+
+
\documentclass[conference]{IEEEtran}
\begin{abstract}
One of the fundamental challenges in Wireless Sensor Networks (WSNs)
-is coverage preservation and extension of the network lifetime
+is the coverage preservation and the extension of the network lifetime
continuously and effectively when monitoring a certain area (or
region) of interest. In this paper a coverage optimization protocol to
improve the lifetime in heterogeneous energy wireless sensor networks
is proposed. The area of interest is first divided into subregions
-using a divide-and-conquer method and then scheduling of sensor node
+using a divide-and-conquer method and then the scheduling of sensor node
activity is planned for each subregion. The proposed scheduling
considers rounds during which a small number of nodes, remaining
active for sensing, is selected to ensure coverage. Each round
carried out by a leader node which solves an integer program.
Simulation results show that the proposed approach can prolong the
network lifetime and improve the coverage performance.
-\end{abstract}
+\end{abstract*&^@!U&*T@}
%\keywords{Area Coverage, Wireless Sensor Networks, lifetime Optimization, Distributed Protocol.}
\noindent Recent years have witnessed significant advances in wireless
communications and embedded micro-sensing MEMS technologies which have
-made emerge wireless sensor networks as one of the most promising
+led to the emergence of wireless sensor networks as one of the most promising
technologies~\cite{asc02}. In fact, they present huge potential in
several domains ranging from health care applications to military
applications. A sensor network is composed of a large number of tiny
sensing devices deployed in a region of interest. Each device has
-processing and wireless communication capabilities, which enable to
+processing and wireless communication capabilities, which enable it to
sense its environment, to compute, to store information and to deliver
report messages to a base station.
%These sensor nodes run on batteries with limited capacities. To achieve a long life of the network, it is important to conserve battery power. Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
spatial redundancy can then be exploited to increase the lifetime of
the network. In such a high density network, if all sensor nodes were
to be activated at the same time, the lifetime would be reduced. To
-extend the lifetime of the network, the main idea is to take benefit
-from the overlapping sensing regions of some sensor nodes to save
+extend the lifetime of the network, the main idea is to take advantage
+of the overlapping sensing regions of some sensor nodes to save
energy by turning off some of them during the sensing phase.
Obviously, the deactivation of nodes is only relevant if the coverage
-of the monitored area is not affected. Consequently, future software
+of the monitored area is not affected. Consequently, future softwares
may need to adapt appropriately to achieve acceptable quality of
-service for applications. In this paper we concentrate on area
+service for applications. In this paper we concentrate on the area
coverage problem, with the objective of maximizing the network
lifetime by using an adaptive scheduling. The area of interest is
divided into subregions and an activity scheduling for sensor nodes is
planned for each subregion.
-% DEBUT AJOUT
-{\bf In fact, the nodes in a subregion can be seen as a cluster where
+ In fact, the nodes in a subregion can be seen as a cluster where
each node sends sensing data to the cluster head or the sink node.
Furthermore, the activities in a subregion/cluster can continue even
- if another cluster stops due to too much node failures.}
-% FIN AJOUT
+ if another cluster stops due to too many node failures.
Our scheduling scheme considers rounds, where a round starts with a
discovery phase to exchange information between sensors of the
-subregion, in order to choose in suitable manner a sensor node to
+subregion, in order to choose in a suitable manner a sensor node to
carry out a coverage strategy. This coverage strategy involves the
solving of an integer program which provides the activation of the
sensors for the sensing phase of the current round.
proposed approach. Finally, we give concluding remarks and some
suggestions for future works in Section~\ref{sec:conclusion}.
-\section{Related Works}
+\section{Related works}
\label{rw}
\noindent This section is dedicated to the various approaches proposed
in the literature for the coverage lifetime maximization problem,
where the objective is to optimally schedule sensors' activities in
order to extend network lifetime in a randomly deployed network. As
-this problem is subject to a wide range of interpretations, we suggest
-to recall main definitions and assumptions related to our work.
+this problem is subject to a wide range of interpretations, we have chosen
+to recall the main definitions and assumptions related to our work.
%\begin{itemize}
%\item Area Coverage: The main objective is to cover an area. The area coverage requires
The most discussed coverage problems in literature can be classified
into two types \cite{ma10}: area coverage (also called full or blanket
coverage) and target coverage. An area coverage problem is to find a
-minimum number of sensors to work such that each physical point in the
+minimum number of sensors to work, such that each physical point in the
area is within the sensing range of at least one working sensor node.
