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-\begin{document}
%\title{Authors' Instructions \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
-\title{Distributed Lifetime Coverage Optimization Protocol \\in Wireless Sensor Networks}
+\title{Distributed Lifetime Coverage Optimization Protocol \\
+ in Wireless Sensor Networks}
-\author{\authorname{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
-\affiliation{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, Belfort, France}
-%\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry}
-\email{ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
-%\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu}
-}
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$,\\ Michel Salomon$^{a}$, and Rapha\"el Couturier$^{a}$\\
+$^{a}$FEMTO-ST Institute, UMR 6174 CNRS, \\ University Bourgogne Franche-Comt\'e, Belfort, France\\
+$^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}\\
+email: ali.idness@edu.univ-fcomte.fr,\\ $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
-\keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,
-Optimization, Scheduling.}
-
-\abstract{One of the fundamental challenges in Wireless Sensor Networks (WSNs) 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 Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
-the coverage and to improve the lifetime in wireless sensor networks is
-proposed. The area of interest is first divided into subregions using a
-divide-and-conquer method and then the DiLCO protocol is distributed on the
-sensor nodes in each subregion. The DiLCO combines two efficient techniques:
-leader election for each subregion, followed by an optimization-based planning
-of activity scheduling decisions for each subregion. The proposed DiLCO works
-into periods during which a small number of nodes, remaining active for sensing,
-is selected to ensure coverage so as to maximize the lifetime of wireless sensor
-network. Each period consists of 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. Compared with
-some existing protocols, simulation results show that the proposed protocol can
-prolong the network lifetime and improve the coverage performance effectively.}
-
-\onecolumn \maketitle \normalsize \vfill
+%\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$,\\ Michel Salomon$^{a}$, and Rapha\"el Couturier $^{a}$ \\
+%$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University Bourgogne Franche-Comt\'e,\\ Belfort, France}} \\
+%$^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}} }
+
+\begin{document}
+ \maketitle
+%\keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,Optimization, Scheduling.}
+
+\abstract{ One of the main research challenges faced in Wireless Sensor Networks
+ (WSNs) is to preserve continuously and effectively the coverage of an area (or
+ region) of interest to be monitored, while simultaneously preventing as much
+ as possible a network failure due to battery-depleted nodes. In this paper we
+ propose a protocol, called Distributed Lifetime Coverage Optimization protocol
+ (DiLCO), which maintains the coverage and improves the lifetime of a wireless
+ sensor network. First, we partition the area of interest into subregions using
+ a classical divide-and-conquer method. Our DiLCO protocol is then distributed
+ on the sensor nodes in each subregion in a second step. To fulfill our
+ objective, the proposed protocol combines two effective techniques: a leader
+ election in each subregion, followed by an optimization-based node activity
+ scheduling performed by each elected leader. This two-step process takes
+ place periodically, in order to choose a small set of nodes remaining active
+ for sensing during a time slot. Each set is built to ensure coverage at a low
+ energy cost, allowing to optimize the network lifetime.
+%More precisely, a
+ %period consists of four phases: (i)~Information Exchange, (ii)~Leader
+ %Election, (iii)~Decision, and (iv)~Sensing. The decision process, which
+% results in an activity scheduling vector, is carried out by a leader node
+% through the solving of an integer program.
+% MODIF - BEGIN
+ Simulations are conducted using the discret event simulator
+ OMNET++. We refer to the characterictics of a Medusa II sensor for
+ the energy consumption and the computation time. In comparison with
+ two other existing methods, our approach is able to increase the WSN
+ lifetime and provides improved coverage performance. }
+% MODIF - END
+
+%\onecolumn
+
+
+%\normalsize \vfill
\section{\uppercase{Introduction}}
\label{sec:introduction}
-\noindent
-Energy efficiency is very important issue in WSNs since sensors are powered by batteries. Therefore, reducing energy consumption and extending network lifetime are the main challenges in the design of WSNs. One of the major scientific research challenges in WSNs, which has been addressed by a large amount of literature during the last few years, is the design of energy efficient approaches for coverage and connectivity~\cite{conti2014mobile}.
-Coverage reflects how well a sensor field is monitored. The most discussed coverage problems in literature can be classified
-into three types \cite{li2013survey}: area coverage (where every
-point inside an area is to be monitored), target coverage (where the main objective is to cover only a finite number of discrete
-points called targets), and barrier coverage (the problem of preventing an intruder from entering a region of interest is referred to as the barrier coverage).
- It is required to monitor the area of interest efficiently~\cite{Nayak04}, but in the same time the power consumption should be minimized. Sensor nodes runs on batteries with limited capacities~\cite{Sudip03} and it is impossible, difficult or expensive to recharge and/or replace batteries in remote, hostile, or unpractical environments. Therefore, it is desired that the WSNs are deployed with high densities so as to exploit the overlapping sensing regions of some sensor nodes to save energy by turning off some of them during the sensing phase to prolong the network lifetime.
-
-In this paper we concentrate on the area coverage problem with the objective of
-maximizing the network lifetime by using DiLCO protocol to maintain the coverage and to improve the lifetime in WSNs. The area of interest is divided into subregions using divide-and-conquer method and an activity scheduling for sensor nodes is planned by the elected leader in 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 DiLCO protocol considers periods, where a period starts with a discovery phase to exchange information between sensors of the subregion, in order to choose in a suitable manner a sensor node (the leader) to carry out the coverage strategy. Our DiLCO protocol involves solving an integer program, which provides the activation of the sensors for the sensing phase of the current period.
-The remainder of the paper is organized as follows. The next section reviews the related work in the field. Section~\ref{sec:The DiLCO Protocol Description} is devoted to the DiLCO 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} shows the simulation results. Finally, we give concluding remarks and some suggestions for
-future works in Section~\ref{sec:Conclusion and Future Works}.
+\noindent
+Energy efficiency is a crucial issue in wireless sensor networks since sensory
+consumption, in order to maximize the network lifetime, represents the major
+difficulty when designing WSNs. As a consequence, one of the scientific research
+challenges in WSNs, which has been addressed by a large amount of literature
+during the last few years, is the design of energy efficient approaches for
+coverage and connectivity~\cite{conti2014mobile}. Coverage reflects how well a
+sensor field is monitored. On the one hand we want to monitor the area of
+interest in the most efficient way~\cite{Nayak04}, \textcolor{blue}{which means
+ that we want to maintain the best coverage as long as possible}. On the other
+hand we want to use as little energy as possible. Sensor nodes are
+battery-powered with no means of recharging or replacing, usually due to
+environmental (hostile or unpractical environments) or cost reasons. Therefore,
+it is desired that the WSNs are deployed with high densities so as to exploit
+the overlapping sensing regions of some sensor nodes to save energy by turning
+off some of them during the sensing phase to prolong the network
+lifetime. \textcolor{blue}{A WSN can use various types of sensors such as
+ \cite{ref17,ref19}: thermal, seismic, magnetic, visual, infrared, acoustic,
+ and radar. These sensors are capable of observing different physical
+ conditions such as: temperature, humidity, pressure, speed, direction,
+ movement, light, soil makeup, noise levels, presence or absence of certain
+ kinds of objects, and mechanical stress levels on attached objects.
