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\begin{document}
-\title{Lifetime Coverage Optimization Protocol in Wireless Sensor Networks} %LiCO Protocol
-
-
+\title{Lifetime Coverage Optimization Protocol \\
+ in Wireless Sensor Networks} %LiCO Protocol
\author{Ali Kadhum Idrees,~\IEEEmembership{}
Karine Deschinkel,~\IEEEmembership{}
Michel Salomon,~\IEEEmembership{}
and~Rapha\"el Couturier ~\IEEEmembership{}
-\thanks{The authors are with 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}}
-%\thanks{J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
-%\thanks{Manuscript received April 19, 2005; revised December 27, 2012.}}
-
-\markboth{IEEE Communications Letters,~Vol.~11, No.~4, December~2014}%
-{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
+ \thanks{The authors are with 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}}
+\markboth{IEEE Communications Letters,~Vol.~XX, No.~Y, January 2015}%
+{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
\maketitle
-
\begin{abstract}
-
-
- One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The surveillance region is divided into subregions and LiCO protocol is distributed among sensor nodes in each subregion. LiC0 protocols works into periods, each period is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. Schedules node activities (wakeup and sleep of sensors) is performed in each subregion by a leader whose selection is the result of cooperation between nodes within the same subregion. The novelty of the approach lies essentially in the formulation of a new mathematical optimization model based on perimeter coverage level to schedule sensors activities. Extensive simulation experiments have been performed using OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible in comparison with some other protocols.
-
-\end{abstract}
-
+The most important problem in Wireless Sensor Networks (WSNs) is to optimize the
+use of its limited energy provision, so that it can fulfill its monitoring task
+as long as possible. Among known available approaches that can be used to
+improve power management, lifetime coverage optimization provides activity
+scheduling which ensures sensing coverage while minimizing the energy cost. In
+this paper, we propose a such approach called Lifetime Coverage Optimization
+protocol (LiCO). It is a hybrid of centralized and distributed methods: the
+region of interest is first subdivided into subregions and our protocol is then
+distributed among sensor nodes in each subregion. A sensor node which runs LiCO
+protocol repeats periodically four stages: information exchange, leader
+election, optimization decision, and sensing. More precisely, the scheduling of
+nodes activities (sleep/wake up duty cycles) is achieved in each subregion by a
+leader selected after cooperation between nodes within the same subregion. The
+novelty of approach lies essentially in the formulation of a new mathematical
+optimization model based on perimeter coverage level to schedule sensors
+activities. Extensive simulation experiments have been performed using OMNeT++,
+the discrete event simulator, to demonstrate that LiCO is capable to offer
+longer lifetime coverage for WSNs in comparison with some other protocols.
+\end{abstract}
% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
\end{IEEEkeywords}
-
\IEEEpeerreviewmaketitle
-
-
-
-
-\section{\uppercase{Introduction}}
+\section{Introduction}
\label{sec:introduction}
-\noindent The great development in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}.Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover, the energy needed by the sensor node is supplied by a power supply, to accomplish the scheduled task. This power supply is composed of a battery with a limited lifetime. And it maybe be unsuitable or impossible to replace or recharge the batteries in most applications. It is then necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible while ensuring a high level of coverage? Many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}. \\
+
+\noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
+wireless communication hardware has given rise to the opportunity to use large
+networks of tiny sensors, called Wireless Sensor Networks
+(WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
+tasks. A WSN consists of small low-powered sensors working together by
+communicating with one another through multihop radio communications. Each node
+can send the data it collects in its environment, thanks to its sensor, to the
+user by means of sink nodes. The features of a WSN made it suitable for a wide
+range of application in areas such as business, environment, health, industry,
+military, and son~\cite{yick2008wireless}. Typically, a sensor node contains
+three main components~\cite{anastasi2009energy}: a sensing unit able to measure
+physical, chemical, or biological phenomena observed in the environment; a
+processing unit which will process and store the collected measurements; a radio
+communication unit for data transmission and receiving.