Target coverage problem is to cover only a finite number of discrete
points called targets. This type of coverage has mainly military
applications. Our work will concentrate on the area coverage by design
and implementation of a strategy which efficiently selects the active
nodes that must maintain both sensing coverage and network
-connectivity and in the same time improve the lifetime of the wireless
+connectivity and at the same time improve the lifetime of the wireless
sensor network. But requiring that all physical points of the
considered region are covered may be too strict, especially where the
sensor network is not dense. Our approach represents an area covered
{\bf Lifetime}
Various definitions exist for the lifetime of a sensor
-network~\cite{die09}. Main definitions proposed in the literature are
-related to the remaining energy of the nodes or to the percentage of
-coverage. The lifetime of the network is mainly defined as the amount
-of time that the network can satisfy its coverage objective (the
+network~\cite{die09}. The main definitions proposed in the literature are
+related to the remaining energy of the nodes or to the coverage percentage.
+The lifetime of the network is mainly defined as the amount
+of time during which the network can satisfy its coverage objective (the
amount of time that the network can cover a given percentage of its
area or targets of interest). In this work, we assume that the network
is alive until all nodes have been drained of their energy or the
{\bf Activity scheduling}
-Activity scheduling is to schedule the activation and deactivation of
+Activitiy scheduling is to schedule the activation and deactivation of
sensor nodes. The basic objective is to decide which sensors are in
-what states (active or sleeping mode) and for how long, such that the
+what states (active or sleeping mode) and for how long, so that the
application coverage requirement can be guaranteed and the network
lifetime can be prolonged. Various approaches, including centralized,
distributed, and localized algorithms, have been proposed for activity
-scheduling. In the distributed algorithms, each node in the network
+scheduling. In distributed algorithms, each node in the network
autonomously makes decisions on whether to turn on or turn off itself
only using local neighbor information. In centralized algorithms, a
central controller (a node or base station) informs every sensors of
Some distributed algorithms have been developed
in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02} to perform the
scheduling. Distributed algorithms typically operate in rounds for
-predetermined duration. At the beginning of each round, a sensor
-exchange information with its neighbors and makes a decision to either
+a predetermined duration. At the beginning of each round, a sensor
+exchanges information with its neighbors and makes a decision to either
remain turned on or to go to sleep for the round. This decision is
-basically based on simple greedy criteria like the largest uncovered
+basically made on simple greedy criteria like the largest uncovered
area \cite{Berman05efficientenergy}, maximum uncovered targets
\cite{1240799}. In \cite{Tian02}, the scheduling scheme is divided
into rounds, where each round has a self-scheduling phase followed by
-a sensing phase. Each sensor broadcasts a message containing node ID
-and node location to its neighbors at the beginning of each round. A
+a sensing phase. Each sensor broadcasts a message containing the node ID
+and the node location to its neighbors at the beginning of each round. A
sensor determines its status by a rule named off-duty eligible rule
which tells him to turn off if its sensing area is covered by its
neighbors. A back-off scheme is introduced to let each sensor delay
the decision process with a random period of time, in order to avoid
-that nodes make conflicting decisions simultaneously and that a part
-of the area is no longer covered.
+simultaneous conflicting decisions between nodes and lack of coverage on any area.
\cite{Prasad:2007:DAL:1782174.1782218} defines a model for capturing
the dependencies between different cover sets and proposes localized
heuristic based on this dependency. The algorithm consists of two
phases, an initial setup phase during which each sensor computes and
-prioritize the covers and a sensing phase during which each sensor
+prioritizes the covers and a sensing phase during which each sensor
first decides its on/off status, and then remains on or off for the
rest of the duration. Authors in \cite{chin2007} propose a novel
distributed heuristic named Distributed Energy-efficient Scheduling
for k-coverage (DESK) so that the energy consumption among all the
sensors is balanced, and network lifetime is maximized while the
-coverage requirements is being maintained. This algorithm works in
+coverage requirement is being maintained. This algorithm works in
round, requires only 1-sensing-hop-neighbor information, and a sensor
decides its status (active/sleep) based on its perimeter coverage
computed through the k-Non-Unit-disk coverage algorithm proposed in
\cite{Huang:2003:CPW:941350.941367}.
-Some others approaches do not consider synchronized and predetermined
+Some other approaches do not consider a synchronized and predetermined
period of time where the sensors are active or not. Indeed, each
-sensor maintains its own timer and its time wake-up is randomized
+sensor maintains its own timer and its wake-up time is randomized
\cite{Ye03} or regulated \cite{cardei05} over time.
