% v4.0 released April 2013
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-%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
-%\renewcommand{\algorithmcfname}{ALGORITHM}
+
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\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}}
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
+scheduling which ensures sensing coverage while minimizing the energy cost. In
+this paper an approach called Perimeter-based Coverage Optimization protocol
+(PeCO) is proposed. 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 the 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
architecture.
\item A new mathematical optimization model is proposed. Instead of trying to
cover a set of specified points/targets as in most of the methods proposed in
- the literature, we formulate 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.
+ the literature, a mixed-integer program based on the perimeter coverage of
+ each sensor is formulated. 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 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.
+ simulator OMNeT++, to demonstrate the efficiency of the PeCO protocol. The
+ PeCO protocol has been compared to two approaches found in the literature:
+ DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to the 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
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
+ points, the 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
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 the DiLCO protocol, we formulate an integer
- program based on the perimeter coverage of each sensor. The model involves
+ of specified points/targets as in the DiLCO protocol, an integer program based
+ on the perimeter coverage of each sensor is formulated. 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.
-
-
\subsection{Assumptions and Models}
\label{CI}
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
+this sensor. The communication range $R_c$ is assumed to satisfy : $R_c
\geq 2 \cdot R_s$. 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.
(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 neighboring point of view. The resulting couples of intersection points
+sensor~$0$ has nine neighbors. For each neighbor the two points resulting from
+the intersection of the two sensing areas have been reported on its perimeter
+(the perimeter of the disk covered by the sensor~$0$). 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!]
coverage is determined for each interval defined by two successive points. The
maximum level of coverage is equal to the number of overlapping arcs. For
example, between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
-(the value is highlighted in yellow at the bottom of Figure~\ref{figure2}), which
+(the value is given 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
\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
+subregions using a divide-and-conquer algorithm. In a second step the protocol
will be executed in a distributed way in each subregion simultaneously to
schedule nodes' activities for one sensing period. Sensor nodes are assumed to
be deployed almost uniformly over the region. The regular subdivision is made
\label{figure4}
\end{figure}
-We define two types of packets to be used by the PeCO protocol:
+Two types of packets used by the PeCO protocol are defined:
\begin{itemize}
\item INFO packet: sent by each sensor node to all the nodes inside a same
subregion for information exchange.
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{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} \;
\label{alg:PeCO}
\caption{PeCO pseudocode}
\eIf{$RE_k \geq E_{th}$}{
}
\end{algorithm2e}
-%\begin{algorithm}
-%\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
-%\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
-%\hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
-%\hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
-%\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
-%\hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
-%\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
-%\hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
-%\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
-%\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
-%\hspace*{1.2cm} {\bf end}\\
-%\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
-%\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
-%\hspace*{1.2cm} {\bf end}\\
-%\hspace*{1.2cm} {\bf else}\\
-%\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
-%\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
-%\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
-%\hspace*{1.2cm} {\bf end}\\
-%\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
-%\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
-%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-%\hspace*{0.6cm} {\bf end}\\
-%\hspace*{0.6cm} {\bf else}\\
-%\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
-%\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
-%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-%\hspace*{0.6cm} {\bf end}\\
-%{\bf end}\\
-%{\bf else}\\
-%\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
-%{\bf end}\\
-%\label{alg:PeCO}
-%\end{algorithm}
-
In this algorithm, $K.CurrentSize$ and $K.PreviousSize$ respectively represent
the current number and the previous number of living nodes in the subnetwork of
the subregion. At the beginning of the first period $K.PreviousSize$ is
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.
-\textcolor{blue}{Both INFO packet and ActiveSleep packet contain two parts: header and data payload. The sensor ID is included in the header, where the header size is 8 bits. The data part includes position coordinates (64 bits), remaining energy (32 bits), and the number of one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112 bits. The ActiveSleep packet is 16 bits size, 8 bits for the header and 8 bits for data part that includes only sensor status (0 or 1).}
-The sensors inside a same region cooperate to elect a leader. The selection
-criteria for the leader are (in order of priority):
+Both INFO packet and ActiveSleep packet contain two parts: header and data
+payload. The sensor ID is included in the header, where the header size is 8
+bits. The data part includes position coordinates (64 bits), remaining energy
+(32 bits), and the number of one-hop live neighbors (8 bits). Therefore the size
+of the INFO packet is 112 bits. The ActiveSleep packet is 16 bits size, 8 bits
+for the header and 8 bits for data part that includes only sensor status (0 or
+1). 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.
+program which allows to build the set of active sensors in the sensing stage.
\section{Perimeter-based Coverage Problem Formulation}
\label{cp}
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
+effective number. And these deviations are minimized, 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.
\end{aligned}
\end{equation}
-%\begin{equation}
-%\left \{
-%\begin{array}{ll}
-%\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) & \\
-%\textrm{subject to :} &\\
-%\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
-%\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
-%X_{k} \in \{0,1\}, \forall k \in A \\
-%M^j_i, V^j_i \in \mathbb{R}^{+}
-%\end{array}
-%\right.