+ Consequently, there is a wide range of WSN applications such as~\cite{ref22}:
+ health-care, environment, agriculture, public safety, military, transportation
+ systems, and industry applications.}
+
+In this paper we design a protocol that focuses on the area coverage problem
+with the objective of maximizing the network lifetime. Our proposition, the
+Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the
+coverage and improves the lifetime in WSNs. The area of interest is first
+divided into subregions using a divide-and-conquer algorithm and an activity
+scheduling for sensor nodes is then planned by the elected leader in 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 DiLCO protocol considers periods, where a period
+starts with a discovery phase to exchange information between sensors of the
+same subregion, in order to choose in a suitable manner a sensor node (the
+leader) to carry out the coverage strategy. In each subregion the activation of
+the sensors for the sensing phase of the current period is obtained by solving
+an integer program. The resulting activation vector is broadcast by a leader
+to every node of its subregion.
+
+% MODIF - BEGIN
+Our previous paper ~\cite{idrees2014coverage} relies almost exclusively on the
+framework of the DiLCO approach and the coverage problem formulation. In this
+paper we made more realistic simulations by taking into account the
+characteristics of a Medusa II sensor ~\cite{raghunathan2002energy} to measure
+the energy consumption and the computation time. We have implemented two other
+existing \textcolor{blue}{and distributed approaches} (DESK ~\cite{ChinhVu}, and
+GAF ~\cite{xu2001geography}) in order to compare their performances with our
+approach. We also focus on performance analysis based on the number of
+subregions.
+% MODIF - END
+
+The remainder of the paper continues with Section~\ref{sec:Literature Review}
+where a review of some related works is presented. The next section describes
+the DiLCO protocol, followed in Section~\ref{cp} by the coverage model
+formulation which is used to schedule the activation of
+sensors. Section~\ref{sec:Simulation Results and Analysis} shows the simulation
+results. The paper ends with a conclusion and some suggestions for further work
+in Section~\ref{sec:Conclusion and Future Works}.
\section{\uppercase{Literature Review}}
\label{sec:Literature Review}
-\noindent In this section, we summarize some related works regarding coverage lifetime maximization and scheduling, and distinguish our DiLCO protocol from the works presented in the literature. Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
-
-
-Yang et al.~\cite{yang2014energy} investigated full area coverage problem
-under the probabilistic sensing model in the sensor networks. They have studied the relationship between the
-coverage of two adjacent points mathematically and then convert the problem of full area coverage into point coverage problem. They proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select a subset
-of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
-
-
-Vu et al.~\cite{ChinhVu} proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-area coverage for the whole network.
-
-
-Qu et al.~\cite{qu2013distributed} developed a distributed algorithm using adjustable sensing sensors
-for maintaining the full coverage of such sensor networks. The
-algorithm contains two major parts: the first part aims at
-providing $100\%$ coverage and the second part aims at saving
-energy by decreasing the sensing radius.
-
-Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be changed into a set coverage
-problem. By using this model, they are proposed an Energy-Efficient central-Scheduling greedy algorithm, which can reduces energy consumption and increases network lifetime, by selecting a appropriate subset of sensor nodes to support the networks periodically.
-
-The work in~\cite{cheng2014achieving} presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to provide a flexible and efficient coverage in sensor networks.
-
- In~\cite{ling2009energy}, The lifetime of
-a sensor node is divided into epochs. At each epoch, the
-base station deduces the current sensing coverage requirement
-from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch. After that, the produced schedule is sent to the sensor nodes in the network.
-
-
-\iffalse
-
-The work in ~\cite{vu2009delaunay} considered the area coverage problem for variable sensing radii in WSNs by improving the energy balancing heuristic proposed in ~\cite{wang2007energy} so that the area of interest can be full covered using Delaunay triangulation structure.
-
-Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep scheduling algorithm for lifetime maximization in wireless sensor networks (ALARM). The proposed approach permits to schedule redundant nodes according to the weibull distribution. This work did not analyze the ALARM scheme under the coverage problem.
-
-
-In~\cite{xin2009area}, the authors proposed a circle intersection localized coverage algorithm
-to maintain connectivity based on loose connectivity critical condition
-. By using the connected coverage node set, it can maintain network
-connection in the case which loose condition is not meet.
-The authors in ~\cite{vashistha2007energy} addressed the full area coverage problem using information
-coverage. They are proposed a low-complexity heuristic algorithm to obtain full area information covers (FAIC), which they refer to as Grid Based FAIC (GB-FAIC) algorithm. Using these FAICs, they are obtained the optimal schedule for applying the sensing activity of sensor nodes in order to
-achieve increased sensing lifetime of the network.
-
-
-\fi
-
-
-
-In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
-
-The main contributions of our DiLCO Protocol can be summarized as follows:
-(1) The distributed optimization over the subregions in the area of interest,
-(2) The distributed dynamic leader election at each round by each sensor node in the subregion,
-(3) The primary point coverage model to represent each sensor node in the network,
-(4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion, and (5) The improved energy consumption model.
-
-\iffalse
-The work presented in~\cite{luo2014parameterized,tian2014distributed} tries to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
-%Je ne comprends pas la phrase ci-dessus
-The work proposed in~\cite{kim2013maximum} considers the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
-%inutile de parler de ce papier car il concerne barrier coverage
-In \cite{ChinhVu}, the authors propose a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network.
-Our Work in~\cite{idrees2014coverage} proposes a coverage optimization protocol to improve the lifetime in heterogeneous energy wireless sensor networks. In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We are considered only distributing the coverage protocol over two subregions.
-
-The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
-
-The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
-\fi
-
-\iffalse
-Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to extend the network lifetime with connectivity and coverage constraints. They are included two heuristic methods within the CG framework so as to accelerate the solution process.
-In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution taking into consideration frequent nodes failure.
-Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
-approach (CWSC) to maintain k-coverage and connectivity. This approach try to select the minimum number of connected sensor nodes that can provide k-coverage ($k \geq 1$).
-In~\cite{cheng2014achieving}, the authors are presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to provide a flexible and efficient coverage in sensor networks.
-
-In~\cite{yang2013energy}, the authors are investigated full area coverage problem
-under the probabilistic sensing model in the sensor networks. %They are designed $\varepsilon-$full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
-In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
-The main contributions of our DiLCO Protocol can be summarized as follows:
-(1) The distributed optimization over the subregions in the area of interest,
-(2) The distributed dynamic leader election at each round by each sensor node in the subregion,
-(3) The primary point coverage model to represent each sensor node in the network,
-(4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion,
-(5) The improved energy consumption model.
-
-\fi
-
-\section{ The DiLCO Protocol Description}
+\noindent In this section, we summarize some related works regarding the
+coverage problem and distinguish our DiLCO 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. {\it In DiLCO protocol, the area coverage, i.e. the coverage of
+ every point in the sensing region, is transformed to the coverage of a
+ fraction of points called primary points. }
+
+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
+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, DiLCO 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 DiLCO protocol, the area coverage 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{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
+(maximization of the lifetime or number of cover sets) under target coverage and
+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 DiLCO
+ protocol, each leader, in each subregion, solves an integer program with a
+ double objective consisting in minimizing the overcoverage and limiting the
+ undercoverage. This program is inspired from the work of \cite{pedraza2006}
+ where the objective is to maximize the number of cover sets.}
+
+\section{\uppercase{Description of the DiLCO protocol}}
\label{sec:The DiLCO Protocol Description}
-\noindent In this section, we introduce a Distributed Lifetime Coverage Optimization protocol, which is called DiLCO. It is distributed on each subregion in the area of interest. It is based on two efficient techniques: network leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.
