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+\usepackage{graphicx,epstopdf}
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\begin{document}
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 it to
-sense its environment, to compute, to store information and to deliver
+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.
One of the main design issues in Wireless Sensor Networks (WSNs) is to
prolong the network lifetime, while achieving acceptable quality of
service for applications. Indeed, sensor nodes have limited resources
-in terms of memory, energy and computational power.
+in terms of memory, energy, and computational power.
Since sensor nodes have limited battery life and without being able to
replace batteries, especially in remote and hostile environments, it
the scheduling strategy for energy-efficient coverage.
Section~\ref{cp} gives the coverage model formulation which is used to
schedule the activation of sensors. Section~\ref{exp} shows the
-simulation results obtained using the discrete event simulator on
-OMNET++ \cite{varga}. They fully demonstrate the usefulness of the
+simulation results obtained using the discrete event simulator OMNeT++ \cite{varga}. They fully demonstrate the usefulness of the
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
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}, provably 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
that there is a threshold in terms of network size to switch from a
localized to a centralized algorithm. Indeed the exchange of
messages in large networks may consume a considerable amount of
- energy in a localized approach compared to a centralized one. Our
+ energy in a centralized approach compared to a distributed 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 number of local neighbours $NBR_j$ to all wireless sensor nodes in
its subregion by using an INFO packet and then listens to the packets
sent from other nodes. After that, each node will have information
about all the sensor nodes in the subregion. In our model, the
%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
based on the received information from all other nodes in the same
subregion. The selection criteria in order of priority are: larger
-number of neighbors, larger remaining energy, and then in case of
+number of neighbours, 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 primary 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
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 $w_{U}=|P^2|$.
+$R_s=5~m$, $w_{\Theta}=1$, 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}
+\includegraphics[scale=0.5]{TheCoverageRatio150g.eps} %\\~ ~ ~(a)
+\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
network lifetime. This point is assessed through the Active Sensors
-Ratio, which is defined as follows:
+Ratio (ASR), which is defined as follows:
\begin{equation*}
\scriptsize
\mbox{ASR}(\%) = \frac{\mbox{Number of active sensors
\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 }
+\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
+\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:
+This metric, called Energy Saving Ratio (ESR), 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 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.
%\centering
% \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}
+\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
+\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 percentage 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.
-Figure~\ref{fig6} illustrates the average number of stopped simulation
+We will now study the percentage of simulations which stopped due to
+network disconnections per round for each of the three approaches.
+Figure~\ref{fig6} illustrates the percentage 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 }
+\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps}
+\caption{The percentage 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
between networks having different densities.
-Figure~\ref{fig7} illustrates the Energy Consumption for the different
+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 }
+\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps}
+\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.
+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~2 & Strategy~1 & 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.
- We do not consider anymore the centralized Strategy with One
- Leader, because, as shown above, this strategy results in execution
+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 }
+\includegraphics[scale=0.5]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
+\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 works}
\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
-computes all active sensor schedules in a single round, using
+In future work, we plan to study and propose a coverage protocol which
+computes all active sensor schedules in one time, using
optimization methods such as swarms optimization or evolutionary
-algorithms. This single round will still consists of 4 phases, but the
+algorithms. The round will still consist 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.
-The computation of all cover sets in one round is far more
+ which, aggregated together, define a kind of meta-sensing phase.
+The computation of all cover sets in one time is far more
difficult, but will reduce the communication overhead.
-
% use section* for acknowledgement
%\section*{Acknowledgment}
