
\label{figure2}
\end{figure*}
-
-
-
- \begin{table}
- \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}
+\begin{table}
+\tbl{Coverage intervals and contributing sensors for node 0 \label{my-label}}
{\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 coverage interval\end{tabular}} \\ \hline
\end{table}
-
-
-
-In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an
-integer program based on coverage intervals. The formulation of the coverage
+In the PeCO protocol, the scheduling of the sensor nodes' activities is
+formulated with an mixed-integer program based on coverage
+intervals~\citep{doi:10.1155/2010/926075}. 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{figure3}, the maximum coverage level for this arc is set to $\infty$
+Figure~\ref{figure3}, 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.
- \newpage
+%\newpage
\begin{figure}[h!]
\centering
-\includegraphics[width=62.5mm]{figure3.eps}
+\includegraphics[width=57.5mm]{figure3.eps}
\caption{Sensing range outside the WSN's area of interest.}
\label{figure3}
-\end{figure}
-
-
-\subsection{The Main Idea}
-
-The WSN area of interest is, in a first step, divided into regular
-homogeneous subregions using a divide-and-conquer algorithm. In a second step
-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{figure4}, 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
-PeCO, are more robust against an unexpected node failure. On the one hand, if
-a node failure is discovered before taking the decision, the corresponding sensor
-node will not be considered by the optimization algorithm. On the other
+\end{figure}
+
+\vspace{-0.25cm}
+
+\subsection{Main Idea}
+
+The WSN area of interest is, in a first step, divided into regular homogeneous
+subregions using a divide-and-conquer algorithm. In a second step our protocol
+will be executed in a distributed way in each subregion simultaneously to
+schedule nodes' activities for one sensing period. Sensor nodes are assumed to
+be deployed almost uniformly over the region. The regular subdivision is made
+such that the number of hops between any pairs of sensors inside a subregion is
+less than or equal to 3.
+
+As shown in Figure~\ref{figure4}, node activity scheduling is produced by the
+proposed 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 PeCO, are more robust against an unexpected node failure. On the one hand,
+if 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
information (including their residual energy) at the beginning of each period.
However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
are energy consuming, even for nodes that will not join the set cover to monitor
-the area.
+the area. Sensing period duration is adapted according to the QoS requirements
+of the application.
\begin{figure}[t!]
\centering
\end{figure}
We define two types of packets to be used by PeCO protocol:
-
\begin{itemize}
\item INFO packet: sent by each sensor node to all the nodes inside a same
subregion for information exchange.
sensing phase.
\end{itemize}
-
Five statuses are possible for a sensor node in the network:
-
\begin{itemize}
\item LISTENING: waits for a decision (to be active or not);
\item COMPUTATION: executes the optimization algorithm as leader to
\item COMMUNICATION: transmits or receives packets.
\end{itemize}
-
\subsection{PeCO Protocol Algorithm}
-The pseudocode implementing the protocol on a node is given below.
-More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
-protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
+The pseudocode implementing the protocol on a node is given below. More
+precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the protocol
+applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
-
-\begin{algorithm}
+\begin{algorithm2e}
% \KwIn{all the parameters related to information exchange}
% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
% \BlankLine
- %\emph{Initialize the sensor node and determine it's position and subregion} \;
-
-\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
-\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
-\hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
-\hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
-\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
-\hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
-\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
-\hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
-\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
-\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
-\hspace*{1.2cm} {\bf end}\\
-\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
-\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
-\hspace*{1.2cm} {\bf end}\\
-\hspace*{1.2cm} {\bf else}\\
-\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
-\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
-\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
-\hspace*{1.2cm} {\bf end}\\
-\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
-\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
-\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-\hspace*{0.6cm} {\bf end}\\
-\hspace*{0.6cm} {\bf else}\\
-\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
-\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
-\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-\hspace*{0.6cm} {\bf end}\\
-{\bf end}\\
-{\bf else}\\
-\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
-{\bf end}\\
-\label{alg:PeCO}
-\end{algorithm}
-
-
-
-In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
-current number and the previous number of living 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 numbers 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.
