\hyphenation{op-tical net-works semi-conduc-tor}
-
+\usepackage{etoolbox}
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-
\begin{document}
%
% paper title
% can use linebreaks \\ within to get better formatting as desired
-\title{Coverage and Lifetime Optimization in Heterogeneous Energy Wireless Sensor Networks}
+\title{Coverage and Lifetime Optimization \\
+in Heterogeneous Energy Wireless Sensor Networks}
-\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
+\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon,
+and Rapha\"el Couturier}
\IEEEauthorblockA{FEMTO-ST Institute, UMR 6174 CNRS \\
University of Franche-Comt\'e \\
Belfort, France\\
-Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
+Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon,
+raphael.couturier$\rbrace$@univ-fcomte.fr}}
\maketitle
-
\begin{abstract}
One of the fundamental challenges in Wireless Sensor Networks (WSNs)
-is the coverage preservation and the 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 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
-consists of four phases: (i)~Information Exchange, (ii)~Leader
+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 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 consists in four phases: (i)~Information Exchange, (ii)~Leader
Election, (iii)~Decision, and (iv)~Sensing. The decision process is
-carried out by a leader node, which solves an integer program.
+carried out by a leader node, which solves an integer program.
Simulation results show that the proposed approach can prolong the
network lifetime and improve the coverage performance.
\end{abstract}
\begin{IEEEkeywords}
-Area Coverage, Network lifetime, Optimization, Scheduling, Distributed Protocol.
+Wireless Sensor Networks, Area Coverage, Network lifetime,
+Optimization, Scheduling.
\end{IEEEkeywords}
%\keywords{Area Coverage, Network lifetime, Optimization, Distributed Protocol}
\IEEEpeerreviewmaketitle
-
-
-
-
-
\section{Introduction}
-\noindent The fast developments in the low-cost sensor devices and wireless communications have allowed the emergence the WSNs. WSN includes a large number of small , limited-power sensors that can sense, process and transmit
- data over a wireless communication . They communicate with each other by using multi-hop wireless communications , cooperate together to monitor the area of interest, and the measured data can be reported
- to a monitoring center
-called, sink, for analysis it~\cite{Ammari01, Sudip03}. There are several applications used the WSN including health, home, environmental, military,and industrial applications~\cite{Akyildiz02}.
-The coverage problem is one of the fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and continuously the area of interest. The limited energy of sensors represents the main challenge in the WSNs design~\cite{Ammari01}, where it is difficult to replace and/or
- recharge their batteries because the the area of interest nature (such as hostile environments) and the cost. So, it is necessary that a WSN deployed with high density because spatial redundancy can then be exploited to increase the lifetime of the network . However, turn on all the sensor nodes, which monitor the same region at the same time leads to decrease the lifetime of the network. To 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~\cite{Misra05}. WSNs require energy-efficient solutions to improve the network lifetime that is constrained by the limited power of each sensor node ~\cite{Akyildiz02}.
-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.
- 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
+%\indent The fast developments in the low-cost sensor devices and
+%wireless communications have allowed the emergence the WSNs. WSN
+%includes a large number of small, limited-power sensors that can
+%sense, process and transmit data over a wireless communication. They
+%communicate with each other by using multi-hop wireless
+%communications, cooperate together to monitor the area of interest,
+%and the measured data can be reported to a monitoring center called
+%sink for analysis it~\cite{Sudip03}. There are several applications
+%used the WSN including health, home, environmental, military, and
+%industrial applications~\cite{Akyildiz02}. The coverage problem is one
+%of the fundamental challenges in WSNs~\cite{Nayak04} that consists in
+%monitoring efficiently and continuously the area of
+%interest. Thelimited energy of sensors represents the main challenge
+%in the WSNs design~\cite{Sudip03}, where it is difficult to replace
+%and/or recharge their batteries because the the area of interest
+%nature (such as hostile environments) and the cost. So, it is
+%necessary that a WSN deployed with high density because spatial
+%redundancy can then be exploited to increase the lifetime of the
+%network. However, turn on all the sensor nodes, which monitor the same
+%region at the same time leads to decrease the lifetime of the network.
+
+Recent years have witnessed significant advances in wireless
+communications and embedded micro-sensing MEMS technologies which have
+led to the emergence of Wireless Sensor Networks (WSNs) as one of the
+most promising technologies \cite{Akyildiz02}. 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 it to sense its environment, to compute, to
+store information and to deliver report messages to a base station
+\cite{Sudip03}. One of the main design issues in WSNs is to prolong
+the network lifetime, while achieving acceptable quality of service
+for applications. Indeed, sensors nodes have limited resources in
+terms of memory, energy and computational power.