-\iffalse The main features of our DiLCO protocol:
-i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into rounds, iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi) it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative set of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our protocol.
-\fi
-\subsection{ Assumptions and Models}
-\noindent We consider a randomly and uniformly deployed network consisting of
-static wireless sensors. The wireless sensors are deployed in high
-density to ensure initially a high coverage ratio of the interested area. We
-assume that all nodes are homogeneous in terms of communication and
-processing capabilities and heterogeneous in term of energy provision.
-The location information is available to the sensor node either
-through hardware such as embedded GPS or through location discovery
-algorithms. 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 Instead of working with the coverage area, we consider for each
-sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the
-sensing disk defined by a sensor is covered if all the primary points of
-this sensor are covered.
-
-\iffalse
-By knowing the position (point center: ($p_x,p_y$)) of a wireless
-sensor node and its $R_s$, we calculate the primary points directly
-based on the proposed model. We use these primary points (that can be
-increased or decreased if necessary) as references to ensure that the
-monitored region of interest is covered by the selected set of
-sensors, instead of using all the points in the area.
-
-\indent We can calculate the positions of the selected primary
-points in the circle disk of the sensing range of a wireless sensor
-node (see figure~\ref{fig1}) as follows:\\
-$(p_x,p_y)$ = point center of wireless sensor node\\
-$X_1=(p_x,p_y)$ \\
-$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
-$X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
-$X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
-$X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
-$X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
-$X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
-$X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
-$X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
-$X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
-$X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
-$X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
-$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
-
- \begin{figure}[h!]
-\centering
- \begin{multicols}{3}
-\centering
-%\includegraphics[scale=0.20]{fig21.pdf}\\~ ~ ~ ~ ~(a)
-%\includegraphics[scale=0.20]{fig22.pdf}\\~ ~ ~ ~ ~(b)
-\includegraphics[scale=0.25]{principles13.pdf}%\\~ ~ ~ ~ ~(c)
-%\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
-%\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{Wireless Sensor Node represented by (a)5, (b)9 and (c)13 primary points respectively}
-\label{fig1}
-\end{figure}
-
-\fi
+\noindent In this section, we introduce the DiLCO protocol which is distributed
+on each subregion in the area of interest. It is based on two efficient
+techniques: network leader election and sensor activity scheduling for coverage
+preservation and energy conservation, applied periodically to efficiently
+maximize the lifetime in the network.
+
+\subsection{Assumptions and models}
+
+\noindent We consider a sensor network composed of static nodes distributed
+independently and uniformly at random. A high density deployment ensures a high
+coverage ratio of the interested area at the start. The nodes are supposed to
+have homogeneous characteristics from a communication and a processing point of
+view, whereas they have heterogeneous energy provisions. Each node has access
+to its location thanks, either to a hardware component (like a GPS unit), or a
+location discovery algorithm.
+
+\indent We consider a boolean disk coverage model which is the most widely used
+sensor coverage model in the literature. Thus, since a sensor has a constant
+sensing range $R_s$, every space points within a disk centered at a 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
+Hou~\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 For each sensor we also define a set of points called primary
+points~\cite{idrees2014coverage} to approximate the area coverage it provides,
+rather than working with a continuous coverage. Thus, a sensing disk
+corresponding to a sensor node is covered by its neighboring nodes if all its
+primary points are covered. Obviously, the approximation of coverage is more or
+less accurate according to the number of primary points.
+
+
+\subsection{Main idea}
+\label{main_idea}
+\noindent We start by applying a divide-and-conquer algorithm to partition the
+area of interest into smaller areas called subregions and then our protocol is
+executed simultaneously in each subregion. \textcolor{blue}{Sensor nodes are assumed to
+be deployed almost uniformly over the region and the subdivision of the area of interest is regular.}
-\subsection{The Main Idea}
-\noindent The area of interest can be divided using the
-divide-and-conquer strategy into smaller areas called subregions and
-then our coverage protocol will be implemented in each subregion
-simultaneously. Our DiLCO protocol works in periods fashion as shown in figure~\ref{fig2}.
\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{FirstModel.pdf} % 70mm
\label{fig2}
\end{figure}
-%Modifier la figure pour faire apparaitre des periodes et dans le schema en bleu, indiquer sensing round au lieu de sensing tout seul.
-
-Each period is divided into 4 phases : Information (INFO) Exchange,
-Leader Election, Decision, and Sensing. For each period there is
-exactly one set cover responsible for the sensing task. This protocol is
-more reliable against an unexpected node failure because it works
-in periods. On the one hand, if a node failure is detected before
-making the decision, the node will not participate to this phase, and,
-on the other hand, if the node failure occurs after the decision, the
-sensing task of the network will be temporarily affected: only during
-the period of sensing until a new period starts, since a new set cover
-will take charge of the sensing task in the next period. The energy
-consumption and some other constraints can easily be taken into
-account since the sensors can update and then exchange their
-information (including their residual energy) at the beginning of each
-period. However, the pre-sensing phases (INFO Exchange, Leader
-Election, Decision) are energy consuming for some nodes, even when
-they do not join the network to monitor the area.
-We define two types of packets to be used by our DiLCO protocol.
+As shown in Figure~\ref{fig2}, the proposed DiLCO protocol is a periodic
+protocol where each period is decomposed into 4~phases: Information Exchange,
+Leader Election, Decision, and Sensing. For each period there will be exactly
+one cover set in charge of the sensing task. A periodic scheduling is
+interesting because it enhances the robustness of the network against node failures.
+% \textcolor{blue}{Many WSN applications have communication requirements that are periodic and known previously such as collecting temperature statistics at regular intervals. This periodic nature can be used to provide a regular schedule to sensor nodes and thus avoid a sensor failure. If the period time increases, the reliability and energy consumption are decreased and vice versa}.
+First, a node that has not enough energy to complete a period, or
+which fails before the decision is taken, will be excluded from the scheduling
+process. Second, if a node fails later, whereas it was supposed to sense the
+region of interest, it will only affect the quality of the coverage until the
+definition of a new cover set in the next period. Constraints, like energy
+consumption, can be easily taken into consideration since the sensors can update
+and exchange their information during the first phase. Let us notice that the
+phases before the sensing one (Information Exchange, Leader Election, and
+Decision) are energy consuming for all the nodes, even nodes that will not be
+retained by the leader to keep watch over the corresponding area.
+
+During the execution of the DiLCO protocol, two kinds of packet will be used:
%\begin{enumerate}[(a)]
\begin{itemize}
-\item INFO packet: sent by each sensor node to all the nodes inside a same subregion for information exchange.
-\item ActiveSleep packet: sent by the leader to all the nodes in its subregion to inform them to be Active or Sleep during the sensing phase.
+\item INFO packet: sent by each sensor node to all the nodes inside a same
+ subregion for information exchange.