%A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
where each set completely covers an interest region and to activate
these set covers successively.
-First algorithms proposed in the literature consider that the cover
+The first algorithms proposed in the literature consider that the cover
sets are disjoint: a sensor node appears in exactly one of the
generated cover sets. For instance, Slijepcevic and Potkonjak
\cite{Slijepcevic01powerefficient} propose an algorithm which
al.~\cite{Abrams:2004:SKA:984622.984684} design three approximation
algorithms for a variation of the set k-cover problem, where the
objective is to partition the sensors into covers such that the number
-of covers that include an area, summed over all areas, is maximized.
+of covers that includes an area, summed over all areas, is maximized.
Their work builds upon previous work
in~\cite{Slijepcevic01powerefficient} and the generated cover sets do
not provide complete coverage of the monitoring zone.
can monitor all targets. They first transform the problem into a
maximum flow problem which is formulated as a mixed integer
programming (MIP). Then their heuristic uses the output of the MIP to
-compute disjoint set covers. Results show that these heuristic
+compute disjoint set covers. Results show that this heuristic
provides a number of set covers slightly larger compared to
\cite{Slijepcevic01powerefficient} but with a larger execution time
due to the complexity of the mixed integer programming resolution.
lifetime increases compared with related
work~\cite{Cardei:2005:IWS:1160086.1160098}. In~\cite{berman04}, the
authors have formulated the lifetime problem and suggested another
-(LP) technique to solve this problem. A centralized provably near
-optimal solution based on the Garg-K\"{o}nemann
-algorithm~\cite{garg98} is also proposed.
+(LP) technique to solve this problem. A centralized solution based on the Garg-K\"{o}nemann
+algorithm~\cite{garg98}, probably near
+the optimal solution, is also proposed.
{\bf Our contribution}
\item {\bf What are the rules to decide which node has to be turned on
or off?} Our algorithm tends to limit the overcoverage of points of
- interest to avoid turning on too much sensors covering the same
+ interest to avoid turning on too many sensors covering the same
areas at the same time, and tries to prevent undercoverage. The
decision is a good compromise between these two conflicting
objectives.
-\item {\bf Which node should make such decision?} As mentioned in
+\item {\bf Which node should make such a decision?} As mentioned in
\cite{pc10}, both centralized and distributed algorithms have their
own advantages and disadvantages. Centralized coverage algorithms
have the advantage of requiring very low processing power from the
messages in large networks may consume a considerable amount of
energy in a localized approach compared to a centralized one. Our
work does not consider only one leader to compute and to broadcast
- the schedule decision to all the sensors. When the network size
- increases, the network is divided in many subregions and the
+ the scheduling decision to all the sensors. When the network size
+ increases, the network is divided into many subregions and the
decision is made by a leader in each subregion.
\end{itemize}
-\section{Activity Scheduling}
+\section{Activity scheduling}
\label{pd}
We consider a randomly and uniformly deployed network consisting of
Each round is divided into 4 phases : Information (INFO) Exchange,
Leader Election, Decision, and Sensing. For each round there is
-exactly one set cover responsible for sensing task. This protocol is
-more reliable against the unexpectedly node failure because it works
+exactly one set cover responsible for the sensing task. This protocol is
+more reliable against an unexpected node failure because it works
in rounds. On the one hand, if a node failure is detected before
-taking the decision, the node will not participate to this phase, and,
+making the decision, the node will not participate to this phase, and,
on the other hand, if the node failure occurs after the decision, the
-sensing task of the network will be affected temporarily: only during
+sensing task of the network will be temporarily affected: only during
the period of sensing until a new round starts, since a new set cover
will take charge of the sensing task in the next round. The energy
consumption and some other constraints can easily be taken into
round. However, the pre-sensing phases (INFO Exchange, Leader
Election, Decision) are energy consuming for some nodes, even when
they do not join the network to monitor the area. Below, we describe
-each phase in more detail.
+each phase in more details.
