\title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
-
% author names and affiliations
% use a multiple column layout for up to three different
% affiliations
\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
\IEEEpeerreviewmaketitle
\section{Introduction}
+
\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. 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 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.
+planned for each subregion.
+ 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 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 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.
The remainder of the paper is organized as follows. The next section
% Section~\ref{rw}
proposed approach. Finally, we give concluding remarks and some
suggestions for future works in Section~\ref{sec:conclusion}.
-\section{\uppercase{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.
+
+\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 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
minimizing overcoverage (points covered by multiple active sensors
simultaneously).
-\newpage
-
{\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
Activity 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
{\bf Distributed approaches}
Some distributed algorithms have been developed
-in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02} to perform the schelduling. 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 remain turned on or to go to
-sleep for the round. This decision is basically based on simple greedy
-criteria like the largest uncovered area
-\cite{Berman05efficientenergy}, maximum uncovered targets
+in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02} to perform the
+scheduling. Distributed algorithms typically operate in rounds for
+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 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
+phases, an initial setup phase during which each sensor computes and
+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
+generated cover sets. For instance, Slijepcevic and Potkonjak
\cite{Slijepcevic01powerefficient} propose an algorithm which
allocates sensor nodes in mutually independent sets to monitor an area
-divided into several fields. Their algorithm builds a cover set by
+divided into several fields. Their algorithm builds a cover set by
including in priority the sensor nodes which cover critical fields,
that is to say fields that are covered by the smallest number of
sensors. The time complexity of their heuristic is $O(n^2)$ where $n$
into a maximum number of disjoint dominating sets which are activated
successively. The dominating sets do not guarantee the coverage of the
whole region of interest. Abrams et
-al.~\cite{Abrams:2004:SKA:984622.984684} design three approximation
+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.
to describe our approach before going into details in the subsequent
sections.
\begin{itemize}
-\item {\bf How must the phases for information exchange,
- decision and sensing be planned over time?} Our algorithm divides the time
- line into a number of rounds. Each round contains 4 phases:
- Information Exchange, Leader Election, Decision, and Sensing.
+\item {\bf How must the phases for information exchange, decision and
+ sensing be planned over time?} Our algorithm divides the time line
+ into a number of rounds. Each round contains 4 phases: Information
+ Exchange, Leader Election, Decision, and Sensing.
\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
decision is made by a leader in each subregion.
\end{itemize}
-\section{\uppercase{Activity scheduling}}
+\section{Activity Scheduling}
\label{pd}
We consider a randomly and uniformly deployed network consisting of
they do not join the network to monitor the area. Below, we describe
each phase in more detail.
-\subsection{\textbf 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{\textbf 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
subregion in the area of interest will select its own WSNL
-independently for each round. All the sensor nodes cooperates to
+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
equality, larger index.
-\subsection{\textbf 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
%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{\textbf 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
the same for all wireless sensor nodes in the network. Each sensor
-will receive an Active-Sleep packet from WSNL telling him to stay
+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
starting a new round.
\label{fig2}
\end{figure}
-\section{\uppercase{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}:\\
\end{array} \right.
%\label{eq12}
\end{equation}
-The number of sensors that are covering point $p$ is equal to
-$\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+The number of active sensors that cover the primary point $p$ is equal
+to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
\begin{equation}
X_{j} = \left \{
\begin{array}{l l}
\begin{equation}
\Theta_{p} = \left \{
\begin{array}{l l}
- 0 & \mbox{if point $p$ is not covered,}\\
+ 0 & \mbox{if point $p$ is not covered,}\\
\left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
\end{array} \right.
\label{eq13}
\right.
\end{equation}
\begin{itemize}
-\item $X_{j}$ : indicates whether or not sensor $j$ is actively
+\item $X_{j}$ : indicates whether or not the sensor $j$ is actively
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 point $p$;
+ one that are covering the primary point $p$;
\item $U_{p}$ : {\it undercoverage}, indicates whether or not point
$p$ is being covered (1 if not covered and 0 if covered).