+\item ActiveSleep packet: sent by the leader to all the nodes in its subregion
+ to inform them to stay Active or to go Sleep during the sensing phase.
\end{itemize}
%\end{enumerate}
-
-There are five status for each sensor node in the network :
+and each sensor node will have five possible status in the network:
%\begin{enumerate}[(a)]
\begin{itemize}
-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: sensor is waiting for a decision (to be active or not);
+\item COMPUTATION: sensor applies the optimization process as leader;
+\item ACTIVE: sensor is active;
+\item SLEEP: sensor is turned off;
+\item COMMUNICATION: sensor is transmitting or receiving packet.
\end{itemize}
%\end{enumerate}
-%Below, we describe each phase in more details.
-Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_j$ for a sensor node indexed by $j$).
-Initially, the sensor node checks its remaining energy in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy $RE_j$, sensor node id, and the number of its one-hop live neighbors during the information exchange.
-Then all the sensor nodes in the same subregion will select the leader based on the received informations. The selection criteria for the leader in order of priority are: larger number of neighbours, larger remaining energy, and then in case of equality, larger index. After that, if the sensor node is leader, it will execute the integer program algorithm (see section~\ref{cp}) which provides a set of sensors planned to be active in the sensing round. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to indicate it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing round.
-
-
-
-\iffalse
-\subsubsection{Information Exchange Phase}
-
-Each sensor node $j$ sends its position, remaining energy $RE_j$, and
-the number of neighbours $NBR_j$ to all wireless sensor nodes in
-its subregion by using an INFO packet and then listens to the packets
-sent from other nodes. After that, each node will have information
-about all the sensor nodes in the subregion. In our model, the
-remaining energy corresponds to the time that a sensor can live in the
-active mode.
-
-\subsubsection{Leader Election Phase}
-This step includes choosing the Wireless Sensor Node Leader (WSNL),
-which will be responsible for executing the coverage algorithm. Each
-subregion in the area of interest will select its own WSNL
-independently for each round. All the sensor nodes cooperate to
-select WSNL. The nodes in the same subregion will select the leader
-based on the received information from all other nodes in the same
-subregion. The selection criteria in order of priority are: larger
-number of neighbours, larger remaining energy, and then in case of
-equality, larger index.
-
-\subsubsection{Decision phase}
-The WSNL will solve an integer program (see section~\ref{cp}) to
-select which sensors will be activated in the following sensing phase
-to cover the subregion. WSNL will send Active-Sleep packet to each
-sensor in the subregion based on the algorithm's results.
-
-
-\subsubsection{Sensing phase}
-Active sensors in the round will execute their sensing task to
-preserve maximal coverage in the region of interest. We will assume
-that the cost of keeping a node awake (or asleep) for sensing task is
-the same for all wireless sensor nodes in the network. Each sensor
-will receive an Active-Sleep packet from WSNL informing it to stay
-awake or to go to sleep for a time equal to the period of sensing until
-starting a new round. Algorithm 1, which
-will be executed by each node at the beginning of a round, explains how the
-Active-Sleep packet is obtained.
-
-\fi
-
-\iffalse
-\subsection{DiLCO protocol Algorithm}
-we first show the pseudo-code of DiLCO protocol, which is executed by each sensor in the subregion and then describe it in more detail.
-\fi
+An outline of the protocol implementation is given by Algorithm~\ref{alg:DiLCO}
+which describes the execution of a period by a node (denoted by $s_j$ for a
+sensor node indexed by $j$). At the beginning a node checks whether it has
+enough energy \textcolor{blue}{(its energy should be greater than a fixed
+ treshold $E_{th}$)} to stay active during the next sensing phase. If yes, it
+exchanges information with all the other nodes belonging to the same subregion:
+it collects from each node its position coordinates, remaining energy ($RE_j$),
+ID, and the number of one-hop neighbors still alive. \textcolor{blue}{INFO
+ packet contains two parts: header and data payload. The sensor ID is included
+ in the header, where the header size is 8 bits. The data part includes
+ position coordinates (64 bits), remaining energy (32 bits), and the number of
+ one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112
+ bits.} Once the first phase is completed, the nodes of a subregion choose a
+leader to take the decision based on the following criteria with decreasing
+importance: larger number of neighbors, larger remaining energy, and then in
+case of equality, larger index. After that, if the sensor node is leader, it
+will solve an integer program (see Section~\ref{cp}). \textcolor{blue}{This
+ integer program contains boolean variables $X_j$ where ($X_j=1$) means that
+ sensor $j$ will be active in the next sensing phase. Only sensors with enough
+ remaining energy are involved in the integer program ($J$ is the set of all
+ sensors involved). As the leader consumes energy (computation energy is
+ denoted by $E^{comp}$) to solve the optimization problem, it will be included
+ in the integer program only if it has enough energy to achieve the computation
+ and to stay alive during the next sensing phase, that is to say if $RE_j >
+ E^{comp}+E_{th}$. Once the optimization problem is solved, each leader will
+ send an ActiveSleep packet to each sensor in the same subregion to indicate it
+ if it has to be active or not. Otherwise, if the sensor is not the leader, it
+ will wait for the ActiveSleep packet to know its state for the coming sensing
+ phase.}
+%which provides a set of sensors planned to be
+%active in the next sensing phase.
\begin{algorithm}[h!]
- % \KwIn{all the parameters related to information exchange}
-% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+
\BlankLine
%\emph{Initialize the sensor node and determine it's position and subregion} \;
- \If{ $RE_j \geq E_{R}$ }{
+ \If{ $RE_j \geq E_{th}$ }{
\emph{$s_j.status$ = COMMUNICATION}\;
\emph{Send $INFO()$ packet to other nodes in the subregion}\;
\emph{Wait $INFO()$ packet from other nodes in the subregion}\;
\Else{
\emph{$s_j.status$ = LISTENING}\;
\emph{Wait $ActiveSleep()$ packet from the Leader}\;
- % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
+
\emph{Update $RE_j $}\;
}
% }
\end{algorithm}
-\iffalse
-The DiLCO protocol work in rounds and executed at each sensor node in the network , each sensor node can still sense data while being in
-LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
-sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow:
-Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
-The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will select the set of sensor nodes to take the mission of coverage during the sensing phase. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's status during the period of sensing, either Active or sleep until the starting of next round. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, all the sensor nodes in the same subregion will start new round by executing the DiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
-\fi
+\section{\uppercase{Coverage problem formulation}}
+\label{cp}
+
+% MODIF - BEGIN
+We formulate the coverage optimization problem with an integer program.
+The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}.
+The area coverage problem is expressed as the coverage of a fraction of points called primary points.
+Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
+and the set of alive sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of active sensors that cover the primary point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :
+\begin{equation}
+ \Theta_{p} = \left \{
+\begin{array}{l l}
+ 0 & \mbox{if the primary point}\\
+ & \mbox{$p$ is not covered,}\\
+ \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq13}
+\end{equation}
+More precisely, $\Theta_{p}$ represents the number of active sensor
+nodes minus one that cover the primary point~$p$.