-%\end{equation}
If a given level of coverage $l$ is required for one sensor, the sensor is said
to be undercovered (respectively overcovered) if the level of coverage of one of
\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
+and the energy consumption model used is described in previous
work~\citep{Idrees2}. Table~\ref{table3} gives the chosen parameters settings.
\begin{table}[ht]
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. 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.
+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
because without network connectivity a sensor may not be able to send to a
base station an event it has sensed.
\item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
- observe the area of interest. In our case, the sensor field is discretized as
+ observe the area of interest. Here the sensor field is discretized as
a regular grid, which yields the following equation:
\begin{equation*}
\scriptsize
subregions during the current sensing phase and $N$ is total number of grid
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
- overhead and maximize the WSN lifetime. The active sensors ratio is defined as
- follows:
+\item {\bf Active Sensors Ratio (ASR)}: a major objective of the proposed
+ protocol is to 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:
\begin{equation*}
\scriptsize
- \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
+ \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
\end{equation*}
where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
sensing period~$p$, $R$ is the number of subregions, and $|J|$ is the number
of sensors in the network.
-\item {\bf \textcolor{blue}{Energy Saving Ratio (ESR)}}:
-\textcolor{blue}{this metric, which shows the ability of a protocol to save energy, is defined by:
+\item {\bf Energy Saving Ratio (ESR)}: this metric, which shows the ability of a
+ protocol to save energy, is defined by:
\begin{equation*}
\scriptsize
\mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
{\mbox{Total number of sensors in the network}} \times 100.
\end{equation*}
- }
\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
\subsection{Simulation Results}
-In order to assess and analyze the performance of our protocol we have
-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}.
+The PeCO protocol has been implemented in OMNeT++~\citep{varga} simulator in
+order to assess and analyze its performance. 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
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
+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
+huge memory use. Fortunately, to solve the optimization problem, the use of
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.
+consuming and more efficient is possible, or a lightweight heuristic may be
+implemented. 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
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
+protocol~\citep{Idrees2}, is an improved version of a research work presented
+in~\citep{idrees2014coverage}. 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
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 ($l=1$).
+is to reach a desired level of coverage for each sensor perimeter. In the
+experimentations, a level of coverage equal to one ($l=1$) is chosen
+.
\subsubsection{Coverage Ratio}
\subsubsection{Active Sensors Ratio}
-Minimizing the number of active sensor nodes in each period is essential to minimize the
-energy consumption and thus to maximize the network lifetime.
+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
+nodes. 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}.
\label{figure6}
\end{figure}
-\subsubsection{\textcolor{blue}{Energy Saving Ratio (ESR)}}
-
-%\textcolor{blue}{In this experiment, we study the energy saving ratio, see Figure~\ref{fig5}, for 200 deployed nodes.
-%The larger the ratio is, the more redundant sensor nodes are switched off, and consequently the longer the network may liv%e. }
-
-\textcolor{blue}{The simulation results show that our protocol PeCO allows to
- efficiently save energy by turning off some sensors during the sensing phase.
- As shown in Figure~\ref{fig5}, GAF provides better energy saving than PeCO for
- the first fifty rounds, because GAF balances the energy consumption among
- sensor nodes inside each small fixed grid and thus permits to extend the life of
- sensors in each grid fairly but in the same time turn on large number of
- sensors during sensing that lead later to quickly deplete sensor's batteries
- together. After that GAF provide less energy saving compared with other
- approaches because of the large number of dead nodes. DESK algorithm shows less
- energy saving compared with other approaches due to activate a large number of
- sensors during the sensing. DiLCO protocol provides less energy saving ratio
- compared with PeCO because it generally activate a larger number of sensor
- nodes during sensing. Note that again as the number of rounds increases PeCO
- becomes the most performing one, since it consumes less energy compared with
- other approaches.}
+\subsubsection{Energy Saving Ratio}
+
+The simulation results show that the protocol PeCO saves efficiently energy by
+turning off some sensors during the sensing phase. As shown in
+Figure~\ref{figure7}, GAF provides better energy saving than PeCO for the first
+fifty rounds. Indeed GAF balances the energy consumption among sensor nodes
+inside each small fixed grid and thus permits to extend the life of sensors in
+each grid fairly. However, at the same time it turns on a large number of
+sensors and that leads later to quickly deplete sensor's batteries. DESK
+algorithm shows less energy saving compared with other approaches. In
+comparison with PeCO, DiLCO protocol usually provides lower energy saving
+ratios. Moreover, it can be noticed that after round fifty, PeCO protocol
+exhibits the slowest decrease among all the considered protocols.
\begin{figure}[h!]
%\centering
% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{ESR.eps} %\\~ ~ ~(a)
-\caption{Energy Saving Ratio for 200 deployed nodes}
-\label{fig5}
-\end{figure}
-
-
+\includegraphics[scale=0.5]{figure7.eps} %\\~ ~ ~(a)
+\caption{Energy Saving Ratio for 200 deployed nodes.}
+\label{figure7}
+\end{figure}
\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)
+network densities and the four approaches compared. Figures~\ref{figure8}(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.