-\subsection{INFOrmation Exchange Phase}
+\subsection{Information exchange phase}
Each sensor node $j$ sends its position, remaining energy $RE_j$, and
the number of local neighbors $NBR_j$ to all wireless sensor nodes in
%The working phase works in rounding fashion. Each round include 3 steps described as follow :
-\subsection{Leader Election Phase}
+\subsection{Leader election phase}
This step includes choosing the Wireless Sensor Node Leader (WSNL)
-which will be responsible of executing coverage algorithm. Each
+which will be responsible for executing the coverage algorithm. Each
subregion in the area of interest will select its own WSNL
independently for each round. All the sensor nodes cooperate to
select WSNL. The nodes in the same subregion will select the leader
number of neighbors, larger remaining energy, and then in case of
equality, larger index.
-\subsection{Decision Phase}
+\subsection{Decision phase}
The WSNL will solve an integer program (see section~\ref{cp}) to
select which sensors will be activated in the following sensing phase
to cover the subregion. WSNL will send Active-Sleep packet to each
-sensor in the subregion based on algorithm's results.
+sensor in the subregion based on the algorithm's results.
%The main goal in this step after choosing the WSNL is to produce the best representative active nodes set that will take the responsibility of covering the whole region $A^k$ with minimum number of sensor nodes to prolong the lifetime in the wireless sensor network. For our problem, in each round we need to select the minimum set of sensor nodes to improve the lifetime of the network and in the same time taking into account covering the region $A^k$ . We need an optimal solution with tradeoff between our two conflicting objectives.
%The above region coverage problem can be formulated as a Multi-objective optimization problem and we can use the Binary Particle Swarm Optimization technique to solve it.
-\subsection{Sensing Phase}
+\subsection{Sensing phase}
Active sensors in the round will execute their sensing task to
preserve maximal coverage in the region of interest. We will assume
-that the cost of keeping a node awake (or sleep) for sensing task is
+that the cost of keeping a node awake (or asleep) for sensing task is
the same for all wireless sensor nodes in the network. Each sensor
will receive an Active-Sleep packet from WSNL informing it to stay
-awake or go sleep for a time equal to the period of sensing until
+awake or to go to sleep for a time equal to the period of sensing until
starting a new round.
%\subsection{Sensing coverage model}
constant sensing range $R_s$. All space points within a disk centered
at the sensor with the radius of the sensing range is said to be
covered by this sensor. We also assume that the communication range is
-at least twice of the sensing range. In fact, Zhang and
-Zhou~\cite{Zhang05} prove that if the transmission range fulfills the
+at least twice the size of the sensing range. In fact, Zhang and
+Zhou~\cite{Zhang05} proved that if the transmission range fulfills the
previous hypothesis, a complete coverage of a convex area implies
connectivity among the working nodes in the active mode.
%To calculate the coverage ratio for the area of interest, we can propose the following coverage model which is called Wireless Sensor Node Area Coverage Model to ensure that all the area within each node sensing range are covered. We can calculate the positions of the points in the circle disc of the sensing range of wireless sensor node based on the Unit Circle in figure~\ref{fig:cluster1}:
%We choose to representEach wireless sensor node will be represented into a selected number of primary points by which we can know if the sensor node is covered or not.
% Figure ~\ref{fig:cluster2} shows the selected primary points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
-\noindent Instead of working with area coverage, we consider for each
+\noindent Instead of working with the coverage area, we consider for each
sensor a set of points called primary points. We also assume that the
-sensing disk defined by a sensor is covered if all primary points of
+sensing disk defined by a sensor is covered if all the primary points of
this sensor are covered.
%\begin{figure}[h!]
%\centering
based on the proposed model. We use these primary points (that can be
increased or decreased if necessary) as references to ensure that the
monitored region of interest is covered by the selected set of
-sensors, instead of using all points in the area.
+sensors, instead of using all the points in the area.
\noindent We can calculate the positions of the selected primary
points in the circle disk of the sensing range of a wireless sensor
\label{fig2}
\end{figure}
-\section{Coverage Problem Formulation}
+\section{Coverage problem formulation}
\label{cp}
%We can formulate our optimization problem as energy cost minimization by minimize the number of active sensor nodes and maximizing the coverage rate at the same time in each $A^k$ . This optimization problem can be formulated as follow: Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake is the same for all wireless sensor nodes in the network. We can define the decision parameter $X_j$ as in \eqref{eq11}:\\
\noindent Our model is based on the model proposed by
\cite{pedraza2006} where the objective is to find a maximum number of
-disjoint cover sets. To accomplish this goal, authors propose an
+disjoint cover sets. To accomplish this goal, authors proposed an
integer program which forces undercoverage and overcoverage of targets
to become minimal at the same time. They use binary variables
$x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
\begin{equation}
\Theta_{p} = \left \{
\begin{array}{l l}
- 0 & \mbox{if point $p$ is not covered,}\\
+ 0 & \mbox{if the primary point}\\
+ & \mbox{$p$ is not covered,}\\
\left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
\end{array} \right.