-
+ %\emph{Initialize the sensor node and determine it's position and subregion} \;
+ \label{alg:PeCO}
+ \caption{PeCO pseudocode}
+ \eIf{$RE_k \geq E_{th}$}{
+ $s_k.status$ = COMMUNICATION\;
+ Send $INFO()$ packet to other nodes in subregion\;
+ Wait $INFO()$ packet from other nodes in subregion\;
+ Update K.CurrentSize\;
+ LeaderID = Leader election\;
+ \eIf{$s_k.ID = LeaderID$}{
+ $s_k.status$ = COMPUTATION\;
+ \If{$ s_k.ID $ is Not previously selected as a Leader}{
+ Execute the perimeter coverage model\;
+ }
+ \eIf{($s_k.ID $ is the same Previous Leader) {\bf and} \\
+ \indent (K.CurrentSize = K.PreviousSize)}{
+ Use the same previous cover set for current sensing stage\;
+ }{
+ Update $a^j_{ik}$; prepare data for IP~Algorithm\;
+ $\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)\;
+ K.PreviousSize = K.CurrentSize\;
+ }
+ $s_k.status$ = COMMUNICATION\;
+ Send $ActiveSleep()$ to each node $l$ in subregion\;
+ Update $RE_k $\;
+ }{
+ $s_k.status$ = LISTENING\;
+ Wait $ActiveSleep()$ packet from the Leader\;
+ Update $RE_k $\;
+ }
+ }{
+ Exclude $s_k$ from entering in the current sensing stage\;
+ }
+\end{algorithm2e}
+
+%\begin{algorithm}
+%\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
+%\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
+%\hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
+%\hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
+%\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
+%\hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
+%\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
+%\hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
+%\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
+%\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
+%\hspace*{1.2cm} {\bf end}\\
+%\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
+%\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
+%\hspace*{1.2cm} {\bf end}\\
+%\hspace*{1.2cm} {\bf else}\\
+%\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
+%\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
+%\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
+%\hspace*{1.2cm} {\bf end}\\
+%\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
+%\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
+%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+%\hspace*{0.6cm} {\bf end}\\
+%\hspace*{0.6cm} {\bf else}\\
+%\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
+%\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
+%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+%\hspace*{0.6cm} {\bf end}\\
+%{\bf end}\\
+%{\bf else}\\
+%\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
+%{\bf end}\\
+%\label{alg:PeCO}
+%\end{algorithm}
+
+In this algorithm, $K.CurrentSize$ and $K.PreviousSize$ respectively represent
+the current number and the previous number of living nodes in the subnetwork of
+the subregion. At the beginning of the first period $K.PreviousSize$ is
+initialized to zero. 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 are (in order of priority):
+\begin{enumerate}
+\item larger number of neighbors;
+\item larger remaining energy;
+\item and then in case of equality, larger index.
+\end{enumerate}
+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.
\section{Perimeter-based Coverage Problem Formulation}
\label{cp}
-In this section, the coverage model is mathematically formulated. The following
-notations are used throughout the
-section.\\
+In this section, the perimeter-based coverage problem is mathematically
+formulated. It has been proved to be a NP-hard problem
+by \citep{doi:10.1155/2010/926075}. Authors study the coverage of the perimeter
+of a large object requiring to be monitored. For the proposed formulation in
+this paper, the large object to be monitored is the sensor itself (or more
+precisely its sensing area).
+
+The following notations are used throughout the section.
+
First, the following sets:
\begin{itemize}
-\item $S$ represents the set of WSN sensor nodes;
+\item $S$ represents the set of sensor nodes;
\item $A \subseteq S $ is the subset of alive sensors;
\item $I_j$ designates the set of coverage intervals (CI) obtained for
sensor~$j$.
\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 $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
+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
in coverage interval~$i$ of sensor~$j$, that is:
\begin{equation}
a^j_{ik} = \left \{
\end{equation}
Note that $a^k_{ik}=1$ by definition of the interval.
-Second, several binary and integer variables are defined. Hence, each binary
-variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
-($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
-variable which measures the undercoverage for the coverage interval $i$
-corresponding to sensor~$j$. In the same way, the overcoverage for the same
-coverage interval is given by the variable $V^j_i$.
-
-If we decide to sustain a level of coverage equal to $l$ all along the perimeter
-of sensor $j$, we have to ensure that at least $l$ sensors involved in each
-coverage interval $i \in I_j$ of sensor $j$ are active. According to the
-previous notations, the number of active sensors in the coverage interval $i$ of
-sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
-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 variables $M^j_i$ and $V^j_i$ are introduced 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
-desired coverage level, and if the desired level cannot be completely satisfied,
-to reach a coverage level as close as possible to the desired one.