+$Lifetime_{95}$ 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. The energy overhead when increasing network size
+is the lowest with PeCO.
\begin{figure}[h!]
\centering
\begin{tabular}{@{}cr@{}}
- \includegraphics[scale=0.5]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
- \includegraphics[scale=0.5]{figure7b.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{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
- \label{figure7}
+ \label{figure8}
\end{figure}
\subsubsection{Network Lifetime}
-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\%.
+In comparison with the two other approaches, PeCO and DiLCO protocols are better
+for prolonging the network lifetime. In Figures~\ref{figure9}(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\%, it
+can be observed on Figure~\ref{figure9}(b) that the lifetime is about twice
+longer with PeCO compared to the DESK protocol. The performance difference is
+more obvious in Figure~\ref{figure9}(b) than in Figure~\ref{figure9}(a) because
+the gain induced by protocols (PeCO and DiLCO) 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=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
- \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)}
+ \includegraphics[scale=0.5]{figure9a.eps} & \raisebox{2.75cm}{(a)} \\
+ \includegraphics[scale=0.5]{figure9b.eps} & \raisebox{2.75cm}{(b)}
\end{tabular}
\caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
- \label{figure8}
+ \label{figure9}
\end{figure}
-Figure~\ref{figure9} compares the lifetime coverage of the DiLCO and PeCO protocols
-for different coverage ratios. We denote by Protocol/70, Protocol/80,
-Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the
+Figure~\ref{figure10} compares the lifetime coverage of the DiLCO and PeCO
+protocols for different coverage ratios. Protocol/70, Protocol/80, Protocol/85,
+Protocol/90, and Protocol/95 correspond to the amount of time during which the
network can satisfy an area coverage greater than $70\%$, $80\%$, $85\%$,
$90\%$, and $95\%$ respectively, where the term Protocol refers to DiLCO or
-PeCO. \textcolor{blue}{Indeed there are applications that do not require a 100\% coverage of the
-area to be monitored. For example, forest
-fire application might require complete coverage
-in summer seasons while only require 80$\%$ of the area to be covered in rainy seasons~\citep{li2011transforming}. As another example, birds habit study requires only 70$\%$-coverage at nighttime when the birds are sleeping while requires 100$\%$-coverage at daytime when the birds are active~\citep{1279193}.
-%Mudflows monitoring applications may require part of the area to be covered in sunny days. Thus, to extend network lifetime, the coverage quality can be decreased if it is acceptable~\citep{wang2014keeping}}.
- PeCO always outperforms DiLCO for the three lower coverage ratios, moreover the
-improvements grow with the network size. DiLCO outperforms PeCO when the coverage ratio is required to be $>90\%$, but PeCo extends the network lifetime significantly when coverage ratio can be relaxed.}
-%DiLCO is better for coverage ratios near 100\%, but in that case PeCO is not ineffective for the smallest network sizes.
+PeCO. Indeed there are applications that do not require a 100\% coverage of the
+area to be monitored. For example, forest fire application might require
+complete coverage in summer seasons while only require 80$\%$ of the area to be
+covered in rainy seasons~\citep{li2011transforming}. As another example, birds
+habit study requires only 70$\%$-coverage at nighttime when the birds are
+sleeping while requires 100$\%$-coverage at daytime when the birds are
+active~\citep{1279193}. PeCO always outperforms DiLCO for the three lower
+coverage ratios, moreover the improvements grow with the network size. DiLCO
+outperforms PeCO when the coverage ratio is required to be $>90\%$, but PeCO
+extends the network lifetime significantly when coverage ratio can be relaxed.
\begin{figure}[h!]
-\centering \includegraphics[scale=0.55]{figure9.eps}
+\centering \includegraphics[scale=0.55]{figure10.eps}
\caption{Network lifetime for different coverage ratios.}
-\label{figure9}
+\label{figure10}
\end{figure}
\subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}
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
+coverage ratio. On the other hand, when $\alpha \gg \beta$ is chosen, the
+coverage is favored 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
+ratio. That explains why this setting has been chosen for the experiments
presented in the previous subsections.
-%As can be seen in Table~\ref{my-labelx}, it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
-
\begin{table}[h]
\centering
\caption{The impact of $\alpha$ and $\beta$ on PeCO's performance}
\section{Conclusion and Future Works}
\label{sec:Conclusion and Future Works}
-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
+In this paper the problem of perimeter coverage optimization in WSNs has been
+studied. A new protocol called Perimeter-based Coverage Optimization is
+designed. This protocol 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.
+This 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.
+
+This framework will be extented so that the schedules are planned for multiple
+sensing periods. The integer program would be improved 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
+Ali Kadhum Idrees is supported in part by University of Babylon (Iraq).
+This work is also partially funded by the Labex ACTION program
(contract ANR-11-LABX-01-01).
\bibliographystyle{gENO}
-\bibliography{biblio} %articleeo
+\bibliography{biblio}
\end{document}