+
+The energy needed by an active sensor node to perform sensing, processing, and
+communication is supplied by a power supply which is a battery. This battery has
+a limited energy provision and it may be unsuitable or impossible to replace or
+recharge it in most applications. Therefore it is necessary to deploy WSN with
+high density in order to increase the reliability and to exploit node redundancy
+thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
+of sensing areas can be exploited to schedule alternatively some sensors in a
+low power sleep mode and thus save energy. Overall, the main question that must
+be answered is: how to extend the lifetime coverage of a WSN as long as possible
+while ensuring a high level of coverage? So, this last years many
+energy-efficient mechanisms have been suggested to retain energy and extend the
+lifetime of the WSNs~\cite{rault2014energy}.
%The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches.
%From a certain standpoint, the high coverage ratio is required by many applications such as military and health-care. Therefore, a suitable number of sensors are being chosen so as to cover the area of interest, is the first challenge. Meanwhile, the sensor nodes have a limited capabilities in terms of memory, processing, communication, and battery power being the most important and critical one. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible?. There are many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}.
-%\uppercase{\textbf{Our contributions.}}
-This paper makes the following contributions.\\
+%\uppercase{\textbf{Our contributions.}}
+
+This paper makes the following contributions.
\begin{enumerate}
-\item We devise a framework to schedules nodes to be activated alternatively, such that the network lifetime may be prolonged ans certain coverage requirement can still be met.
-This framework is based on the division of the area of interest into several smaller subregions; on the division of timeline into periods of equal length.
-One leader is elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture
-\item We propose a new mathematical optimization model. Instead of trying to cover a set of specified points/targets as in most of the methods proposed in the literature,
-we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations between the
-actual level of coverage and the required level. And a weighted sum of these deviations is minimized.
-\item We conducted extensive simulation experiments using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocol, compared to two approaches found in the literature, DESK \ref{} and GAF \ref{}, and compared to our previous work using another optimization model for sensor scheduling.
+\item We devise a framework to schedule nodes to be activated alternatively such
+ that the network lifetime is prolonged while ensuring that a certain level of
+ coverage is preserved. A key idea in our framework is to exploit spatial an
+ temporal subdivision. On the one hand the area of interest if divided into
+ several smaller subregions and on the other hand the time line is divided into
+ periods of equal length. In each subregion the sensor nodes will cooperatively
+ choose a leader which will schedule nodes activities, and this grouping of
+ sensors is similar to typical cluster architecture.
+\item We propose a new mathematical optimization model. Instead of trying to
+ cover a set of specified points/targets as in most of the methods proposed in
+ the literature, we formulate an integer program based on perimeter coverage of
+ each sensor. The model involves integer variables to capture the deviations
+ between the actual level of coverage and the required level. So that an
+ optimal scheduling will be obtained by minimizing a weighted sum of these
+ deviations.
+\item We conducted extensive simulation experiments, using the discrete event
+ simulator OMNeT++, to demonstrate the efficiency of our protocol. We compared
+ our LiCO protocol to two approaches found in the literature:
+ DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous
+ work published in~\cite{Idrees2} which is based on another optimization model
+ for sensor scheduling.
\end{enumerate}
-
%Two combined integrated energy-efficient techniques have been used by LiCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
% the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
-
-The remainder of the paper is organized as follows. The next section reviews the related work in the field. Section~\ref{sec:The LiCO Protocol Description} is devoted to the LiCO protocol Description. Section~\ref{cp} gives the coverage model
-formulation which is used to schedule the activation of sensors.
-Section~\ref{sec:Simulation Results and Analysis} presents simulations results. Finally, we give concluding remarks and some suggestions for
-future works in Section~\ref{sec:Conclusion and Future Works}.