+
+Since sensor nodes have limited battery life and since it is impossible to
+replace batteries, especially in remote and hostile environments, it
+is desirable that a WSN should be deployed with high density because
+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 advantage
+of the overlapping sensing regions of some sensor nodes to save energy
+by turning off some of them during the sensing phase~\cite{Misra05}.
+Obviously, the deactivation of nodes is only relevant if the coverage
+of the monitored area is not affected. In this paper, we concentrate
+on the area coverage problem \cite{Nayak04}, 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. 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}
reviews the related work in the field. Section~\ref{pd} is devoted to
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 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~\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 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}
\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 have chosen
-to recall the main definitions and assumptions related to our work.
-
+\indent In this section, we only review some recent works dealing with
+the coverage lifetime maximization problem, where the objective is to
+optimally schedule sensors' activities in order to extend WSNs
+lifetime.
+
+In \cite{chin2007}, the author proposed a novel distributed heuristic,
+called Distributed Energy-efficient Scheduling for k-coverage (DESK),
+which ensures that the energy consumption among the sensors is
+balanced and the lifetime maximized while the coverage requirement is
+maintained. This heuristic works in rounds, requires only 1-hop
+neighbor information, and each sensor decides its status (active or
+sleep) based on the perimeter coverage model proposed in
+\cite{Huang:2003:CPW:941350.941367}. More recently, Shibo et
+al. \cite{Shibo} expressed the coverage problem as a minimum weight
+submodular set cover problem and proposed a Distributed Truncated
+Greedy Algorithm (DTGA) to solve it. They take in particular advantage
+from both temporal and spatial correlations between data sensed by
+different sensors.
+
+The works presented in \cite{Bang, Zhixin, Zhang} focus on the
+definition of coverage-aware, distributed energy-efficient and
+distributed clustering methods respectively. They aim to extend the
+network lifetime while ensuring the coverage. S. Misra et al.
+\cite{Misra05} proposed a localized algorithm which conserves energy and
+coverage by activating the subset of sensors with the minimum
+overlapping area. It preserves the network connectivity thanks to the
+formation of the network backbone. J.~A.~Torkestani \cite{Torkestani}
+designed a Learning Automata-based Energy-Efficient Coverage protocol
+(LAEEC) to construct a Degree-constrained Connected Dominating Set
+(DCDS) in WSNs. He showed that the correct choice of the
+degree-constraint of DCDS balances the network load on the active
+nodes and leads to enhance the coverage and network lifetime.
+
+The main contribution of our approach addresses three main questions
+to build a scheduling strategy.\\
%\begin{itemize}
-%\item Area Coverage: The main objective is to cover an area. The area coverage requires
-%that the sensing range of working Active nodes cover the whole targeting area, which means any
-%point in target area can be covered~\cite{Mihaela02,Raymond03}.
-
-%\item Target Coverage: The objective is to cover a set of targets. Target coverage means that the discrete target points can be covered in any time. The sensing range of working Active nodes only monitors a finite number of discrete points in targeting area~\cite{Mihaela02,Raymond03}.
+%\item
+{\indent \bf How must the phases for information exchange, decision
+ and sensing be planned over time?} Our algorithm divides the timeline into rounds. Each round contains 4 phases: Information Exchange,
+Leader Election, Decision, and Sensing.
-%\item Barrier Coverage An objective to determine the maximal support/breach paths that traverse a sensor field. Barrier coverage is expressed as finding one or more routes with starting position and ending position when the targets pass through the area deployed with sensor nodes~\cite{Santosh04,Ai05}.
-%\end{itemize}
-\subsection{Coverage}
-%{\bf Coverage}
-
-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
-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 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
-by a sensor as a set of primary points and tries to maximize the total
-number of primary points that are covered in each round, while
-minimizing overcoverage (points covered by multiple active sensors
-simultaneously).
-
-\subsection{Lifetime}
-%{\bf Lifetime}
-
-Various definitions exist for the lifetime of a sensor
-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
-sensor network becomes disconnected, and we measure the coverage ratio
-during the WSN lifetime. Network connectivity is important because an
-active sensor node without connectivity towards a base station cannot
-transmit information on an event in the area that it monitors.
-
-\subsection{Activity scheduling}
-%{\bf Activity scheduling}
-
-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, 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 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
-the time intervals to be activated.
-
-\subsection{Distributed approaches}
-%{\bf Distributed approaches}
-
-Some distributed algorithms have been developed
-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 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
-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
-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 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 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 wake-up time is randomized
-\cite{Ye03} or regulated \cite{cardei05} over time.