-
-
-
-
-Our coverage optimization problem can then be mathematically expressed as follows:
-
-\begin{equation}
-\left \{
-\begin{array}{ll}
-\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
-\textrm{subject to :}&\\
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i = l \quad \forall i \in I_j, \forall j \in S\\
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i = l \quad \forall i \in I_j, \forall j \in S\\
-X_{k} \in \{0,1\}, \forall k \in A
-\end{array}
-\right.
+Second, several variables are defined. Hence, each binary variable $X_{k}$
+determines the activation of sensor $k$ in the sensing phase ($X_k=1$ if the
+sensor $k$ is active or 0 otherwise). $M^j_i$ is a variable which measures the
+undercoverage for the coverage interval $i$ corresponding to sensor~$j$. In the
+same way, the overcoverage for the same coverage interval is given by the
+variable $V^j_i$.
+
+To sustain a level of coverage equal to $l$ all along the perimeter of sensor
+$j$, at least $l$ sensors involved in each coverage interval $i \in I_j$ of
+sensor $j$ have to be active. According to the previous notations, the number
+of active sensors in the coverage interval $i$ of sensor $j$ is given by
+$\sum_{k \in A} a^j_{ik} X_k$. To extend the network 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
+variables $M^j_i$ and $V^j_i$ are introduced 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 desired coverage level,
+and if the desired level cannot be completely satisfied, to reach a coverage
+level as close as possible to the desired one.
+
+The coverage optimization problem can then be mathematically expressed as follows:
+\begin{equation}
+ \begin{aligned}
+ \text{Minimize } & \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) \\
+ \text{Subject to:} & \\
+ & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S \\
+ & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S \\
+ & X_{k} \in \{0,1\}, \forall k \in A \\
+ & M^j_i, V^j_i \in \mathbb{R}^{+}
+ \end{aligned}
\end{equation}
+%\begin{equation}
+%\left \{
+%\begin{array}{ll}
+%\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) & \\
+%\textrm{subject to :} &\\
+%\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
+%\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
+%X_{k} \in \{0,1\}, \forall k \in A \\
+%M^j_i, V^j_i \in \mathbb{R}^{+}
+%\end{array}
+%\right.
+%\end{equation}
+
+If a given level of coverage $l$ is required for one sensor, the sensor is said
+to be undercovered (respectively overcovered) if the level of coverage of one of
+its CI is less (respectively greater) than $l$. If the sensor $j$ is
+undercovered, there exists at least one of its CI (say $i$) for which the number
+of active sensors (denoted by $l^{i}$) covering this part of the perimeter is
+less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. Conversely,
+if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$)
+for which the number of active sensors (denoted by $l^{i}$) covering this part
+of the perimeter is greater than $l$ and in this case: $M_{i}^{j}=0$,
+$V_{i}^{j}=l^{i}-l$.
+
$\alpha^j_i$ 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 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
-\citep{0031-9155-44-1-012}. The integer program must be solved by the leader in
-each subregion at the beginning of each sensing phase, whenever the environment
-has changed (new leader, death of some sensors). Note that the number of
-constraints in the model is constant (constraints of coverage expressed for all
-sensors), whereas the number of variables $X_k$ decreases over periods, since
-only alive sensors (sensors with enough energy to be alive during one
-sensing phase) are considered in the model.
+be given by a relatively larger magnitude than weights associated with another
+region. This kind of mixed-integer program is inspired from the model developed
+for brachytherapy treatment planning for optimizing dose distribution
+\citep{0031-9155-44-1-012}. The choice of the values for variables $\alpha$ and
+$\beta$ should be made according to the needs of the application. $\alpha$
+should be large enough to prevent undercoverage and so to reach the highest
+possible coverage ratio. $\beta$ should be large enough to prevent overcoverage
+and so to activate a minimum number of sensors. The mixed-integer program must
+be solved by the leader in each subregion at the beginning of each sensing
+phase, whenever the environment has changed (new leader, death of some sensors).
+Note that the number of constraints in the model is constant (constraints of
+coverage expressed for all sensors), whereas the number of variables $X_k$
+decreases over periods, since only alive sensors (sensors with enough energy to
+be alive during one sensing phase) are considered in the model.