+In the same way, we define the undercoverage variable
+$U_{p}$ of the primary point $p$ as:
+\begin{equation}
+U_{p} = \left \{
+\begin{array}{l l}
+ 1 &\mbox{if the primary point $p$ is not covered,} \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq14}
+\end{equation}
+There is, of course, a relationship between the three variables $X_j$, $\Theta_p$, and $U_p$ which can be formulated as follows :
+\begin{equation}
+\sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, \forall p \in P
+\end{equation}
+If the point $p$ is not covered, $U_p=1$, $\sum_{j \in J} \alpha_{jp} X_{j}=0$ and $\Theta_{p}=0$ by definition, so the equality is satisfied.
+On the contrary, if the point $p$ is covered, $U_p=0$, and $\Theta_{p}=\left( \sum_{j \in J} \alpha_{jp} X_{j} \right)- 1$.
+\noindent Our coverage optimization problem can then be formulated as follows:
+\begin{equation} \label{eq:ip2r}
+\left \{
+\begin{array}{ll}
+\min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
+\textrm{subject to :}&\\
+\sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
+%\label{c1}
+%\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
+%\label{c2}
+\Theta_{p}\in \mathbb{N}, &\forall p \in P\\
+U_{p} \in \{0,1\}, &\forall p \in P \\
+X_{j} \in \{0,1\}, &\forall j \in J
+\end{array}
+\right.
+\end{equation}
+The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage. \textcolor{blue}{ By
+ choosing $w_{U}$ much larger than $w_{\theta}$, the coverage of a
+ maximum of primary points is ensured. Then for the same number of covered
+ primary points, the solution with a minimal number of active sensors is
+ preferred. }
+%Both weights $w_\theta$ and $w_U$ must be carefully chosen in
+%order to guarantee that the maximum number of points are covered during each
+%period.
+% MODIF - END
+
-\section{Coverage problem formulation}
-\label{cp}
-\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
-integer program, which forces undercoverage and overcoverage of targets
-to become minimal at the same time. They use binary variables
-$x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
-model, we consider binary variables $X_{j}$, which determine the
-activation of sensor $j$ in the sensing round. We also
-consider primary points as targets. The set of primary points is
-denoted by $P$ and the set of sensors by $J$.
-
-\noindent For a primary point $p$, let $\alpha_{jp}$ denote the
-indicator function of whether the point $p$ is covered, that is:
+
+
+
+\iffalse
+
+\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, the authors proposed an integer program which forces undercoverage
+and overcoverage of targets to become minimal at the same time. They use binary
+variables $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
+model, we consider that the binary variable $X_{j}$ determines the activation of
+sensor $j$ in the sensing phase. We also consider primary points as targets.
+The set of primary points is denoted by $P$ and the set of sensors by $J$.
+
+\noindent Let $\alpha_{jp}$ denote the indicator function of whether the primary
+point $p$ is covered, that is:
\begin{equation}
\alpha_{jp} = \left \{
\begin{array}{l l}
\end{array} \right.
%\label{eq12}
\end{equation}
-The number of active sensors that cover the primary point $p$ is equal
-to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+The number of active sensors that cover the primary point $p$ can then be
+computed by $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
\begin{equation}
X_{j} = \left \{
\begin{array}{l l}
\end{array} \right.
\label{eq13}
\end{equation}
-\noindent More precisely, $\Theta_{p}$ represents the number of active
-sensor nodes minus one that cover the primary point $p$.\\
-The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
-by:
+\noindent More precisely, $\Theta_{p}$ represents the number of active sensor
+nodes minus one that cover the primary point~$p$. The Undercoverage variable
+$U_{p}$ of the primary point $p$ is defined by:
\begin{equation}
U_{p} = \left \{
\begin{array}{l l}
\label{eq14}
\end{equation}
-\noindent Our coverage optimization problem can then be formulated as follows
+\noindent Our coverage optimization problem can then be formulated as follows:
\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
%\label{c1}
%\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
%\label{c2}
-\Theta_{p}\in \mathbb{N} , &\forall p \in P\\
+\Theta_{p}\in \mathbb{N}, &\forall p \in P\\
U_{p} \in \{0,1\}, &\forall p \in P \\
X_{j} \in \{0,1\}, &\forall j \in J
\end{array}
\right.
\end{equation}
-
-
\begin{itemize}
-\item $X_{j}$ : indicates whether or not the sensor $j$ is actively
- sensing in the round (1 if yes and 0 if not);
-\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
- one that are covering the primary point $p$;
-\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
+\item $X_{j}$ : indicates whether or not the sensor $j$ is actively sensing (1
+ if yes and 0 if not);
+\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that
+ are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
$p$ is being covered (1 if not covered and 0 if covered).
\end{itemize}
-The first group of constraints indicates that some primary point $p$
-should be covered by at least one sensor and, if it is not always the
-case, overcoverage and undercoverage variables help balancing the
-restriction equations by taking positive values. There are two main
-objectives. First, we limit the overcoverage of primary points in order to
-activate a minimum number of sensors. Second we prevent the absence of monitoring on
- some parts of the subregion by minimizing the undercoverage. The
-weights $w_\theta$ and $w_U$ must be properly chosen so as to
-guarantee that the maximum number of points are covered during each
-round.
-
-
+The first group of constraints indicates that some primary point $p$ should be
+covered by at least one sensor and, if it is not always the case, overcoverage
+and undercoverage variables help balancing the restriction equations by taking
+positive values. Two objectives can be noticed in our model. First, we limit the
+overcoverage of primary points to activate as few sensors as possible. Second,
+to avoid a lack of area monitoring in a subregion we minimize the
+undercoverage. Both weights $w_\theta$ and $w_U$ must be carefully chosen in
+order to guarantee that the maximum number of points are covered during each
+period.
+\fi
-\section{\uppercase{Simulation Results and Analysis}}
+\section{\uppercase{Protocol evaluation}}
\label{sec:Simulation Results and Analysis}
-\noindent \subsection{Simulation Framework}
-In this subsection, we conducted a series of simulations to evaluate the
-efficiency and the relevance of our DiLCO protocol, using the discrete event
-simulator OMNeT++ \cite{varga}. The simulation parameters are summarized in
-Table~\ref{table3}.
+\noindent \subsection{Simulation framework}
+
+To assess the performance of our DiLCO protocol, we have used the discrete
+event simulator OMNeT++ \cite{varga} to run different series of simulations.
+Table~\ref{table3} gives the chosen parameters setting.
\begin{table}[ht]
\caption{Relevant parameters for network initializing.}
% is used to refer this table in the text
\end{table}
-We performed simulations for five different densities varying from 50 to 250~nodes. Experimental results are the average obtained from 25 randomly generated networks (25 for each network density) in which nodes are deployed over a $(50 \times 25)~m^2 $ sensing field. More precisely, the deployment is controlled at a coarse scale in order to ensure that the deployed nodes can cover the sensing field with a high coverage ratio.\\
-
-We first concentrate on the required number of subregions making effective our protocol. Thus our DiLCO protocol is declined into five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$ or $32$ subregions (leaders).
-
-We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
-The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
-% We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node.
-%The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU.
-%revoir la phrase
-
-For our energy consumption model, we refer to the sensor node Medusa II which uses Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The typical architecture of a sensor is composed of four subsystems : the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for
-transmitting/receiving messages, sensing subsystem that collects data, and the power supply which powers the complete sensor node ~\cite{raghunathan2002energy}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table4}.