-%A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
-
-%The scheduling information is disseminated throughout the network and only sensors in the active state are responsible
-%for monitoring all targets, while all other nodes are in a low-energy sleep mode. The nodes decide cooperatively which of them will remain in sleep mode for a certain
-%period of time.
-
- %one way of increasing lifeteime is by turning off redundant nodes to sleep mode to conserve energy while active nodes provide essential coverage, which improves fault tolerance.
-
-%In this paper we focus on centralized algorithms because distributed algorithms are outside the scope of our work. Note that centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Moreover, a recent study conducted in \cite{pc10} concludes 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.
-
-\subsection{Centralized approaches}
-%{\bf Centralized approaches}
-
-Power efficient centralized schemes differ according to several
-criteria \cite{Cardei:2006:ECP:1646656.1646898}, such as the coverage
-objective (target coverage or area coverage), the node deployment
-method (random or deterministic) and the heterogeneity of sensor nodes
-(common sensing range, common battery lifetime). The major approach is
-to divide/organize the sensors into a suitable number of set covers
-where each set completely covers an interest region and to activate
-these set covers successively.
-
-The first algorithms proposed in the literature consider that the cover
-sets are disjoint: a sensor node appears in exactly one of the
-generated cover sets. For instance, Slijepcevic and Potkonjak
-\cite{Slijepcevic01powerefficient} propose an algorithm, which
-allocates sensor nodes in mutually independent sets to monitor an area
-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 $n$
-is the number of sensors. In~\cite{cardei02}, a graph coloring
-technique is described to achieve energy savings by organizing the sensor nodes
-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
-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 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.
-
-%examine the target coverage problem by disjoint cover sets but relax the requirement that every cover set monitor all the targets and try to maximize the number of times the targets are covered by the partition. They propose various algorithms and establish approximation ratio.
-
-In~\cite{Cardei:2005:IWS:1160086.1160098}, the authors propose a
-heuristic to compute the disjoint set covers (DSC). In order to
-compute the maximum number of covers, they first transform DSC into a
-maximum-flow problem, which is then formulated as a mixed integer
-programming problem (MIP). Based on the solution of the MIP, they
-design a heuristic to compute the final number of covers. The results
-show a slight performance improvement in terms of the number of
-produced DSC in comparison to~\cite{Slijepcevic01powerefficient}, but
-it incurs higher execution time due to the complexity of the mixed
-integer programming solving. %Cardei and Du
-\cite{Cardei:2005:IWS:1160086.1160098} propose a method to efficiently
-compute the maximum number of disjoint set covers such that each set
-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 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.
-Zorbas et al. \cite{Zorbas2007} present B\{GOP\}, a centralized
-coverage algorithm introducing sensor candidate categorization
-depending on their coverage status and the notion of critical target
-to call targets that are associated with a small number of
-sensors. The total running time of their heuristic is $0(m n^2)$ where
-$n$ is the number of sensors, and $m$ the number of targets. Compared
-to algorithm's results of Slijepcevic and Potkonjak
-\cite{Slijepcevic01powerefficient}, their heuristic produces more
-cover sets with a slight growth rate in execution time.
-%More recently Manju and Pujari\cite{Manju2011}
-
-In the case of non-disjoint algorithms \cite{Manju2011}, sensors may
-participate in more than one cover set. In some cases, this may
-prolong the lifetime of the network in comparison to the disjoint
-cover set algorithms, but designing algorithms for non-disjoint cover
-sets generally induces a higher order of complexity. Moreover, in
-case of a sensor's failure, non-disjoint scheduling policies are less
-resilient and less reliable because a sensor may be involved in more
-than one cover sets. For instance, Cardei et al.~\cite{cardei05bis}
-present a linear programming (LP) solution and a greedy approach to
-extend the sensor network lifetime by organizing the sensors into a
-maximal number of non-disjoint cover sets. Simulation results show
-that by allowing sensors to participate in multiple sets, the network
-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 solution based on the Garg-K\"{o}nemann
-algorithm~\cite{garg98}, provably near
-the optimal solution, is also proposed.
-
-\subsection{Our contribution}
-%{\bf Our contribution}
-
-There are three main questions, which should be addressed to build a
-scheduling strategy. We give a brief answer to these three questions
-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 What are the rules to decide which node has to be turned on
+%\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 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 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
- sensor nodes, which have usually limited processing capabilities.