\label{eq13}
\begin{equation}
U_{p} = \left \{
\begin{array}{l l}
- 1 &\mbox{if point $p$ is not covered,} \\
+ 1 &\mbox{if the primary point $p$ is not covered,} \\
0 & \mbox{otherwise.}\\
\end{array} \right.
\label{eq14}
sensing in the round (1 if yes and 0 if not);
\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
one that are covering the primary point $p$;
-\item $U_{p}$ : {\it undercoverage}, indicates whether or not point
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the principal point
$p$ is being covered (1 if not covered and 0 if covered).
\end{itemize}
The first group of constraints indicates that some primary point $p$
should be covered by at least one sensor and, if it is not always the
-case, overcoverage and undercoverage variables help balance the
-restriction equation by taking positive values. There are two main
-objectives. First we limit overcoverage of primary points in order to
-activate a minimum number of sensors. Second we prevent that parts of
-the subregion are not monitored by minimizing undercoverage. The
+case, overcoverage and undercoverage variables help balancing the
+restriction equations by taking positive values. There are two main
+objectives. First we limit the overcoverage of primary points in order to
+activate a minimum number of sensors. Second we prevent the absence of monitoring on
+ some parts of the subregion by minimizing the undercoverage. The
weights $w_\theta$ and $w_U$ must be properly chosen so as to
guarantee that the maximum number of points are covered during each
round.
%\end{itemize}
-\section{Simulation Results}
+\section{Simulation results}
\label{exp}
In this section, we conducted a series of simulations to evaluate the
-efficiency and relevance of our approach, using the discrete event
+efficiency and the relevance of our approach, using the discrete event
simulator OMNeT++ \cite{varga}. We performed simulations for five
different densities varying from 50 to 250~nodes. Experimental results
were obtained from randomly generated networks in which nodes are
deployed over a $(50 \times 25)~m^2 $ sensing field.
-% DEBUT MODIFICATION
-{\bf More precisely, the deployment is controlled at a coarse scale in
+More precisely, the deployment is controlled at a coarse scale in
order to ensure that the deployed nodes can fully cover the sensing
- field with the given sensing range.}
-% FIN MODIFICATION
+ field with the given sensing range.
10~simulation runs are performed with
different network topologies for each node density. The results
presented hereafter are the average of these 10 runs. A simulation
ends when all the nodes are dead or the sensor network becomes
-disconnected (some nodes may not be able to sent to a base station an
+disconnected (some nodes may not be able to send, to a base station, an
event they sense).
Our proposed coverage protocol uses the radio energy dissipation model
wireless sensor node when transmitting or receiving packets. The
energy of each node in a network is initialized randomly within the
range 24-60~joules, and each sensor node will consume 0.2 watts during
-the sensing period which will have a duration of 60 seconds. Thus, an
-active node will consume 12~joules during sensing phase, while a
+the sensing period which will last 60 seconds. Thus, an
+active node will consume 12~joules during the sensing phase, while a
sleeping node will use 0.002 joules. Each sensor node will not
participate in the next round if its remaining energy is less than 12
joules. In all experiments the parameters are set as follows:
$R_s=5m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
-We evaluate the efficiency of our approach using some performance
+We evaluate the efficiency of our approach by using some performance
metrics such as: coverage ratio, number of active nodes ratio, energy
saving ratio, energy consumption, network lifetime, execution time,
-and number of stopped simulation runs. Our approach called Strategy~2
-(with Two Leaders) works with two subregions, each one having a size
+and number of stopped simulation runs. Our approach called strategy~2
+(with two leaders) works with two subregions, each one having a size
of $(25 \times 25)~m^2$. Our strategy will be compared with two other
-approaches. The first one, called Strategy~1 (with One Leader), works
-as Strategy~2, but considers only one region of $(50 \times 25)$ $m^2$
+approaches. The first one, called strategy~1 (with one leader), works
+as strategy~2, but considers only one region of $(50 \times 25)$ $m^2$
with only one leader. The other approach, called Simple Heuristic,
-consists in dividing uniformly the region into squares of $(5 \times
+consists in uniformly dividing the region into squares of $(5 \times
5)~m^2$. During the decision phase, in each square, a sensor is
randomly chosen, it will remain turned on for the coming sensing
phase.