+Simulations with five different node densities going from 50 to 250~nodes were
+performed considering each time 25~randomly generated networks, to obtain
+experimental results which are relevant. The nodes are deployed on a field of
+interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
+high coverage ratio.
+
+We chose as energy consumption model the one proposed proposed by~\cite{ChinhVu}
+and based on ~\cite{raghunathan2002energy} with slight modifications. The energy
+consumed by the communications is added and the part relative to a variable
+sensing range is removed. We also assume that the nodes have the characteristics
+of the Medusa II sensor node platform \cite{raghunathan2002energy}. A sensor
+node typically consists of four units: a MicroController Unit, an Atmels AVR
+ATmega103L in case of Medusa II, to perform the computations; a communication
+(radio) unit able to send and receive messages; a sensing unit to collect data;
+a power supply which provides the energy consumed by node. Except the battery,
+all the other unit can be switched off to save energy according to the node
+status. Table~\ref{table4} summarizes the energy consumed (in milliWatt per
+second) by a node for each of its possible status.
\begin{table}[ht]
-\caption{The Energy Consumption Model}
+\caption{Energy consumption model}
% title of Table
\centering
% used for centering table
+{\scriptsize
\begin{tabular}{|c|c|c|c|c|}
% centered columns (4 columns)
\hline
%inserts double horizontal lines
-Sensor mode & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
+Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
\hline
% inserts single horizontal line
Listening & ON & ON & ON & 20.05 \\
%\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
\hline
\end{tabular}
+}
\label{table4}
% is used to refer this table in the text
\end{table}
-For the sake of simplicity we ignore the energy needed to turn on the
-radio, to start up the sensor node, the transition from one status to another, etc.
-%We also do not consider the need of collecting sensing data. PAS COMPRIS
-Thus, when a sensor becomes active (i.e., it already decides its status), it can turn its radio off to save battery. DiLCO protocol uses two types of packets for communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24 bits respectively.
-The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets.
-The energy needed to send or receive a 1-bit is equal to $0.2575 mW$.
-
-The initial energy of each node is randomly set in the interval $[500-700]$. Each sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mW) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.\\
-
-
-In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach:
+Less influent energy consumption sources like when turning on the radio,
+starting the sensor node, changing the status of a node, etc., will be neglected
+for the sake of simplicity. Each node saves energy by switching off its radio
+once it has received its decision status from the corresponding leader (it can
+be itself). As explained previously in subsection~\ref{main_idea}, two kinds of
+packets for communication are considered in our protocol: INFO packet and
+ActiveSleep packet. To compute the energy needed by a node to transmit or
+receive such packets, we use the equation giving the energy spent to send a
+1-bit-content message defined in~\cite{raghunathan2002energy} (we assume
+symmetric communication costs), and we set their respective size to 112 and
+24~bits. The energy required to send or receive a 1-bit-content message is thus
+ equal to 0.2575~mW.
+
+Each node has an initial energy level, in Joules, which is randomly drawn in
+$[500-700]$. If its energy provision reaches a value below the threshold
+$E_{th}=36$~Joules, the minimum energy needed for a node to stay active during
+one period, it will no longer take part in the coverage task. This value
+corresponds to the energy needed by the sensing phase, obtained by multiplying
+the energy consumed in active state (9.72 mW) by the time in seconds for one
+period (3,600 seconds), and adding the energy for the pre-sensing phases.
+According to the interval of initial energy, a sensor may be active during at
+most 20 periods.
+
+In the simulations, we introduce the following performance metrics to evaluate
+the efficiency of our approach:
%\begin{enumerate}[i)]
\begin{itemize}
-
-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area of a sensor field is covered. In our case, we treated the sensing fields as a grid, and used each grid point as a sample point
-for calculating the coverage. The coverage ratio can be calculated by:
+\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
+ the coverage ratio drops below a predefined threshold. We denote by
+ $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
+ the network can satisfy an area coverage greater than $95\%$ (respectively
+ $50\%$). We assume that the sensor network can fulfill its task until all its
+ nodes have been drained of their energy or it becomes disconnected. Network
+ connectivity is crucial because an active sensor node without connectivity
+ towards a base station cannot transmit any information regarding an observed
+ event in the area that it monitors.
+
+\item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to
+ observe the area of interest. In our case, we discretized the sensor field
+ as a regular grid, which yields the following equation to compute the
+ coverage ratio:
\begin{equation*}
\scriptsize
\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
\end{equation*}
-where $n$ is the number of covered grid points by the active sensors of all subregions during the current sensing phase and $N$ is total number of grid points in the sensing field of the network. In our simulation $N = 51 \times 26 = 1326$ grid points.
-%The accuracy of this method depends on the distance between grids. In our
-%simulations, the sensing field has been divided into 50 by 25 grid points, which means
-%there are $51 \times 26~ = ~ 1326$ points in total.
-% Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
-
-\iffalse
-
-\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
-in order to minimize the communication overhead and maximize the
-network lifetime. The Active Sensors Ratio is defined as follows:
-\begin{equation*}
-\scriptsize
-\mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r^t$}}{\mbox{$S$}} \times 100 .
-\end{equation*}
-Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round $t$ in the current sensing phase, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
-
-\fi
-
-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until the coverage ratio drops below a predefined threshold. We denoted by $Lifetime95$ (respectively $Lifetime50$) as the amount of time during which the network can satisfy an area coverage greater than $95\%$ (repectively $50\%$). We assume that the network
-is alive until all nodes have been drained of their energy or the
-sensor network becomes disconnected . 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.
-
-
-\item {{\bf Energy Consumption}:}
-
- Energy Consumption (EC) can be seen as the total energy consumed by the sensors during the $Lifetime95$ or $Lifetime50$ divided by the number of periods. The EC can be computed as follow: \\
- \begin{equation*}
-\scriptsize
-\mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m + E^{a}+E^{s} \right)}{M_L},
-\end{equation*}
-
-%\begin{equation*}
-%\scriptsize
-%\mbox{EC} = \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
-%\end{equation*}
-
-where $M_L$ corresponds to the number of periods. The total energy consumed by the sensors
-(EC) comes through taking into consideration four main energy factors. The first
-one , denoted $E^{\scriptsize \mbox{com}}_m$, represent the energy consumption
-spent by all the nodes for wireless communications during period $m$.
-$E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to the energy
-consumed by the sensors in LISTENING status before receiving the decision to go
-active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the
-energy needed by all the leader nodes to solve the integer program during a
-period. Finally, $E^a_{m}$ and $E^s_{m}$ indicate the energy consummed by the whole network in the sensing round.
-
-\iffalse
-\item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power,
-therefore it is important that the proposed algorithm has the shortest
-possible execution time. The energy of a sensor node must be mainly
-used for the sensing phase, not for the pre-sensing ones.
-
-\item {{\bf Stopped simulation runs}:} A simulation
-ends when the sensor network becomes
-disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.
-
-\fi
+where $n$ is the number of covered grid points by active sensors of every
+subregions during the current sensing phase and $N$ is the total number of grid
+points in the sensing field. In our simulations, we have a layout of $N = 51
+\times 26 = 1326$ grid points.