- Distributed algorithms are very adaptable to the dynamic and
- scalable nature of sensors network. Authors in \cite{pc10} conclude
- 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 centralized approach compared to a distributed one. Our
- work does not consider only one leader to compute and to broadcast
- 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}
-
-
+%\item
+{\bf Which node should make such a decision?} A leader node should
+make such a decision. Our work does not consider only one leader to
+compute and to broadcast 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}
\label{pd}
simultaneously. Our protocol works in rounds fashion as shown in
figure~\ref{fig1}.
-%Given the interested Area $A$, the wireless sensor nodes set $S=\lbrace s_1,\ldots,s_N \rbrace $ that are deployed randomly and uniformly in this area such that they are ensure a full coverage for A. The Area A is divided into regions $A=\lbrace A^1,\ldots,A^k,\ldots, A^{N_R} \rbrace$. We suppose that each sensor node $s_i$ know its location and its region. We will have a subset $SSET^k =\lbrace s_1,...,s_j,...,s_{N^k} \rbrace $ , where $s_N = s_{N^1} + s_{N^2} +,\ldots,+ s_{N^k} +,\ldots,+s_{N^R}$. Each sensor node $s_i$ has the same initial energy $IE_i$ in the first time and the current residual energy $RE_i$ equal to $IE_i$ in the first time for each $s_i$ in A. \\
-
\begin{figure}[ht!]
\centering
\includegraphics[width=85mm]{FirstModel.eps} % 70mm
widely used sensor coverage model in the literature. Each sensor has a
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 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}:
+covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$ ~\cite{Zhang05}.
+
+
%\begin{figure}[h!]
%\centering
%\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
%\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
%\end{multicols}
-\caption{Wireless sensor node represented by 13 primary points}
+\caption{Sensor node represented by 13 primary points}
\label{fig2}
\end{figure}
\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}:\\
-%To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$ that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
-
\indent 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 proposed an
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.
-%\subsection{Notations and assumptions}
-
-%\begin{itemize}
-%\item $m$ : the number of targets
-%\item $n$ : the number of sensors
-%\item $K$ : maximal number of cover sets
-%\item $i$ : index of target ($i=1..m$)
-%\item $j$ : index of sensor ($j=1..n$)
-%\item $k$ : index of cover set ($k=1..K$)
-%\item $T_0$ : initial set of targets
-%\item $S_0$ : initial set of sensors
-%\item $T $ : set of targets which are not covered by at least one cover set
-%\item $S$ : set of available sensors
-%\item $S_0(i)$ : set of sensors which cover the target $i$
-%\item $T_0(j)$ : set of targets covered by sensor $j$
-%\item $C_k$ : cover set of index $k$
-%\item $T(C_k)$ : set of targets covered by the cover set $k$
-%\item $NS(i)$ : set of available sensors which cover the target $i$
-%\item $NC(i)$ : set of cover sets which do not cover the target $i$
-%\item $|.|$ : cardinality of the set
-
-%\end{itemize}
-
\section{Simulation results}
\label{exp}
\parskip 0pt
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheCoverageRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{CR1.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the coverage ratio for 150 deployed nodes}
\label{fig3}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ASR1.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
\label{fig4}
\end{figure}
usually continues the optimization process, and this extends the
lifetime of the network.
-\subsection{The impact of the number of rounds on the energy saving ratio}
+\subsection{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 (ESR), is defined by:
%\centering
% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ESR1.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
\label{fig5}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps}
+\includegraphics[scale=0.36]{SR1.eps}
\caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
\label{fig6}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps}
+\includegraphics[scale=0.37]{EC1.eps}
\caption{The energy consumption}
\label{fig7}
\end{figure}
distributed method is clearly required.
\begin{table}[ht]
-\caption{THE EXECUTION TIME(S) VS THE NUMBER OF SENSORS}
+\caption{EXECUTION TIME(S) VS. NUMBER OF SENSORS}
% title of Table
\centering
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 has become disconnected. In figure~\ref{fig8}, the
+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.
+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]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{LT1.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 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
+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 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
-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{Conclusion and future works}
+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 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{Conclusion and future work}
\label{sec:conclusion}
-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
-is divided into smaller subregions using the concept of
+In this paper, we have addressed the problem of the coverage and the
+lifetime optimization in WSNs. To cope with this problem, the field of
+sensing is divided into smaller subregions using the concept of
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
include how to select the most efficient leader in each subregion and
-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 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 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. 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 time is far more
-difficult, but will reduce the communication overhead.
+the best representative active nodes. Results from 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 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 work, we
+plan to study a coverage protocol which computes all active sensor
+schedules in only one step for many rounds, using optimization methods
+such as swarms optimization or evolutionary algorithms.
% use section* for acknowledgement
%\section*{Acknowledgment}
-
-
-
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-
\end{document}