+The rest of the paper is organized as follows. In the next section we review
+some related work in the field. Section~\ref{sec:The LiCO Protocol Description}
+is devoted to the LiCO protocol description and Section~\ref{cp} focuses on the
+coverage model formulation which is used to schedule the activation of sensor
+nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
+results and discusses the comparison with other approaches. Finally, concluding
+remarks are drawn and some suggestions given for future works in
+Section~\ref{sec:Conclusion and Future Works}.
% that show that our protocol outperforms others protocols.
-\section{\uppercase{Related Literature}}
+\section{Related Literature}
\label{sec:Literature Review}
-
\noindent In this section, we summarize some related works regarding the
-coverage problem and distinguish our LiCO protocol from the works presented in
+coverage problem and distinguish our LiCO protocol from the works presented in
the literature.
-The most discussed coverage problems in literature can be classified into three
-types \cite{li2013survey}: area coverage \cite{Misra} where every point inside
-an area is to be monitored, target coverage \cite{yang2014novel} where the main
-objective is to cover only a finite number of discrete points called targets,
-and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders
-from entering into the region of interest. In \cite{Deng2012} authors transform
-the area coverage problem to the target coverage problem taking into account the
-intersection points among disks of sensors nodes or between disk of sensor nodes
-and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(n d log d)$ time to compute the perimeter-coverage of each sensor ($d$ the maximum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in the network). {\it In LiCO protocol, rather than determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.}
-
-The major approach to extend network lifetime while preserving coverage is to
-divide/organize the sensors into a suitable number of set covers (disjoint or
-non-disjoint), where each set completely covers a region of interest, and to
-activate these set covers successively. The network activity can be planned in
-advance and scheduled for the entire network lifetime or organized in periods,
+The most discussed coverage problems in literature can be classified in three
+categories~\cite{li2013survey} according to their respective monitoring
+objective. Hence, area coverage \cite{Misra} means that every point inside a
+fixed area must be monitored, while target coverage~\cite{yang2014novel} refer
+to the objective of coverage for a finite number of discrete points called
+targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on
+preventing intruders from entering into the region of interest. In
+\cite{Deng2012} authors transform the area coverage problem to the target
+coverage one taking into account the intersection points among disks of sensors
+nodes or between disk of sensor nodes and boundaries. In
+\cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
+sensors are sufficiently covered it will be the case for the whole area. They
+provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
+each sensor, where $d$ denotes the maximum number of sensors that are
+neighboring to a sensor and $n$ is the total number of sensors in the
+network. {\it In LiCO protocol, instead of determining the level of coverage of
+ a set of discrete points, our optimization model is based on checking the
+ perimeter-coverage of each sensor to activate a minimal number of sensors.}
+
+The major approach to extend network lifetime while preserving coverage is to
+divide/organize the sensors into a suitable number of set covers (disjoint or
+non-disjoint), where each set completely covers a region of interest, and to
+activate these set covers successively. The network activity can be planned in
+advance and scheduled for the entire network lifetime or organized in periods,
and the set of active sensor nodes is decided at the beginning of each period
\cite{ling2009energy}. Active node selection is determined based on the problem
-requirements (e.g. area monitoring, connectivity, power efficiency). For
-instance, Jaggi et al. \cite{jaggi2006} address the problem of maximizing
-network lifetime by dividing sensors into the maximum number of disjoint subsets
-such that each subset can ensure both coverage and connectivity. A greedy
+requirements (e.g. area monitoring, connectivity, or power efficiency). For
+instance, Jaggi {\em et al.}~\cite{jaggi2006} address the problem of maximizing
+the lifetime by dividing sensors into the maximum number of disjoint subsets
+such that each subset can ensure both coverage and connectivity. A greedy
algorithm is applied once to solve this problem and the computed sets are
activated in succession to achieve the desired network lifetime. Vu
-\cite{chin2007}, Padmatvathy et al. \cite{pc10}, propose algorithms working in a
-periodic fashion where a cover set is computed at the beginning of each period.