\section{Performance Evaluation and Analysis}
\label{sec:Simulation Results and Analysis}
-
\subsection{Simulation Settings}
-
The WSN area of interest is supposed to be divided into 16~regular subregions
-and we use the same energy consumption model as in our previous work~\citep{Idrees2}.
-Table~\ref{table3} gives the chosen parameters settings.
+and we use the same energy consumption model as in our previous
+work~\citep{Idrees2}. Table~\ref{table3} gives the chosen parameters settings.
\begin{table}[ht]
\tbl{Relevant parameters for network initialization \label{table3}}{
-
\centering
-
\begin{tabular}{c|c}
-
\hline
Parameter & Value \\ [0.5ex]
-
\hline
% inserts single horizontal line
-Sensing field & $(50 \times 25)~m^2 $ \\
-
-WSN size & 100, 150, 200, 250, and 300~nodes \\
-
-Initial energy & in range 500-700~Joules \\
-
+Sensing field & $(50 \times 25)~m^2 $ \\
+WSN size & 100, 150, 200, 250, and 300~nodes \\
+Initial energy & in range 500-700~Joules \\
Sensing period & duration of 60 minutes \\
-$E_{th}$ & 36~Joules\\
-$R_s$ & 5~m \\
-$R_c$ & 10~m \\
-$\alpha^j_i$ & 0.6 \\
-
+$E_{th}$ & 36~Joules \\
+$R_s$ & 5~m \\
+$R_c$ & 10~m \\
+$\alpha^j_i$ & 0.6 \\
$\beta^j_i$ & 0.4
-
\end{tabular}}
-
-
\end{table}
+
To obtain experimental results which are relevant, simulations with five
different node densities going from 100 to 300~nodes were performed considering
each time 25~randomly generated networks. The nodes are deployed on a field of
interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
high coverage ratio. Each node has an initial energy level, in Joules, which is
-randomly drawn in the interval $[500-700]$. If its energy provision reaches a
+randomly drawn in the interval $[500-700]$. If its energy provision reaches a
value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
-node to stay active during one period, it will no longer participate in the
+node to stay active during one period, it will no longer participate in the
coverage task. This value corresponds to the energy needed by the sensing phase,
-obtained by multiplying the energy consumed in the active state (9.72 mW) with the
-time in seconds for one period (3600 seconds), and adding the energy for the
+obtained by multiplying the energy consumed in the active state (9.72 mW) with
+the time in seconds for one period (3600 seconds), and adding the energy for the
pre-sensing phases. According to the interval of initial energy, a sensor may
-be active during at most 20 periods.
+be active during at most 20 periods. Information exchange to update the coverage
+is executed every hour, but the length of the sensing period could be reduced
+and adapted dynamically. On the one hand a small sensing period would allow to
+be more reliable but would have result in higher communication costs. On the
+other hand the choice of a long duration may cause problems in case of nodes
+failure during the sensing period.
The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
-network coverage and a longer WSN lifetime. Higher priority is given to
-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,
-$\beta^j_i$ is assigned to a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
-in covering the interval.
+network coverage and a longer WSN lifetime. Higher priority is given to 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, $\beta^j_i$ is assigned to a value which is slightly lower so as
+to minimize the number of active sensor nodes which contribute in covering the
+interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of
+both parameters affect the performance of PeCO protocol.
The following performance metrics are used to evaluate the efficiency of the
approach.
-
-
\begin{itemize}
\item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
\item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
observe the area of interest. In our case, the sensor field is discretized as
a regular grid, which yields the following equation:
-
-
-\[
+ \begin{equation*}
\scriptsize
\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
-\]
-
-
+ \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 simulations a layout of
- $N~=~51~\times~26~=~1326$~grid points is considered.
+ points in the sensing field. A layout of $N~=~51~\times~26~=~1326$~grid points
+ is considered in the simulations.
\item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
- activate as few nodes as possible, in order to minimize the communication
+ activate as few nodes as possible, in order to minimize the communication
overhead and maximize the WSN lifetime. The active sensors ratio is defined as
follows:
-
-\[
- \scriptsize
- \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
-\]
-
+ \begin{equation*}
+ \scriptsize
+ \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
+ \end{equation*}
where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
- current sensing period~$p$, $|J|$ is the number of sensors in the network, and
- $R$ is the number of subregions.