+
+\item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
+ total amount of energy consumed by the sensors during $Lifetime_{95}$
+ or $Lifetime_{50}$, divided by the number of periods. Formally, the computation
+ of EC can be expressed as follows:
+ \begin{equation*}
+ \scriptsize
+ \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m
+ + E^{a}_m+E^{s}_m \right)}{M},
+ \end{equation*}
+
+where $M$ corresponds to the number of periods. The total amount of energy
+consumed by the sensors (EC) comes through taking into consideration four main
+energy factors. The first one, denoted $E^{\scriptsize \mbox{com}}_m$,
+represents the energy consumption spent by all the nodes for wireless
+communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
+factor, corresponds to the energy consumed by the sensors in LISTENING status
+before receiving the decision to go active or sleep in period $m$.
+$E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
+nodes to solve the integer program during a period. Finally, $E^a_{m}$ and
+$E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase
+(active and sleeping nodes).
\end{itemize}
%\end{enumerate}
-
-%\subsection{Performance Analysis for differnet subregions}
-\subsection{Performance Analysis}
+%\subsection{Performance Analysis for different subregions}
+\subsection{Performance analysis}
\label{sub1}
-In this subsection, we study the performance of our DiLCO protocol for different number of subregions (Leaders).
-The DiLCO-1 protocol is a centralized approach on all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLC0-1 protocol in our simulation results because it requires high execution time to solve the integer program and thus it is too costly in term of energy.
-
-Our method is compared with other two approaches. The first approach, called DESK and proposed by ~\cite{ChinhVu} is a full distributed coverage algorithm. The second approach, 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 on during the sensing phase time.
+In this subsection, we first focus on the performance of our DiLCO protocol for
+different numbers of subregions. We consider partitions of the WSN area into
+$2$, $4$, $8$, $16$, and $32$ subregions. Thus the DiLCO protocol is declined in
+five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32. Simulations
+without partitioning the area of interest, cases which correspond to a
+centralized approach, are not presented because they require high execution
+times to solve the integer program and therefore consume too much energy.
+
+We compare our protocol to two other approaches. The first one, called DESK and
+proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm. The
+second one, 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.
+
+\subsubsection{Coverage ratio}
+
+Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. It
+can be seen that both DESK and GAF provide a coverage ratio which is slightly
+better compared to DiLCO in the first thirty periods. This can be easily
+explained by the number of active nodes: the optimization process of our
+protocol activates less nodes than DESK or GAF, resulting in a slight decrease
+of the coverage ratio. In case of DiLCO-2 (respectively DiLCO-4), the coverage
+ratio exhibits a fast decrease with the number of periods and reaches zero value
+in period~18 (respectively 46), whereas the other versions of DiLCO, DESK, and
+GAF ensure a coverage ratio above 50\% for subsequent periods. We believe that
+the results obtained with these two methods can be explained by a high
+consumption of energy and we will check this assumption in the next subsection.
+
+Concerning DiLCO-8, DiLCO-16, and DiLCO-32, these methods seem to be more
+efficient than DESK and GAF, since they can provide the same level of coverage
+(except in the first periods where DESK and GAF slightly outperform them) for a
+greater number of periods. In fact, when our protocol is applied with a large
+number of subregions (from 8 to 32~regions), it activates a restricted number of
+nodes, and thus enables the extension of the network lifetime.
-\subsubsection{Coverage Ratio}
-In this experiment, Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.
\parskip 0pt
-\begin{figure}[h!]
+\begin{figure}[t!]
\centering
- \includegraphics[scale=0.45] {R/CR.pdf}
-\caption{The Coverage Ratio}
+ \includegraphics[scale=0.45] {CR.pdf}
+\caption{Coverage ratio}
\label{fig3}
\end{figure}
-Figure~\ref{fig3} shows that DESK and GAF provide a
-a little better coverage ratio compared to DiLCO in the first thirty periods. This is due to the fact that our DiLCO protocol versions put in sleep mode some sensors through optimization process (which slightly decreases the coverage ratio) while there are more active nodes with DESK or GAF. With DiLCO-2 (respectively DiLCO-4), the coverage ratio decreases rapidly to reach zero value in period ... (respectively in period ....) whereas other methods guarantee a coverage ratio greater than $50\%$ after this period. We believe that the results obtained with these two methods can be explained by a high consumption of energy
-and we will check this assumption in the next paragraph. Concerning DiLCO-8, DiLCO-16 and DiLCO-32, these methods seem to be more efficient than DESK and GAF because they can provide the same level of coverage (except in the first periods, slightly lower) for a greater number of periods. Unlike other methods, their strategy enables to activate a restricted number of nodes, and thus extends the lifetime of the network.
-%As shown in the figure ~\ref{fig3}, as the number of subregions increases, the coverage preservation for area of interest increases for a larger number of periods. Coverage ratio decreases when the number of periods increases due to dead nodes. Although some nodes are dead,
-%thanks to DiLCO-8, DiLCO-16 and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16 and DiLCO-32 protocols are
-%slightly more efficient than other protocols, because they subdivides
-%the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%
+\subsubsection{Energy consumption}
+Based on the results shown in Figure~\ref{fig3}, we focus on the DiLCO-16 and
+DiLCO-32 versions of our protocol, and we compare their energy consumption with
+the DESK and GAF approaches. For each sensor node we measure the energy consumed
+according to its successive status, for different network densities. We denote
+by $\mbox{\it Protocol}/50$ (respectively $\mbox{\it Protocol}/95$) the amount
+of energy consumed while the area coverage is greater than $50\%$ (repectively
+$95\%$), where {\it Protocol} is one of the four protocols we compare.
+Figure~\ref{fig95} presents the energy consumptions observed for network sizes
+going from 50 to 250~nodes. Let us notice that the same network sizes will be
+used for the different performance metrics.
-\subsubsection{The Energy Consumption}
-Based on previous results in figure~\ref{fig3}, we keep DiLCO-16 and DiLCO-32 and we compare their performances in terms of energy consumption with the two other approaches. We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities. Figure~\ref{fig95} illustrates the energy consumption for different network sizes.
-% for $Lifetime95$ and $Lifetime50$.
-We denote by $DiLCO-/50$ (respectively $DiLCO-/95$) as the amount of energy consumed during which the network can satisfy an area coverage greater than $50\%$ (repectively $95\%$) and we refer to the same definition for the two other approaches.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/EC.pdf}
-\caption{The Energy Consumption}
+\includegraphics[scale=0.45]{EC.pdf}
+\caption{Energy consumption per period}
\label{fig95}
\end{figure}
-The results show that DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes.
-
-
-%In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
-%As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.
-
-
-\subsubsection{Execution Time}
-We observe the impact of the network size and of the number of subregions on the computation time. We report the average execution times in seconds needed to solve the optimization problem for the different approaches and various numbers of sensors.
-The original execution time is computed 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 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6}\right)$ and reported on Figure~\ref{fig8}.
+The results depict the good performance of the different versions of our
+protocol. Indeed, the protocols DiLCO-16/50, DiLCO-32/50, DiLCO-16/95, and
+DiLCO-32/95 consume less energy than their DESK and GAF counterparts for a
+similar level of area coverage. This observation reflects the larger number of
+nodes set active by DESK and GAF.
