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
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
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
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
\noindent Recent years have witnessed significant advances in wireless
communications and embedded micro-sensing MEMS technologies which have
\noindent Recent years have witnessed significant advances in wireless
communications and embedded micro-sensing MEMS technologies which have
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
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
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.
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
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
energy by turning off some of them during the sensing phase.
Obviously, the deactivation of nodes is only relevant if the coverage
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
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
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
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
Our scheduling scheme considers rounds, where a round starts with a
discovery phase to exchange information between sensors of the
Our scheduling scheme considers rounds, where a round starts with a
discovery phase to exchange information between sensors of the
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.
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}.
proposed approach. Finally, we give concluding remarks and some
suggestions for future works in Section~\ref{sec:conclusion}.
\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
\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.
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
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
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
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
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
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
-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
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
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
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
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
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
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
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
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
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
\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
\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
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
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
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}.
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}.
\cite{Ye03} or regulated \cite{cardei05} over time.
%A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
\cite{Ye03} or regulated \cite{cardei05} over time.
%A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
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
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
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
Their work builds upon previous work
in~\cite{Slijepcevic01powerefficient} and the generated cover sets do
not provide complete coverage of the monitoring zone.
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
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
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.
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
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.
\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
\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
areas at the same time, and tries to prevent undercoverage. The
decision is a good compromise between these two conflicting
objectives.
areas at the same time, and tries to prevent undercoverage. The
decision is a good compromise between these two conflicting
objectives.
\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
\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
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
Each round is divided into 4 phases : Information (INFO) Exchange,
Leader Election, Decision, and Sensing. For each round there is
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
-taking the decision, the node will not participate to this phase, and,
+making the decision, the node will not participate to this phase, and,
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
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
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 sensor node $j$ sends its position, remaining energy $RE_j$, and
the number of local neighbors $NBR_j$ to all wireless sensor nodes in
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
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
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
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 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.
%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.
Active sensors in the round will execute their sensing task to
preserve maximal coverage in the region of interest. We will assume
Active sensors in the round will execute their sensing task to
preserve maximal coverage in the region of interest. We will assume
the same for all wireless sensor nodes in the network. Each sensor
will receive an Active-Sleep packet from WSNL informing it to stay
the same for all wireless sensor nodes in the network. Each sensor
will receive an Active-Sleep packet from WSNL informing it to stay
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
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}:
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.
%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.
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
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
\noindent We can calculate the positions of the selected primary
points in the circle disk of the sensing range of a wireless sensor
\noindent We can calculate the positions of the selected primary
points in the circle disk of the sensing range of a wireless sensor
\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}:\\
\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
\noindent Our model is based on the model proposed by
\cite{pedraza2006} where the objective is to find a maximum number of
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
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
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 $p$;
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 $p$;
$p$ 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
$p$ 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 equation by taking positive values. There are two main %%RAPH restriction equations????
+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.
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.
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
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
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
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
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 $w_{U}=|P^2|$.
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 $w_{U}=|P^2|$.
metrics such as: coverage ratio, number of active nodes ratio, energy
saving ratio, energy consumption, network lifetime, execution time,
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
-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 $(50 \times 25)$ $m^2$
5)~m^2$. During the decision phase, in each square, a sensor is
randomly chosen, it will remain turned on for the coming sensing
phase.
5)~m^2$. During the decision phase, in each square, a sensor is
randomly chosen, it will remain turned on for the coming sensing
phase.
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
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
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
It is important to have as few active nodes as possible in each round,
in order to minimize the communication overhead and maximize the
It is important to have as few active nodes as possible in each round,
in order to minimize the communication overhead and maximize the
-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.
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.
In this experiment, we consider a performance metric linked to energy.
This metric, called Energy Saving Ratio, is defined by:
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*}
\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.
Figure~\ref{fig5} shows the average Energy Saving Ratio versus rounds
for all three approaches and 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
\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
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
-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
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
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
compare it with the other two approaches. The average energy
consumption resulting from wireless communications is calculated
compare it with the other two approaches. The average energy
consumption resulting from wireless communications is calculated
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
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
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. 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
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
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
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
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
-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
suitable times. We think that in distributed fashion the solving of
the optimization problem in a subregion can be tackled by sensor
-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]
Finally, we have defined the network lifetime as the time until all
nodes have been drained of their energy or each sensor network
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
-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
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.
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.
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
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
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
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)
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
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.
single global optimization problem by partitioning it in many smaller
problems, one per subregion, that can be solved more easily.
computes all active sensor schedules in a single round, using
optimization methods such as swarms optimization or evolutionary
algorithms. This single round will still consists of 4 phases, but the
decision phase will compute the schedules for several sensing phases
computes all active sensor schedules in a single round, using
optimization methods such as swarms optimization or evolutionary
algorithms. This single round will still consists of 4 phases, but the
decision phase will compute the schedules for several sensing phases
The computation of all cover sets in one round is far more
difficult, but will reduce the communication overhead.
The computation of all cover sets in one round is far more
difficult, but will reduce the communication overhead.