+ sensing period~$p$, $R$ is the number of subregions, and $|J|$ is the number
+ of sensors in the network.
\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:
-
-\[
- \scriptsize
+ \begin{equation*}
+ \scriptsize
\mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
+ E^{a}_p+E^{s}_p \right)}{P},
-\]
-
+ \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
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).
+ program during a period (COMPUTATION status). Finally, $E^a_{p}$ and
+ $E^s_{p}$ indicate the energy consumed by the WSN during the sensing phase
+ ({\it active} and {\it sleeping} nodes).
\end{itemize}
-
\subsection{Simulation Results}
In order to assess and analyze the performance of our protocol we have
-implemented PeCO protocol in OMNeT++~\citep{varga} simulator. Besides PeCO, two
-other protocols, described in the next paragraph, will be evaluated for
-comparison purposes. The simulations were run on a DELL laptop with an Intel
-Core~i3~2370~M (1.8~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)~\citep{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) \citep{glpk} through a Branch-and-Bound method.
-
-As said previously, the PeCO is compared to three other approaches. The first
-one, called DESK, is a fully distributed coverage algorithm proposed by
-\citep{ChinhVu}. The second one, called GAF~\citep{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~\citep{Idrees2}, is an improved version
-of a research work we presented in~\citep{idrees2014coverage}. Let us notice that
-PeCO and DiLCO protocols are based on the same framework. In particular, the
-choice for the simulations of a partitioning in 16~subregions was made because
-it corresponds to the configuration producing the best 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 the PeCO 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{figure5} shows the average coverage ratio for 200 deployed nodes
-obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
-coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
-produced by PeCO for the first periods. This is due to the fact that at the
-beginning the DiLCO protocol puts to 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 PeCO 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 PeCO in the early periods allows later a
-substantial increase of the coverage performance.
+implemented PeCO protocol in OMNeT++~\citep{varga} simulator. The simulations
+were run on a DELL laptop with an Intel Core~i3~2370~M (1.8~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 $\left(\frac{35330}{2} \times
+\frac{1}{6} \right)$. Energy consumption is calculated according to the power
+consumption values, in milliWatt per second, given in Table~\ref{tab:EC}.
+based on the energy model proposed in \citep{ChinhVu}.
+
+\begin{table}[h]
+\centering
+\caption{Power consumption values}
+\label{tab:EC}
+\begin{tabular}{|l||cccc|}
+ \hline
+ {\bf Sensor status} & MCU & Radio & Sensor & {\it Power (mW)} \\
+ \hline
+ LISTENING & On & On & On & 20.05 \\
+ ACTIVE & On & Off & On & 9.72 \\
+ SLEEP & Off & Off & Off & 0.02 \\
+ COMPUTATION & On & On & On & 26.83 \\
+ \hline
+ \multicolumn{4}{|l}{Energy needed to send or receive a 2-bit content message} & 0.515 \\
+ \hline
+\end{tabular}
+\end{table}
+
+The modeling language for Mathematical Programming (AMPL)~\citep{AMPL} is used
+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) \citep{glpk} through a Branch-and-Bound method.
+In practice, executing GLPK on a sensor node is obviously intractable due to the
+huge memory use. Fortunately, to solve the optimization problem we could use
+commercial solvers like CPLEX \citep{iamigo:cplex} which are less memory
+consuming and more efficient, or implement a lightweight heuristic. For example,
+for a WSN of 200 sensor nodes, a leader node has to deal with constraints
+induced by about 12 sensor nodes. In that case, to solve the optimization
+problem a memory consumption of more than 1~MB can be observed with GLPK,
+whereas less than 300~kB would be needed with CPLEX.
+
+Besides PeCO, three other protocols will be evaluated for comparison
+purposes. The first one, called DESK, is a fully distributed coverage algorithm
+proposed by \citep{ChinhVu}. The second one, called
+GAF~\citep{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~\citep{Idrees2}, is an improved version of a research work we presented
+in~\citep{idrees2014coverage}. Let us notice that PeCO and DiLCO protocols are
+based on the same framework. In particular, the choice for the simulations of a
+partitioning in 16~subregions was made because it corresponds to the
+configuration producing the best results for DiLCO. Of course, this number of
+subregions should be adapted according to the size of the area of interest and
+the number of sensors. 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 PeCO 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{Coverage Ratio}
+
+Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes
+obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
+coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the
+98.76\% produced by PeCO for the first periods. This is due to the fact that at
+the beginning DiLCO and PeCO protocols put to sleep status more redundant
+sensors (which slightly decreases the coverage ratio), while the two other
+protocols activate more sensor nodes. Later, when the number of periods is
+beyond~70, it clearly appears that PeCO 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 PeCO in the early periods
+allows later a substantial increase of the coverage performance.