\end{itemize}
-The first group of constraints indicates that some 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 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.
+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
+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.
%In equation \eqref{eq15}, there are two main objectives: the first one using the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the Undercoverage parameter to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
%at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.
%\end{itemize}
-\section{\uppercase{Simulation Results}}
+\section{Simulation Results}
\label{exp}
-In this section, we conducted a series of simulations, to evaluate the
+In this section, we conducted a series of simulations to evaluate the
efficiency and 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. For each network
-deployment, we assume that the deployed nodes can fully cover the
-sensing 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 event they sense).
+deployed over a $(50 \times 25)~m^2 $ sensing field.
+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.
+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
+event they sense).
Our proposed coverage protocol uses the radio energy dissipation model
defined by~\cite{HeinzelmanCB02} as energy consumption model for each
the sensing period which will have a duration of 60 seconds. Thus, an
active node will consume 12~joules during sensing phase, while a
sleeping node will use 0.002 joules. Each sensor node will not
-participate in the next round if it's remaining energy is less than 12
+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 $w_{U}=|P^2|$.
for the three approaches. It can be seen that the three approaches
give similar coverage ratios during the first rounds. From the
9th~round the coverage ratio decreases continuously with the simple
-heuristic, while the other two strategies provide superior coverage to
+heuristic, while the two other strategies provide superior coverage to
$90\%$ for five more rounds. Coverage ratio decreases when the number
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
the second strategy, because the global optimization permit 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 increase the two leader strategy becomes the most
+number of rounds increases the two leader strategy becomes the most
performing, since its takes longer to have the two subregion networks
simultaneously disconnected.
-\subsection{The Network Lifetime}
+\subsection{The Number of Stopped Simulation Runs}
-We have defined the network lifetime as the time until all nodes have
-been drained of their energy or each sensor network monitoring a area
-becomes disconnected. In figure~\ref{fig6}, the network lifetime for
-different network sizes and for the three approaches is illustrated.
+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
+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
+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.
\begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
-\caption{The Network Lifetime }
+\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps}
+\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
\label{fig6}
\end{figure}
-As highlighted by figure~\ref{fig6}, the network lifetime obviously
-increases when the size of the network increase, with our approaches
-that lead to the larger lifetime improvement. By choosing for each
-round the well suited nodes to cover the region of interest and by
-leaving sleep the other ones to be used later in next rounds, both
-proposed strategies efficiently prolong the lifetime. Comparison shows
-that the larger the sensor number, the more our strategies outperform
-the 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.
-
\subsection{The Energy Consumption}
In this experiment, we study the effect of the multi-hop communication
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 on a laptop of
-the decision phase 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 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 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
+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
+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
+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
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 & Strategy & Simple Heuristic \\ [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
% is used to refer this table in the text
\end{table}
-\subsection{The Number of Stopped Simulation Runs}
+\subsection{The Network Lifetime}
-Finally, we will study the number of simulation which stopped due to
-network disconnection, per round for each of the three approaches.
-Figure~\ref{fig8} illustrates the 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
-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.
+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
+ times that quickly become unsuitable for a sensor network.
\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps}
-\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
+\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
+\caption{The Network Lifetime }
\label{fig8}
\end{figure}
-\section{\uppercase{Conclusions and Future Works}}
+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
+letting the other ones sleep in order to be used later in next rounds,
+our strategy efficiently prolongs the 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
+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}
\label{sec:conclusion}
In this paper, we have addressed the problem of coverage and lifetime
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
+Sensing. The simulations results 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
approach like the one we propose allows to reduce the difficulty of a
-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
+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
optimization methods such as swarms optimization or evolutionary
-algorithms. The computation of all cover sets in one round is far more
+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.
+The computation of all cover sets in one round is far more
difficult, but will reduce the communication overhead.
% use section* for acknowledgement
