%\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}
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.
+coverage for WSNs compared to other protocols.
\begin{keywords}
Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
\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
+communication hardware has given rise to the opportunity of using 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,
+user by means of sink nodes. The features of a WSN makes it suitable for a wide
+range of applications 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
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 unit for data transmission and reception.
The energy needed by an active sensor node to perform sensing, processing, and
-communication is supplied by a power supply which is a battery. This battery has
+communication is provided 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
-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
+recharge in most applications. Therefore it is necessary to deploy WSN with 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 is it possible to extend the lifetime coverage of a WSN as long
+as possible 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}.
-This paper makes the following contributions.
+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
+\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 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
+\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 a mixed-integer program based on the 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:
+\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.
\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
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
-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
-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
+coverage one, taking into account the intersection points among disks of sensors
+nodes or between disks of sensor nodes and boundaries. In
+\citep{huang2005coverage} authors prove that if the perimeters of the 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
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.}
+non-disjoint) \citep{wang2011coverage}, where each set completely covers a
+region of interest, and to successively activate these set covers. 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. {\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{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 information on its immediate neighbors only (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, 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.}
+provide nearly optimal solutions since the algorithm has a global view of the
+whole network. The disadvantage of a centralized method is obviously its high
+cost in communications needed to transmit to a single node, the base station
+which will globally schedule nodes' activities, data from all the other sensor
+nodes in the area. The price in communications can be 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 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 the 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
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
+ integer program which has a twofold objective: minimizing 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
+subregions using a divide-and-conquer method. The 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.}
+ of specified points/targets as in the DiLCO protocol, we formulate an integer
+ program based on the 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}
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
+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
+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
+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.
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:
$$
- Dist(u,v)=\sqrt{\vert u_x - v_x \vert^2 + \vert u_y-v_y \vert^2},
+ Dist(u,v)=\sqrt{(u_x - v_x)^2 + (u_y-v_y)^2},
$$
while the angle~$\alpha$ is obtained through the formula:
\[
\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*}
\end{table}
In the PeCO protocol, the scheduling of the sensor nodes' activities is
-formulated with an mixed-integer program based on coverage
+formulated with a 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
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}
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
+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.
\begin{figure}[t!]
\centering
-\includegraphics[width=85mm]{figure4.eps}
+\includegraphics[width=80mm]{figure4.eps}
\caption{PeCO protocol.}
\label{figure4}
\end{figure}
-We define two types of packets to be used by PeCO protocol:
+We define two types of packets to be used by the PeCO protocol:
\begin{itemize}
\item INFO packet: sent by each sensor node to all the nodes inside a same
subregion for information exchange.
\item ActiveSleep packet: sent by the leader to all the nodes in its subregion
to transmit to them their respective status (stay Active or go Sleep) during
- sensing phase.
+ the sensing phase.
\end{itemize}
Five statuses are possible for a sensor node in the network:
% \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} \;
+ \label{alg:PeCO}
\caption{PeCO pseudocode}
\eIf{$RE_k \geq E_{th}$}{
$s_k.status$ = COMMUNICATION\;
%\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.
-
-% TO BE CONTINUED
+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 indexes.
+\end{enumerate}
+Once chosen, the leader collects information to formulate and solve the integer
+program which allows to build the set of active sensors in the sensing
+stage.
\section{Perimeter-based Coverage Problem Formulation}
\label{cp}
-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).
+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.
-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
+$I_j$ refers to the set of coverage intervals which has been defined according
+to the method introduced in Subsection~\ref{CI}. For a coverage interval $i$,
+let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved
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 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}
-\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.
+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}
-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 : $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$.
+%\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 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 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.
+weights associated with coverage intervals of the specified part of a region may
+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 to optimize 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. the 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 the network to
+be more reliable but would have resulted 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 the 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 the 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 & Sensing & {\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 the 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. The DiLCO protocol tries to satisfy the
+coverage of a set of primary points, whereas the objective of the PeCO protocol
+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 the DiLCO and PeCO protocols put more redundant sensors to sleep
+status (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{Active Sensors Ratio}
-
-
-\subsubsection{\bf 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}.
+Minimizing the number of 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 the 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, the 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
+$Lifetime_{95}$ and $Lifetime_{50}$. The results show that the 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 also 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 over 50\% is far longer than with
-95\%.
+We observe the superiority of both the PeCO and DiLCO protocols in comparison with
+the two other approaches in prolonging the network lifetime. In
+Figures~\ref{figure8}(a) and (b), $Lifetime_{95}$ and $Lifetime_{50}$ 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 larger for the 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 the 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 the 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{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 also
+limits 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
+$Lifetime_{50}$ 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 a high coverage ratio is
+reached, but a large number of sensors are activated to achieve this goal.
+Therefore the 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.
-\subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance}
-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]
\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.
-
-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.
-
+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 the PeCO protocol using a
+sensor-testbed to evaluate it in real world applications.
+
+\subsection*{Acknowledgments}
+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).
+
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