\parskip 0pt
\begin{figure}[h!]
\label{figure5}
\end{figure}
-
-
-
-\subsubsection{\bf Active Sensors Ratio}
+\subsubsection{Active Sensors Ratio}
Having the less active sensor nodes in each period is essential to minimize the
-energy consumption and thus to maximize the network lifetime. Figure~\ref{figure6}
-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 PeCO protocols compete perfectly with only 17.92~\% and
-20.16~\% active nodes during the same time interval. As the number of periods
-increases, PeCO 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{figure5}.
+energy consumption and thus to maximize the network lifetime.
+Figure~\ref{figure6} 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 PeCO protocols compete perfectly with
+only 17.92~\% and 20.16~\% active nodes during the same time interval. As the
+number of periods increases, PeCO protocol has a lower number of active nodes in
+comparison with the three other approaches and exhibits a slow decrease, while
+keeping a greater coverage ratio as shown in Figure \ref{figure5}.
\begin{figure}[h!]
\centering
\label{figure6}
\end{figure}
-\subsubsection{\bf Energy Consumption}
-
-We studied the effect of the energy consumed by the WSN during the communication,
-computation, listening, active, and sleep status for different network densities
-and compared it for the four approaches. Figures~\ref{figure7}(a) and (b)
-illustrate the energy consumption for different network sizes and for
-$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
-most competitive from the energy consumption point of view. As shown in both
-figures, PeCO 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.
+\subsubsection{Energy Consumption}
+
+The effect of the energy consumed by the WSN during the communication,
+computation, listening, active, and sleep status is studied for different
+network densities and the four approaches compared. Figures~\ref{figure7}(a)
+and (b) illustrate the energy consumption for different network sizes and for
+$Lifetime95$ and $Lifetime50$. The results show that PeCO protocol is the most
+competitive from the energy consumption point of view. As shown by both figures,
+PeCO consumes much less energy than the 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. Let us notice that the energy overhead when increasing network
+size is the lowest with PeCO.
\begin{figure}[h!]
\centering
\begin{tabular}{@{}cr@{}}
- \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
- \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
+ \includegraphics[scale=0.5]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
+ \includegraphics[scale=0.5]{figure7b.eps} & \raisebox{2.75cm}{(b)}
\end{tabular}
\caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
\label{figure7}
\end{figure}
+\subsubsection{Network Lifetime}
-
-\subsubsection{\bf Network Lifetime}
-
-We observe the superiority of PeCO and DiLCO protocols in comparison with the
-two other approaches in prolonging the network lifetime. In
-Figures~\ref{figure8}(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 largest for DiLCO
-and PeCO protocols. For instance, for a network of 300~sensors and coverage
-ratio greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime
-is about twice longer with PeCO compared to DESK protocol. The performance
-difference is more obvious in Figure~\ref{figure8}(b) than in
-Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
- time, and the lifetime with a coverage of 50\% is far longer than with
-95\%.
+We observe the superiority of both PeCO and DiLCO protocols in comparison with
+the two other approaches in prolonging the network lifetime. In
+Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
+different network sizes. As can be seen in these figures, the lifetime
+increases with the size of the network, and it is clearly largest for DiLCO and
+PeCO protocols. For instance, for a network of 300~sensors and coverage ratio
+greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime is
+about twice longer with PeCO compared to DESK protocol. The performance
+difference is more obvious in Figure~\ref{figure8}(b) than in
+Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
+time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
\begin{figure}[h!]
\centering
\begin{tabular}{@{}cr@{}}
- \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
- \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}
+ \includegraphics[scale=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
+ \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)}
\end{tabular}
- \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
- and (b)~$Lifetime_{50}$.}
+ \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
\label{figure8}
\end{figure}
-
-
-Figure~\ref{figure9} 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 the term Protocol refers to DiLCO or PeCO. Indeed there are applications
-that do not require a 100\% coverage of the area to be monitored. PeCO might be
-an interesting method since it achieves a good balance between a high level
-coverage ratio and network lifetime. PeCO 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 PeCO is
-not ineffective for the smallest network sizes.