-\subsection{The impact of the Number of Rounds on Coverage Ratio}
+\subsection{The impact of the number of rounds on the coverage ratio}
In this experiment, the coverage ratio measures how much the area of a
sensor field is covered. In our case, the coverage ratio is regarded
of rounds increases due to dead nodes. Although some nodes are dead,
thanks to strategy~1 or~2, other nodes are preserved to ensure the
coverage. Moreover, when we have a dense sensor network, it leads to
-maintain the full coverage for larger number of rounds. Strategy~2 is
-slightly more efficient that strategy 1, because strategy~2 subdivides
+maintain the full coverage for a larger number of rounds. Strategy~2 is
+slightly more efficient than strategy 1, because strategy~2 subdivides
the region into 2~subregions and if one of the two subregions becomes
-disconnected, coverage may be still ensured in the remaining
+disconnected, the coverage may be still ensured in the remaining
subregion.
\parskip 0pt
\begin{figure}[h!]
\centering
\includegraphics[scale=0.55]{TheCoverageRatio150.eps} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Coverage Ratio for 150 deployed nodes}
+\caption{The impact of the number of rounds on the coverage ratio for 150 deployed nodes}
\label{fig3}
\end{figure}
-\subsection{The impact of the Number of Rounds on Active Sensors Ratio}
+\subsection{The impact of the number of rounds on the active sensors ratio}
It is important to have as few active nodes as possible in each round,
in order to minimize the communication overhead and maximize the
\begin{figure}[h!]
\centering
\includegraphics[scale=0.55]{TheActiveSensorRatio150.eps} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Active Sensors Ratio for 150 deployed nodes }
+\caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
\label{fig4}
\end{figure}
The results presented in figure~\ref{fig4} show the superiority of
-both proposed strategies, the Strategy with Two Leaders and the one
-with a single Leader, in comparison with the Simple Heuristic. The
-Strategy with One Leader uses less active nodes than the Strategy with
-Two Leaders until the last rounds, because it uses central control on
-the whole sensing field. The advantage of the Strategy~2 approach is
+both proposed strategies, the strategy with two leaders and the one
+with a single leader, in comparison with the simple heuristic. The
+strategy with one leader uses less active nodes than the strategy with
+two leaders until the last rounds, because it uses central control on
+the whole sensing field. The advantage of the strategy~2 approach is
that even if a network is disconnected in one subregion, the other one
usually continues the optimization process, and this extends the
lifetime of the network.
-\subsection{The impact of the Number of Rounds on Energy Saving Ratio}
+\subsection{The impact of the number of rounds on the energy saving ratio}
In this experiment, we consider a performance metric linked to energy.
This metric, called Energy Saving Ratio, is defined by:
\mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
{\mbox{Total number of sensors in the network for the region}} \times 100.
\end{equation*}
-The longer the ratio is high, the more redundant sensor nodes are
-switched off, and consequently the longer the network may be alive.
+The longer the ratio is, the more redundant sensor nodes are
+switched off, and consequently the longer the network may live.
Figure~\ref{fig5} shows the average Energy Saving Ratio versus rounds
for all three approaches and for 150 deployed nodes.
% \begin{multicols}{6}
\centering
\includegraphics[scale=0.55]{TheEnergySavingRatio150.eps} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes}
+\caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
\label{fig5}
\end{figure}
The simulation results show that our strategies allow to efficiently
save energy by turning off some sensors during the sensing phase. As
-expected, the Strategy with One Leader is usually slightly better than
-the second strategy, because the global optimization permit to turn
+expected, the strategy with one leader is usually slightly better than
+the second strategy, because the global optimization permits to turn
off more sensors. Indeed, when there are two subregions more nodes
remain awake near the border shared by them. Note that again as the
-number of rounds increases the two leader strategy becomes the most
-performing, since its takes longer to have the two subregion networks
+number of rounds increases the two leaders' strategy becomes the most
+performing one, since it takes longer to have the two subregion networks
simultaneously disconnected.
-\subsection{The Number of Stopped Simulation Runs}
+\subsection{The number of stopped simulation runs}
-We will now study the number of simulation which stopped due to
-network disconnection, per round for each of the three approaches.
+We will now study the number of simulations which stopped due to
+network disconnections per round for each of the three approaches.
