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-\usepackage{SCITEPRESS}
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+%\usepackage{apalike}
+%\usepackage{SCITEPRESS}
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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-Comt\'e, 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}
+
+%\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}} }
-\keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,
-Optimization, Scheduling.}
+\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
+ (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
+ 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
+ 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. In comparison with some other
- protocols, the simulations done using the discrete event simulator OMNeT++
- show that our approach is able to increase the WSN lifetime and provides
- improved coverage performance. }
+ 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
-\onecolumn \maketitle \normalsize \vfill
+
+%\normalsize \vfill
\section{\uppercase{Introduction}}
\label{sec:introduction}
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.
+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
+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
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.
+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
+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 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. }
-
+\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
+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.
-%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
-%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}.
-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
+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
+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.}
-
-% ***** Part which must be rewritten - Start
-
-% Start of Ali's papers catalog => there's no link between them or with our work
-% (use of subregions; optimization based method; etc.)
-\iffalse
-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.
-
-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 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.
-
-In ~\cite{chenait2013distributed}, the authors presented a coverage-guaranteed
-distributed sleep/wake scheduling scheme so ass to prolong network lifetime
-while guaranteeing network coverage. This scheme mitigates scheduling process to
-be more stable by avoiding useless transitions between states without affecting
-the coverage level required by the application.
-
-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.
-
-% What is the link between the previous work and this paragraph about DiLCO ?
-
-
-
-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.
-
-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
-% Same remark, no link with the two previous citations...
-
-
-% ***** Part which must be rewritten - End
-
-\iffalse
-
-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.
-\fi
-
-\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.
-
-
-
-
-
-
-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 period 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.
-\fi
-\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.
-
-
-
-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
+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}
techniques: network leader election and sensor activity scheduling for coverage
preservation and energy conservation, applied periodically to efficiently
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}
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
-Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous
+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.
primary points are covered. Obviously, the approximation of coverage is more or
less accurate according to the number of primary points.
-\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
\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.
+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.}
\begin{figure}[ht!]
\centering
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. First, a node that has not enough energy to complete a period, or
+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
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 to stay active during the next sensing phase. If yes, it exchanges
+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. Once the first phase is
+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 execute the integer program
-algorithm (see Section~\ref{cp}) which provides a set of sensors planned to be
-active in the next sensing phase. As leader, it will send an Active-Sleep packet
+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, 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 Active-Sleep packet
to each sensor in the same subregion to indicate it if it has to be active or
-not. Alternately, if the sensor is not the leader, it will wait for the
-Active-Sleep packet to know its state for the coming sensing phase.
-
-\iffalse
-\subsubsection{Information Exchange Phase}
-
-Each sensor node $j$ sends its position, remaining energy $RE_j$, and
-the number of neighbors $NBR_j$ 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 neighbors, 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
+not. Otherwise, if the sensor is not the leader, it will wait for the
+Active-Sleep 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.
-\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
\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} \;
\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
+
+
+
+
+
+
+
+\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
order to guarantee that the maximum number of points are covered during each
period.
+\fi
+
\section{\uppercase{Protocol evaluation}}
\label{sec:Simulation Results and Analysis}
\noindent \subsection{Simulation framework}
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 the
-interval $[500-700]$. 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.
+ 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 rounds.
+most 20 periods.
In the simulations, we introduce the following performance metrics to evaluate
the efficiency of our approach:
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
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.
-%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 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
+ 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
+ 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).
-
-
-\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 $M$ 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 different subregions}
\subsection{Performance analysis}
\label{sub1}
\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.
+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
\parskip 0pt
\begin{figure}[t!]
\centering
- \includegraphics[scale=0.45] {R/CR.pdf}
+ \includegraphics[scale=0.45] {CR.pdf}
\caption{Coverage ratio}
\label{fig3}
\end{figure}
-%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}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/EC.pdf}
-\caption{Energy consumption}
+\includegraphics[scale=0.45]{EC.pdf}
+\caption{Energy consumption per period}
\label{fig95}
\end{figure}
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.
-
+nodes set active by DESK and GAF.
-%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.
+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}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/T.pdf}
+\includegraphics[scale=0.45]{T.pdf}
\caption{Execution time in seconds}
\label{fig8}
\end{figure}
subregions. Thus, the optimal number of subregions can be seen as a trade-off
between execution time and coverage performance.
-%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{Network lifetime}
In the next figure, the network lifetime is illustrated. Obviously, the lifetime
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.45]{R/LT.pdf}
+\includegraphics[scale=0.45]{LT.pdf}
\caption{Network lifetime}
\label{figLT95}
\end{figure}
the larger level of coverage ($95\%$) in the case of our protocol, 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 work}}
\label{sec:Conclusion and Future Works}
context a subdivision in $16$~subregions seems to be the most relevant. The
optimal number of subregions will be investigated in the future.
-\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
the Labex ACTION program (contract ANR-11-LABX-01-01).
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