+Figure~\ref{figure9} compares the lifetime coverage of DiLCO and PeCO 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 the term Protocol refers to DiLCO or
+PeCO. Indeed there are applications that do not require a 100\% coverage of the
+area to be monitored. PeCO might be an interesting method since it achieves a
+good balance between a high level coverage ratio and network lifetime. PeCO
+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 PeCO is not ineffective for the smallest network
+sizes.
\begin{figure}[h!]
-\centering \includegraphics[scale=0.5]{figure9.eps}
+\centering \includegraphics[scale=0.55]{figure9.eps}
\caption{Network lifetime for different coverage ratios.}
\label{figure9}
\end{figure}
-
-\subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance}
-Table~\ref{my-labelx} explains all possible network lifetime result of the relation between the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. As can be seen in Table~\ref{my-labelx}, it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
+\subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}
+\label{sec:Impact}
+
+Table~\ref{my-labelx} shows network lifetime results for different values of
+$\alpha$ and $\beta$, and a network size equal to 200 sensor nodes. On the one
+hand, the choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit
+the activation of a large number of sensors, but as $\alpha$ is low, some areas
+may be poorly covered. This explains the results obtained for {\it Lifetime50}
+with $\beta \gg \alpha$: a large number of periods with low coverage ratio. On
+the other hand, when we choose $\alpha \gg \beta$, we favor the coverage even if
+some areas may be overcovered, so high coverage ratio is reached, but a large
+number of sensors are activated to achieve this goal. Therefore network
+lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve
+the best compromise between lifetime and coverage ratio. That explains why we
+have chosen this setting for the experiments presented in the previous
+subsections.
+
+%As can be seen in Table~\ref{my-labelx}, it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
\begin{table}[h]
\centering
0.3 & 0.7 & 134 & 0 \\ \hline
0.4 & 0.6 & 125 & 0 \\ \hline
0.5 & 0.5 & 118 & 30 \\ \hline
-0.6 & 0.4 & 94 & 57 \\ \hline
+{\bf 0.6} & {\bf 0.4} & {\bf 94} & {\bf 57} \\ \hline
0.7 & 0.3 & 97 & 49 \\ \hline
0.8 & 0.2 & 90 & 52 \\ \hline
0.9 & 0.1 & 77 & 50 \\ \hline
\section{Conclusion and Future Works}
\label{sec:Conclusion and Future Works}
-In this paper we have studied the problem of Perimeter-based Coverage Optimization in
-WSNs. We have designed a new protocol, called Perimeter-based 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.
-
-
-We have carried out several simulations to evaluate the proposed protocol. The
-simulation results show that PeCO is more energy-efficient than other
-approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
-energy consumption.
+In this paper we have studied the problem of perimeter coverage optimization in
+WSNs. We have designed a new protocol, called Perimeter-based 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. Several simulations have
+been carried out to evaluate the proposed protocol. The simulation results show
+that PeCO is more energy-efficient than other approaches, with respect to
+lifetime, coverage ratio, active sensors ratio, and energy consumption.
+
+We plan to extend our framework so that the schedules are planned for multiple
+sensing periods. We also want to improve the integer program to take into
+account heterogeneous sensors from both energy and node characteristics point of
+views. Finally, it would be interesting to implement PeCO protocol using a
+sensor-testbed to evaluate it in real world applications.
-We plan to extend our framework so that the schedules are planned for multiple
-sensing periods.
-We also want to improve our integer program to take into account heterogeneous
-sensors from both energy and node characteristics point of views.
-
-Finally, it would be interesting to implement our protocol using a
-sensor-testbed to evaluate it in real world applications.
+\subsection*{Acknowledgements}
+The authors are deeply grateful to the anonymous reviewers for their
+constructive advice, which improved the technical quality of the paper. 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 is also partially funded by the Labex ACTION program
+(contract ANR-11-LABX-01-01).
\bibliographystyle{gENO}
-\bibliography{articleeo}
-
+\bibliography{biblio} %articleeo
\end{document}