Figure~\ref{fig6} illustrates the average number of stopped simulation
runs per round for 150 deployed nodes. It can be observed that the
-heuristic is the approach which stops the earlier because the nodes
-are chosen randomly. Among the two proposed strategies, the
-centralized one first exhibits network disconnection. Thus, as
+simple heuristic is the approach which stops first because the nodes
+are randomly chosen. Among the two proposed strategies, the
+centralized one first exhibits network disconnections. Thus, as
explained previously, in case of the strategy with several subregions
the optimization effectively continues as long as a network in a
subregion is still connected. This longer partial coverage
-optimization participates in extending the lifetime.
+optimization participates in extending the network lifetime.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps}
-\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
+\caption{The number of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
\label{fig6}
\end{figure}
-\subsection{The Energy Consumption}
+\subsection{The energy consumption}
In this experiment, we study the effect of the multi-hop communication
-protocol on the performance of the Strategy with Two Leaders and
+protocol on the performance of the strategy with two leaders and
compare it with the other two approaches. The average energy
consumption resulting from wireless communications is calculated
-considering the energy spent by all the nodes when transmitting and
+by taking into account the energy spent by all the nodes when transmitting and
receiving packets during the network lifetime. This average value,
which is obtained for 10~simulation runs, is then divided by the
average number of rounds to define a metric allowing a fair comparison
Figure~\ref{fig7} illustrates the Energy Consumption for the different
network sizes and the three approaches. The results show that the
-Strategy with Two Leaders is the most competitive from energy
-consumption point of view. A centralized method, like the Strategy
-with One Leader, has a high energy consumption due to the many
+strategy with two leaders is the most competitive from the energy
+consumption point of view. A centralized method, like the strategy
+with one leader, has a high energy consumption due to many
communications. In fact, a distributed method greatly reduces the
number of communications thanks to the partitioning of the initial
network in several independent subnetworks. Let us notice that even if
a centralized method consumes far more energy than the simple
heuristic, since the energy cost of communications during a round is a
small part of the energy spent in the sensing phase, the
-communications have a small impact on the lifetime.
+communications have a small impact on the network lifetime.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.55]{TheEnergyConsumption.eps}
-\caption{The Energy Consumption }
+\caption{The energy consumption}
\label{fig7}
\end{figure}
-\subsection{The impact of Number of Sensors on Execution Time}
+\subsection{The impact of the number of sensors on execution time}
A sensor node has limited energy resources and computing power,
therefore it is important that the proposed algorithm has the shortest
possible execution time. The energy of a sensor node must be mainly
-used for the sensing phase, not for the pre-sensing ones.
-Table~\ref{table1} gives the average execution times {\bf in seconds}
-on a laptop of the decision phase
-% DEBUT AJOUT
-{\bf (resolution of the optimization problem)}
-% FIN AJOUT
+used for the sensing phase, not for the pre-sensing ones.
+Table~\ref{table1} gives the average execution times in seconds
+on a laptop of the decision phase (solving of the optimization problem)
during one round. They are given for the different approaches and
various numbers of sensors. The lack of any optimization explains why
-the heuristic has very low execution times. Conversely, the Strategy
-with One Leader which requires to solve an optimization problem
+the heuristic has very low execution times. Conversely, the strategy
+with one leader which requires to solve an optimization problem
considering all the nodes presents redhibitory execution times.
-Moreover, increasing of 50~nodes the network size multiplies the time
-by almost a factor of 10. The Strategy with Two Leaders has more
+Moreover, increasing the network size by 50~nodes multiplies the time
+by almost a factor of 10. The strategy with two leaders has more
suitable times. We think that in distributed fashion the solving of
the optimization problem in a subregion can be tackled by sensor
-nodes. Overall, to be able deal with very large networks a
+nodes. Overall, to be able to deal with very large networks, a
distributed method is clearly required.
\begin{table}[ht]
-\caption{The Execution Time(s) vs The Number of Sensors}
+\caption{The execution time(s) vs the number of sensors}
% title of Table
\centering
% centered columns (4 columns)
\hline
%inserts double horizontal lines
-Sensors Number & Strategy~1 & Strategy~2 & Simple Heuristic \\ [0.5ex]
- & (with Two Leaders) & (with One Leader) & \\ [0.5ex]
+Sensors number & Strategy~2 & Strategy~1 & Simple heuristic \\ [0.5ex]
+ & (with two leaders) & (with one leader) & \\ [0.5ex]
%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
% inserts table
%heading
% is used to refer this table in the text
\end{table}
-\subsection{The Network Lifetime}
+\subsection{The network lifetime}
Finally, we have defined the network lifetime as the time until all
nodes have been drained of their energy or each sensor network
-monitoring an area becomes disconnected. In figure~\ref{fig8}, the
-network lifetime for different network sizes and for both Strategy
-with Two Leaders and the Simple Heuristic is illustrated.