-{\it Motivated by these works, LiCO protocol works in periods, where each
- period contains a preliminary phase for information exchange and decisions,
- followed by a sensing phase where one cover set is in charge of the sensing
- task.}
-
-Various approaches, including centralized, or distributed algorithms, have been
-proposed to extend the network lifetime. In distributed
-algorithms~\cite{yangnovel,ChinhVu,qu2013distributed}, information is
-disseminated throughout the network and sensors decide cooperatively by
-communicating with their neighbors which of them will remain in sleep mode for a
-certain period of time. The centralized
-algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
-provide nearly or close to optimal solution since the algorithm has global view
-of the whole network. But such a method has the disadvantage of requiring high
-communication costs, since the node (located at the base station) making the
-decision needs information from all the sensor nodes in the area and the amount
-of information can be huge. {\it In order to be suitable for large-scale
- network, in the LiCO protocol, the area of interest is divided into several
- smaller subregions, and in each one, a node called the leader is in charge for
- selecting the active sensors for the current period.}
-
-A large variety of coverage scheduling algorithms has been developed. Many of
-the existing algorithms, dealing with the maximization of the number of cover
-sets, are heuristics. These heuristics involve the construction of a cover set
-by including in priority the sensor nodes which cover critical targets, that is
-to say targets that are covered by the smallest number of sensors
+\cite{chin2007}, Padmatvathy {\em et al.}~\cite{pc10}, propose algorithms
+working in a periodic fashion where a cover set is computed at the beginning of
+each period. {\it Motivated by these works, LiCO protocol works in periods,
+ where each period contains a preliminary phase for information exchange and
+ decisions, followed by a sensing phase where one cover set is in charge of the
+ sensing task.}
+
+Various centralized and distributed approaches, or even a mixing of these two
+concepts, have been proposed to extend the network lifetime. In distributed
+algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensors decides of
+its own activity scheduling after an information exchange with its neighbors.
+The main interest of a such approach is to avoid long range communications and
+thus to reduce the energy dedicated to the communications. Unfortunately, since
+each node has only information on its immediate neighbors (usually the one-hop
+ones) it may take a bad decision leading to a global suboptimal solution.
+Conversely, centralized
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
+provide nearly or close to optimal solution since the algorithm has a global
+view of the whole network. The disadvantage of a centralized method is obviously
+its high cost in communications needed to transmit to a single node, the base
+station which will globally schedule nodes activities, data from all the other
+sensor nodes in the area. The price in communications can be very huge since
+long range communications will be needed. In fact the larger the WNS, the higher
+the communication and thus energy cost. {\it In order to be suitable for
+ large-scale networks, in the LiCO protocol the area of interest is divided
+ into several smaller subregions, and in each one, a node called the leader is
+ in charge for selecting the active sensors for the current period. Thus our
+ protocol is scalable and a globally distributed method, whereas it is
+ centralized in each subregion.}
+
+Various coverage scheduling algorithms have been developed this last years.
+Many of them, dealing with the maximization of the number of cover sets, are
+heuristics. These heuristics involve the construction of a cover set by
+including in priority the sensor nodes which cover critical targets, that is to
+say targets that are covered by the smallest number of sensors
\cite{berman04,zorbas2010solving}. Other approaches are based on mathematical
programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
-and dedicated techniques (solving with a branch-and-bound algorithms available
-in optimization solver). The problem is formulated as an optimization problem
+and dedicated techniques (solving with a branch-and-bound algorithm available in
+optimization solver). The problem is formulated as an optimization problem
(maximization of the lifetime or number of cover sets) under target coverage and
-energy constraints. Column generation techniques, well-known and widely
+energy constraints. Column generation techniques, well-known and widely
practiced techniques for solving linear programs with too many variables, have
also been
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In LiCO
- protocol, each leader, in each subregion, solves an integer program with
-the double objective consisting in minimizing the overcoverage and the
- undercoverage of the perimeter of each sensor.
