%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
%\renewcommand{\algorithmcfname}{ALGORITHM}
\usepackage{indentfirst}
+\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}}
+\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}};}
-
+ Belfort, France}}}
\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
- 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
- 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 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 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 deviations.
+\item We have conducted extensive simulation experiments, 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.
+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.
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
-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
+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 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
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 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.
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
+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. 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 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}
\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}
\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. Node Sensors 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
-\includegraphics[width=80mm]{figure4.eps}
+\includegraphics[width=85mm]{figure4.eps}
\caption{PeCO protocol.}
\label{figure4}
\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}
-
-
+ %\emph{Initialize the sensor node and determine it's position and subregion} \;
+ \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
+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
+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.
+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.
+% TO BE CONTINUED
\section{Perimeter-based Coverage Problem Formulation}
\label{cp}
-In this section, the coverage model is mathematically formulated. The following
-notations are used throughout the
+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}
\end{equation}
Note that $a^k_{ik}=1$ by definition of the interval.
-Second, several binary and integer variables are defined. Hence, each binary
+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 an integer
+($X_k=1$ 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 $V^j_i$.
-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
+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
-Our coverage optimization problem can then be mathematically expressed as follows:
+The 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
+\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 : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In the contrary, 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
+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 integer program must be solved by the leader in
+\citep{0031-9155-44-1-012}. The choice of variables $\alpha$ and $\beta$ should be made according to the needs of the application. $\alpha$ should be enough large to prevent undercoverage and so to reach the highest possible coverage ratio. $\beta$ should be enough large 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.
+sensing phase) are considered in the model.
\section{Performance Evaluation and Analysis}
\label{sec:Simulation Results and Analysis}
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\%.
+ time, and the lifetime with a coverage over 50\% is far longer than with
+95\%.
\begin{figure}[h!]
\centering
\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 $Lifetime_{95}$.
+Table~\ref{my-labelx} shows network lifetime results for the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. 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. With $\alpha \gg \beta$, we priviligie 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.
+%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