-% DEBUT MODIFICATION
-{\bf We do not consider anymore the centralized Strategy with One
- Leader, because, as shown above, this strategy results in execution
- times that quickly become unsuitable for a sensor network.}
-% FIN MODIFICATION
+monitoring an area has become disconnected. In figure~\ref{fig8}, the
+network lifetime for different network sizes and for both strategy
+with two leaders and the simple heuristic is illustrated.
+ We do not consider anymore the centralized strategy with one
+ leader, because, as shown above, this strategy results in execution
+ times that quickly become unsuitable for a sensor network.
\begin{figure}[h!]
%\centering
% \begin{multicols}{6}
\centering
\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
-\caption{The Network Lifetime }
+\caption{The network lifetime }
\label{fig8}
\end{figure}
As highlighted by figure~\ref{fig8}, the network lifetime obviously
-increases when the size of the network increase, with our approach
-that leads to the larger lifetime improvement. By choosing for each
-round the well suited nodes to cover the region of interest and by
+increases when the size of the network increases, with our approach
+that leads to the larger lifetime improvement. By choosing the best
+suited nodes, for each round, to cover the region of interest and by
letting the other ones sleep in order to be used later in next rounds,
-our strategy efficiently prolongs the lifetime. Comparison shows that
+our strategy efficiently prolonges the network lifetime. Comparison shows that
the larger the sensor number is, the more our strategies outperform
-the Simple Heuristic. Strategy~2, which uses two leaders, is the best
+the simple heuristic. Strategy~2, which uses two leaders, is the best
one because it is robust to network disconnection in one subregion. It
also means that distributing the algorithm in each node and
subdividing the sensing field into many subregions, which are managed
independently and simultaneously, is the most relevant way to maximize
the lifetime of a network.
-\section{Conclusions and Future Works}
+\section{Conclusion and future forks}
\label{sec:conclusion}
-In this paper, we have addressed the problem of coverage and lifetime
+In this paper, we have addressed the problem of the coverage and the lifetime
optimization in wireless sensor networks. This is a key issue as
sensor nodes have limited resources in terms of memory, energy and
computational power. To cope with this problem, the field of sensing
divide-and-conquer method, and then a multi-rounds coverage protocol
will optimize coverage and lifetime performances in each subregion.
The proposed protocol combines two efficient techniques: network
-Leader Election and sensor activity scheduling, where the challenges
+leader election and sensor activity scheduling, where the challenges
include how to select the most efficient leader in each subregion and
-the best representative active nodes that will optimize the lifetime
+the best representative active nodes that will optimize the network lifetime
while taking the responsibility of covering the corresponding
subregion. The network lifetime in each subregion is divided into
rounds, each round consists of four phases: (i) Information Exchange,
(ii) Leader Election, (iii) an optimization-based Decision in order to
select the nodes remaining active for the last phase, and (iv)
-Sensing. The simulations results show the relevance of the proposed
-protocol in terms of lifetime, coverage ratio, active sensors Ratio,
+Sensing. The simulations show the relevance of the proposed
+protocol in terms of lifetime, coverage ratio, active sensors ratio,
energy saving, energy consumption, execution time, and the number of
stopped simulation runs due to network disconnection. Indeed, when
dealing with large and dense wireless sensor networks, a distributed
single global optimization problem by partitioning it in many smaller
problems, one per subregion, that can be solved more easily.
-In future, we plan to study and propose a coverage protocol which
+In future work, we plan to study and propose a coverage protocol which
computes all active sensor schedules in a single round, using
optimization methods such as swarms optimization or evolutionary
-algorithms.
-% DEBUT AJOUT
-{\bf This single round will still consists of 4 phases, but the
+algorithms. This single round will still consists of 4 phases, but the
decision phase will compute the schedules for several sensing phases
- which aggregated together define a kind of meta-sensing phase.}
-% FIN AJOUT
+ which, aggregated together, define a kind of meta-sensing phase.
The computation of all cover sets in one round is far more
difficult, but will reduce the communication overhead.