-
-}
-
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In LiCO
+ protocol, each leader, in charge of a subregion, solves an integer program
+ which has a twofold objective: minimize the overcoverage and the undercoverage
+ of the perimeter of each sensor.}
%\noindent Recently, the coverage problem has been received a high attention, which concentrates on how the physical space could be well monitored after the deployment. Coverage is one of the Quality of Service (QoS) parameters in WSNs, which is highly concerned with power depletion~\cite{zhu2012survey}. Most of the works about the coverage protocols have been suggested in the literature focused on three types of the coverage in WSNs~\cite{mulligan2010coverage}: the first, area coverage means that each point in the area of interest within the sensing range of at least one sensor node; the second, target coverage in which a fixed set of targets need to be monitored; the third, barrier coverage refers to detect the intruders crossing a boundary of WSN. The work in this paper emphasized on the area coverage, so, some area coverage protocols have been reviewed in this section, and the shortcomings of reviewed approaches are being summarized.
%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (LiCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a LiCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. LiCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
-
\section{ The LiCO Protocol Description}
\label{sec:The LiCO Protocol Description}
-\noindent In this section, we describe our Lifetime Coverage Optimization Protocol which is called LiCO in more detail.
+
+\noindent In this section, we describe in details our Lifetime Coverage
+Optimization protocol. First we present the assumptions we made and the models
+we considered (in particular the perimeter coverage one), second we describe the
+background idea of our protocol, and third we give the outline of the algorithm
+executed by each node.
+
% It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion; the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period. Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently.
%Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
-\subsection{ Assumptions and Models}
-\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly distributed in a bounded sensor field is considered. The wireless sensors are deployed in high density to ensure initially a high coverage ratio of the interested area. We assume that all the sensor nodes are homogeneous in terms of communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The location information is available to the sensor node either through hardware such as embedded GPS or through location discovery algorithms. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station. We consider a boolean disk coverage model which is the most 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 $R_c \geq 2R_s$. 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.
-
-\indent LiCO protocol uses the perimeter-coverage model which states in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. Huang and Tseng in \cite{huang2005coverage} proves that a network area is $k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
+\subsection{Assumptions and Models}
+
+\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
+distributed in a bounded sensor field is considered. The wireless sensors are
+deployed in high density to ensure initially a high coverage ratio of the area
+of interest. We assume that all the sensor nodes are homogeneous in terms of
+communication, sensing, and processing capabilities and heterogeneous from
+energy provision point of view. The location information is available to a
+sensor node either through hardware such as embedded GPS or location discovery
+algorithms. We assume that each sensor node can directly transmit its
+measurements to a mobile sink node. For example, a sink can be an unmanned
+aerial vehicle (UAV) flying regularly over the sensor field to collect
+measurements from sensor nodes. A mobile sink node collects the measurements and
+transmits them to the base station. We consider a Boolean disk coverage model,
+which is the most widely used sensor coverage model in the literature, and all
+sensor nodes have a constant sensing range $R_s$. Thus, all the space points
+within a disk centered at a sensor with a radius equal to the sensing range are
+said to be covered by this sensor. We also assume that the communication range
+$R_c$ satisfies $R_c \geq 2 \cdot R_s$. 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 active nodes.
+
+\indent LiCO protocol uses the same perimeter-coverage model than Huang and
+Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is
+said to be perimeter covered if all the points on its perimeter are covered by
+at least one sensor other than itself. They proved that a network area is
+$k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
%According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model.
-Figure~\ref{pcmfig} illuminates the perimeter coverage of the sensor node $0$. On this figure, sensor $0$ has $9$ neighbors. We report for each sensor $i$ having an intersection with sensor $0$, the two intersection points, $iL$ for left point and $iR$ for right point. These intersections points subdivide the perimeter of the sensor $0$ (the perimeter of the disk covered by the sensor) into portions called segments.
+Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this
+figure, we can see that sensor~$0$ has nine neighbors and we have reported on
+its perimeter (the perimeter of the disk covered by the sensor) for each
+neighbor the two points resulting from intersection of the two sensing
+areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
+for left and right from neighbor point of view. The resulting couples of
+intersection points subdivide the perimeter of sensor~$0$ into portions called
+arcs.
\begin{figure}[ht!]
-\centering
-\includegraphics[width=75mm]{pcm.pdf}
-\caption{Perimeter coverage of sensor node 0}
-\label{pcmfig}
+ \centering
+ \begin{tabular}{@{}cr@{}}
+ \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)}
+ \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
+ \end{tabular}
+ \caption{Perimeter coverage of sensor node 0 (a) and finding the arc of $u$'s
+ perimeter covered by $v$.}
+ \label{pcm2sensors}
\end{figure}
-Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$.
-
-The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals. For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. The table in figure~\ref{expcm} summarizes the level of coverage for each interval and the sensors involved in.
+Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
+locations of the left and right points of an arc on the perimeter of a sensor
+node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the
+west side of sensor~$u$, with the following respective coordinates in the
+sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
+compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
+ u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
+obtained through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right)$. So, the arc on the perimeter of node~$u$ defined by the angular
+interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
+node $v$.
+
+Every couple of intersection points is placed on the angular interval $[0,2\pi]$
+in a counterclockwise manner, leading to a partitioning of the interval.
+Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
+sensor $0$ and figure~\ref{expcm} gives the position of the corresponding arcs
+in the interval $[0,2\pi]$. More precisely, we can see that the points are
+ordered according to the measures of the angles defined by their respective
+positions. The intersection points are then visited one after another, starting
+from first intersection point after point~zero, and the maximum level of
+coverage is determined for each interval defined by two successive points. The
+maximum level of coverage is equal to the number of overlapping arcs. For
+example, between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
+(the value is highlighted in yellow at the bottom of figure~\ref{expcm}), which
+means that at most 2~neighbors can cover the perimeter in addition to node $0$.
+Table~\ref{my-label} summarizes for each coverage interval the maximum level of
+coverage and the sensor nodes covering the perimeter. The example discussed
+above is thus given by the sixth line of the table.
+
+%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
% to determine the level of the perimeter coverage for each left and right point of a segment.
-\begin{figure}[ht!]
-\centering
-\includegraphics[width=75mm]{twosensors.jpg}
-\caption{Locating the segment of $u$$\rq$s perimeter covered by $v$.}
-\label{twosensors}
-\end{figure}
-\begin{figure}[ht!]
+\begin{figure*}[ht!]
\centering
-\includegraphics[width=75mm]{expcm.pdf}
-\caption{ Coverage levels for sensor node $0$.}
+\includegraphics[width=137.5mm]{expcm.pdf}
+\caption{Maximum coverage levels for perimeter of sensor node $0$.}
\label{expcm}
-\end{figure}
+\end{figure*}
%For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
+\iffalse
+
\begin{figure}[ht!]
\centering
\includegraphics[width=90mm]{ex2pcm.jpg}
\label{ex2pcm}
\end{figure}
-%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
+\fi
-In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}.
