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 result in an activity scheduling vector, is carried
+ 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
\section{\uppercase{Introduction}}
\label{sec:introduction}
+
\noindent
Energy efficiency is a crucial issue in wireless sensor networks since sensory
-consumption, in order to maximize the network lifetime, represent the major
+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}. On the other hand we want to use as less 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.
+sensor field is monitored. On the one hand we want to monitor the area of
+interest in the most efficient way~\cite{Nayak04}. On the other hand we want to
+use as less 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.
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
-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 Distributed Lifetime
-Coverage Optimization (DILCO) protocol considers periods, where a period starts
-with a discovery phase to exchange information between sensors of a same
+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 a 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.
+program. The resulting activation vector is broadcasted by a leader to every
+node of its subregion.
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
\section{\uppercase{Literature Review}}
\label{sec:Literature Review}
-\noindent In this section, we summarize some related works regarding coverage problem , and distinguish our DiLCO protocol from the works presented in the literature.\\
+
+\noindent In this section, we summarize some related works regarding 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 (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 (to prevent intruders from entering into the region of
interest).
-{\it In DiLCO protocol, the area coverage, ie 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 an interest region 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.
-Active node selection is determined based on the problem
-requirements (e.g. area monitoring, connectivity, power
-efficiency). Different methods has been proposed in literature.
-
-{\it DiLCO protocol works in periods, 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 centralised, distributed and localized algorithms, have been proposed to extend the network lifetime.
+{\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.
+Active node selection is determined based on the problem requirements (e.g. area
+monitoring, connectivity, power efficiency). Different methods have been
+proposed in literature.
+{\it 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, distributed, and localized
+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 neighbours 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.
-
-A large variety of coverage scheduling algorithms have been proposed in the literature. Many of the existing algorithms, dealing with the maximisation 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. Other approaches are based on mathematical programming formulations 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, of the 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 been also used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
-
-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 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.
-
-In ~\cite{chenait2013distributed}, the authors presented a coverage-guaranteed distributed sleep/wake scheduling scheme so as 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.
-
-{\it In DiLCO protocol, the area coverage is divided into several smaller subregions, and in each of which, a node called the leader is on charge for selecting the active sensors for the current period.}
-
-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 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.
-
-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.
-
-{\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.}
+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.
+
+A large variety of coverage scheduling algorithms have been proposed. 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. Other
+approaches are based on mathematical programming formulations 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 been also
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+
+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.
+
+{\it In DiLCO protocol, the area coverage is divided into several smaller
+ subregions, and in each of which, a node called the leader is on charge for
+ selecting the active sensors for the current period.}
+
+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.
+
+{\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.}
-
\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.
\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}
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 is equal to $0.2575 mW$.
+24~bits. The energy required to send or receive a 1-bit-content message is thus
+is equal to 0.2575 mW.
Each node has an initial energy level, in Joules, which is randomly drawn in the
-interval $[500-700]$. If it's energy provision reaches a value below
-$E_{th}=36$~Joules, the minimum energy needed for a node to stay active during
-one period, it will no more participate in the coverage task. 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 active during at most 20 rounds.
-
-In the simulations, we introduce the following performance metrics to evaluate
+interval $[500-700]$. If it's 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 more participate 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 (3600 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.
+
+In the simulations, we introduce the follow80ing performance metrics to evaluate
the efficiency of our approach:
%\begin{enumerate}[i)]
\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 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.
+\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
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 {\bf
- 18} (respectively {\bf 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.
+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