+
+Now, if we consider a same protocol, we can notice that the average consumption
+per period increases slightly for our protocol when increasing the level of
+coverage and the number of node, whereas it increases more largely for DESK and
+GAF. In case of DiLCO, it means that even if a larger network allows to improve
+the number of periods with a minimum coverage level value, this improvement has
+a higher energy cost per period due to communication overhead and a more
+difficult optimization problem. However, in comparison with DESK and GAF, our
+approach has a reasonable energy overcost.
+
+\subsubsection{Execution time}
+
+Another interesting point to investigate is the evolution of the execution time
+with the size of the WSN and the number of subregions. Therefore, we report for
+every version of our protocol the average execution times in seconds needed to
+solve the optimization problem for different WSN sizes. The execution times are
+obtained on a laptop DELL which has an Intel Core~i3~2370~M~(2.4~GHz) dual core
+processor and a MIPS rating equal to 35330. The corresponding execution times on
+a MEDUSA II sensor node are then extrapolated according to the MIPS rate of the
+Atmels AVR ATmega103L microcontroller (6~MHz), which is equal to 6, by
+multiplying the laptop times by $\left(\frac{35330}{2} \times
+\frac{1}{6}\right)$. The expected times on a sensor node are reported on
+Figure~\ref{fig8}.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/T.pdf}
-\caption{Execution Time (in seconds)}
+\includegraphics[scale=0.45]{T.pdf}
+\caption{Execution time in seconds}
\label{fig8}
\end{figure}
-
-Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison with other DiLCO versions, because the activity scheduling is tackled by a larger number of leaders and each leader solves an integer problem with a limited number of variables and constraints. Conversely, DiLCO-2 requires to solve an optimization problem with half of the network nodes and thus presents a high execution time. Nevertheless if we refer to figure~\ref{fig3}, we observe that DiLCO-32 is slightly less efficient than DilCO-16 to maintain as long as possible high coverage. Excessive subdivision of the area of interest prevents to ensure good coverage especially on the borders of the subregions.
-
-%The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more. We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
-
-
-\subsubsection{The Network Lifetime}
-In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. The term $/50$ (respectively $/95$) next to the name of the method refers to the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$))
+Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison
+with other DiLCO versions, because the activity scheduling is tackled by a
+larger number of leaders and each leader solves an integer problem with a
+limited number of variables and constraints. Conversely, DiLCO-2 requires to
+solve an optimization problem with half of the network nodes and thus presents a
+high execution time. Nevertheless if we refer to Figure~\ref{fig3}, we observe
+that DiLCO-32 is slightly less efficient than DilCO-16 to maintain as long as
+possible high coverage. In fact an excessive subdivision of the area of interest
+prevents it to ensure a good coverage especially on the borders of the
+subregions. Thus, the optimal number of subregions can be seen as a trade-off
+between execution time and coverage performance.
+
+\subsubsection{Network lifetime}
+
+In the next figure, the network lifetime is illustrated. Obviously, the lifetime
+increases with the network size, whatever the considered protocol, since the
+correlated node density also increases. A high network density means a high
+node redundancy which allows to turn-off many nodes and thus to prolong the
+network lifetime.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/LT.pdf}
-\caption{The Network Lifetime}
+\includegraphics[scale=0.45]{LT.pdf}
+\caption{Network lifetime}
\label{figLT95}
\end{figure}
+As highlighted by Figure~\ref{figLT95}, when the coverage level is relaxed
+($50\%$) the network lifetime also improves. This observation reflects the fact
+that the higher the coverage performance, the more nodes must be active to
+ensure the wider monitoring. For a similar level of coverage, DiLCO outperforms
+DESK and GAF for the lifetime of the network. More specifically, if we focus on
+the larger level of coverage ($95\%$) in the case of our protocol, the subdivision
+in $16$~subregions seems to be the most appropriate.
+
+
+\section{\uppercase{Conclusion and future work}}
+\label{sec:Conclusion and Future Works}
+
+A crucial problem in WSN is to schedule the sensing activities of the different
+nodes in order to ensure both coverage of the area of interest and longer
+network lifetime. The inherent limitations of sensor nodes, in energy provision,
+communication and computing capacities, require protocols that optimize the use
+of the available resources to fulfill the sensing task. To address this
+problem, this paper proposes a two-step approach. Firstly, the field of sensing
+is divided into smaller subregions using the concept of divide-and-conquer
+method. Secondly, a distributed protocol called Distributed Lifetime Coverage
+Optimization is applied in each subregion to optimize the coverage and lifetime
+performances. In a subregion, our protocol consists in electing a leader node
+which will then perform a sensor activity scheduling. The challenges include how
+to select the most efficient leader in each subregion and the best
+representative set of active nodes to ensure a high level of coverage. To assess
+the performance of our approach, we compared it with two other approaches using
+many performance metrics like coverage ratio or network lifetime. We have also
+studied the impact of the number of subregions chosen to subdivide the area of
+interest, considering different network sizes. The experiments show that
+increasing the number of subregions improves the lifetime. The more subregions there are, the more robust the network is against random disconnection
+resulting from dead nodes. However, for a given sensing field and network size
+there is an optimal number of subregions. Therefore, in case of our simulation
+context a subdivision in $16$~subregions seems to be the most relevant. The
+optimal number of subregions will be investigated in the future.
-As highlighted by figure~\ref{figLT95}, the network lifetime obviously
-increases when the size of the network increases. For the same level of coverage, DiLCO outperforms DESK and GAF for the lifetime of the network. If we focus on level of coverage greater than $95\%$, The subdivision in $16$ subregions seems to be the most appropriate.
-
-
-% with our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
-% that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best
-% suited nodes, for each round, to cover the area of interest and by
-% letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol 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{\uppercase{Conclusion and Future Works}}
-\label{sec:Conclusion and Future Works}
-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 divide-and-conquer method, and then a DiLCO protocol for optimizing the 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 set of active nodes to ensure a high level of coverage.
-We have compared this method with two other approaches using many metrics as coverage ratio, execution time, lifetime.
-Some experiments have been performed to study the choice of the number of
-subregions which subdivide the sensing field, considering different network
-sizes. They show that as the number of subregions increases, so does the network
-lifetime. Moreover, it makes the DiLCO protocol more robust against random
-network disconnection due to node failures. However, too much subdivisions
-reduces the advantage of the optimization. In fact, there is a balance between
-the benefit from the optimization and the execution time needed to solve
-it. Therefore, the subdivision in $16$ subregions seems to be the most appropriate.
-\iffalse
-\noindent 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 divide-and-conquer method, and then a DiLCO protocol for optimizing the 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 DiLCO
-protocol in terms of lifetime, coverage ratio, active sensors ratio, 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 are proposed 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 optimization protocol, which
-computes all active sensor schedules in one time, using
-optimization methods. \iffalse 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. \fi
-\fi
\section*{\uppercase{Acknowledgements}}
-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
-
-
-
+\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
+acknowledge the University of Babylon - IRAQ for the financial support and
+Campus France for the received support. This paper is also partially funded by
+the Labex ACTION program (contract ANR-11-LABX-01-01).
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+\bibliographystyle{plain}
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