+ \begin{table}[h]
+ \caption{Coverage intervals and contributing sensors for sensor node 0.}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
+\hline
+\begin{tabular}[c]{@{}c@{}}The angle \\ $\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Segment \\ Left (L) or\\ Right (R)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Sensor \\ Node Id\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ Coverage\\ Level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}The Set of Sensors\\ Involved in Interval \\ Coverage\end{tabular}} \\ \hline
+0.0291 & L & 1 & 4 & 0 & 1 & 3 & 4 & \\ \hline
+0.104 & L & 2 & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
+0.3168 & R & 3 & 4 & 0 & 1 & 4 & 2 & \\ \hline
+0.6752 & R & 4 & 3 & 0 & 1 & 2 & & \\ \hline
+1.8127 & R & 1 & 2 & 0 & 2 & & & \\ \hline
+1.9228 & L & 5 & 3 & 0 & 2 & 5 & & \\ \hline
+2.3959 & L & 6 & 4 & 0 & 2 & 5 & 6 & \\ \hline
+2.4258 & R & 2 & 3 & 0 & 5 & 6 & & \\ \hline
+2.7868 & L & 7 & 4 & 0 & 5 & 6 & 7 & \\ \hline
+2.8358 & L & 8 & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
+2.9184 & R & 5 & 4 & 0 & 6 & 7 & 8 & \\ \hline
+3.3301 & R & 7 & 3 & 0 & 6 & 8 & & \\ \hline
+3.9464 & L & 9 & 4 & 0 & 6 & 8 & 9 & \\ \hline
+4.767 & R & 6 & 3 & 0 & 8 & 9 & & \\ \hline
+4.8425 & L & 3 & 4 & 0 & 3 & 8 & 9 & \\ \hline
+4.9072 & R & 8 & 3 & 0 & 3 & 9 & & \\ \hline
+5.3804 & L & 4 & 4 & 0 & 3 & 4 & 9 & \\ \hline
+5.9157 & R & 9 & 3 & 0 & 3 & 4 & & \\ \hline
+\end{tabular}
-In the case of sensor node, which has a part of its sensing range outside the border of the WSN sensing field as in figure~\ref{ex4pcm}, the coverage level for this segment is set to $\infty$, and the corresponding interval will not be taken into account by the optimization algorithm.
-\begin{figure}[ht!]
+\label{my-label}
+\end{table}
+
+
+%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
+
+In LiCO protocol, scheduling of sensor nodes activities is formulated with an
+integer program based on coverage intervals. The formulation of the coverage
+optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
+node has a part of its sensing range outside the WSN sensing field, as in
+figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
+and the corresponding interval will not be taken into account by the
+optimization algorithm.
+
+\begin{figure}[t!]
\centering
-\includegraphics[width=75mm]{ex4pcm.jpg}
-\caption{Part of sensing range outside the the border of WSN sensing field.}
+\includegraphics[width=62.5mm]{ex4pcm.jpg}
+\caption{Sensing range outside the WSN's area of interest.}
\label{ex4pcm}
\end{figure}
%Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node $0$, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node $0$ has two segments outside the border of the network sensing field, so the left and right points of the two segments called $-1L$, $-1R$, $-2L$, and $-2R$.
%\label{ex5pcm}
%\end{figure}
+% MICHEL TO BE CONTINUED FROM HERE
\subsection{The Main Idea}
\noindent The area of interest can be divided into smaller areas called subregions and
level of coverage. For example, weights associated with coverage intervals of a specified part of a region
may be given a relatively
larger magnitude than weights associated
-with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \ref{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model.
+with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model.
\section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}
According to the interval of initial energy, a sensor may be active during at
most 20 rounds.
+The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen in a way that ensuring a good network coverage and for a longer time during the lifetime of the WSN. We have given a higher priority for the undercoverage ( by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so as to minimize the number of active sensor nodes that contribute in covering the interval i in sensor j.
+
In the simulations, we introduce the following performance metrics to evaluate
the efficiency of our approach:
%\end{enumerate}
\subsection{Simulation Results}
-In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language ????\ref{}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
+In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
We compared LiCO protocol to three other approaches: the first, called DESK and proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm; the second, called GAF ~\cite{xu2001geography}, consists in dividing the region
into fixed squares. During the decision phase, in each square, one sensor is
-chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be actived in each sensing phase. Whereas DilCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
+chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
\subsubsection{\textbf{Coverage Ratio}}
Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
\label{fig333}
\end{figure}
-DESK, GAF, and DiLCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
+DESK, GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
