%\title{Lifetime Coverage Optimization Protocol \\
% in Wireless Sensor Networks}
-\title{Perimeter-based Coverage Optimization Protocol \\
- to Improve Lifetime in Wireless Sensor Networks}
+\title{Perimeter-based Coverage Optimization to Improve \\
+ Lifetime in Wireless Sensor Networks}
\author{Ali Kadhum Idrees,~\IEEEmembership{}
Karine Deschinkel,~\IEEEmembership{}
Michel Salomon,~\IEEEmembership{}
and~Rapha\"el Couturier ~\IEEEmembership{}
- \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,
+ \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
this paper, we propose such an approach called Lifetime Coverage Optimization
protocol (LiCO). It is a hybrid of centralized and distributed methods: the
region of interest is first subdivided into subregions and our protocol is then
-distributed among sensor nodes in each subregion. A sensor node which runs LiCO
-protocol repeats periodically four stages: information exchange, leader
-election, optimization decision, and sensing. More precisely, the scheduling of
-nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
-leader selected after cooperation between nodes within the same subregion. The
-novelty of our approach lies essentially in the formulation of a new
+distributed among sensor nodes in each subregion.
+% A sensor node which runs LiCO protocol repeats periodically four stages:
+%information exchange, leader election, optimization decision, and sensing.
+%More precisely, the scheduling of nodes' activities (sleep/wake up duty cycles)
+%is achieved in each subregion by a leader selected after cooperation between
+%nodes within the same subregion.
+The novelty of our approach lies essentially in the formulation of a new
mathematical optimization model based on perimeter coverage level to schedule
sensors' activities. Extensive simulation experiments have been performed using
-OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to
+OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to
offer longer lifetime coverage for WSNs in comparison with some other protocols.
\end{abstract}
This paper makes the following contributions.
\begin{enumerate}
-\item We devise a framework to schedule nodes to be activated alternatively such
+\item We have devised a framework to schedule nodes to be activated alternatively such
that the network lifetime is prolonged while ensuring that a certain level of
coverage is preserved. A key idea in our framework is to exploit spatial and
- temporal subdivision. On the one hand the area of interest if divided into
- several smaller subregions and on the other hand the time line is divided into
+ temporal subdivision. On the one hand, the area of interest if divided into
+ several smaller subregions and, on the other hand, the time line is divided into
periods of equal length. In each subregion the sensor nodes will cooperatively
choose a leader which will schedule nodes' activities, and this grouping of
sensors is similar to typical cluster architecture.
-\item We propose a new mathematical optimization model. Instead of trying to
+\item We have proposed a new mathematical optimization model. Instead of trying to
cover a set of specified points/targets as in most of the methods proposed in
the literature, we formulate an integer program based on perimeter coverage of
each sensor. The model involves integer variables to capture the deviations
- between the actual level of coverage and the required level. So that an
+ between the actual level of coverage and the required level. Hence, an
optimal scheduling will be obtained by minimizing a weighted sum of these
deviations.
-\item We conducted extensive simulation experiments, using the discrete event
- simulator OMNeT++, to demonstrate the efficiency of our protocol. We compared
+\item We have conducted extensive simulation experiments, using the discrete event
+ simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
our LiCO protocol to two approaches found in the literature:
DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous
work published in~\cite{Idrees2} which is based on another optimization model
coverage model formulation which is used to schedule the activation of sensor
nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
results and discusses the comparison with other approaches. Finally, concluding
-remarks are drawn and some suggestions given for future works in
+remarks are drawn and some suggestions are given for future works in
Section~\ref{sec:Conclusion and Future Works}.
% that show that our protocol outperforms others protocols.
The most discussed coverage problems in literature can be classified in three
categories~\cite{li2013survey} according to their respective monitoring
objective. Hence, area coverage \cite{Misra} means that every point inside a
-fixed area must be monitored, while target coverage~\cite{yang2014novel} refer
+fixed area must be monitored, while target coverage~\cite{yang2014novel} refers
to the objective of coverage for a finite number of discrete points called
targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on
preventing intruders from entering into the region of interest. In
sensors are sufficiently covered it will be the case for the whole area. They
provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
each sensor, where $d$ denotes the maximum number of sensors that are
-neighboring to a sensor and $n$ is the total number of sensors in the
+neighbors to a sensor and $n$ is the total number of sensors in the
network. {\it In LiCO protocol, instead of determining the level of coverage of
a set of discrete points, our optimization model is based on checking the
perimeter-coverage of each sensor to activate a minimal number of sensors.}
decisions, followed by a sensing phase where one cover set is in charge of the
sensing task.}
-Various centralized and distributed approaches, or even a mixing of these two
+Various centralized and distributed approaches, or even a mixing of these two
concepts, have been proposed to extend the network lifetime. In distributed
algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
own activity scheduling after an information exchange with its neighbors. The
-main interest of a such approach is to avoid long range communications and thus
+main interest of such an approach is to avoid long range communications and thus
to reduce the energy dedicated to the communications. Unfortunately, since each
-node has only information on its immediate neighbors (usually the one-hop ones)
+node has only information on its immediate neighbors (usually the one-hop ones)
it may take a bad decision leading to a global suboptimal solution. Conversely,
centralized
-algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
provide nearly or close to optimal solution since the algorithm has a global
view of the whole network. The disadvantage of a centralized method is obviously
-its high cost in communications needed to transmit to a single node, the base
-station which will globally schedule nodes' activities, data from all the other
-sensor nodes in the area. The price in communications can be very huge since
-long range communications will be needed. In fact the larger the WNS, the higher
-the communication and thus energy cost. {\it In order to be suitable for
- large-scale networks, in the LiCO protocol the area of interest is divided
- into several smaller subregions, and in each one, a node called the leader is
- in charge for selecting the active sensors for the current period. Thus our
- protocol is scalable and a globally distributed method, whereas it is
- centralized in each subregion.}
+its high cost in communications needed to transmit to a single node, the base
+station which will globally schedule nodes' activities, data from all the other
+sensor nodes in the area. The price in communications can be very huge since
+long range communications will be needed. In fact the larger the WNS is, the
+higher the communication and thus the energy cost are. {\it In order to be
+ suitable for large-scale networks, in the LiCO protocol, the area of interest
+ is divided into several smaller subregions, and in each one, a node called the
+ leader is in charge of selecting the active sensors for the current
+ period. Thus our protocol is scalable and is a globally distributed method,
+ whereas it is centralized in each subregion.}
Various coverage scheduling algorithms have been developed this last years.
Many of them, dealing with the maximization of the number of cover sets, are
energy constraints. Column generation techniques, well-known and widely
practiced techniques for solving linear programs with too many variables, have
also been
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In LiCO
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the LiCO
protocol, each leader, in charge of a subregion, solves an integer program
which has a twofold objective: minimize the overcoverage and the undercoverage
of the perimeter of each sensor.}
proved that if the transmission range fulfills the previous hypothesis, a
complete coverage of a convex area implies connectivity among active nodes.
-\indent LiCO protocol uses the same perimeter-coverage model than Huang and
+The LiCO protocol uses the same perimeter-coverage model as Huang and
Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is
said to be perimeter covered if all the points on its perimeter are covered by
at least one sensor other than itself. They proved that a network area is
\begin{figure}[ht!]
\centering
\begin{tabular}{@{}cr@{}}
- \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)}
- \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
+ \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} \\
+ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
\end{tabular}
\caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
$u$'s perimeter covered by $v$.}
sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
-obtained through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s}
-\right)$. So, the arc on the perimeter of node~$u$ defined by the angular
-interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
-node $v$.
+obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
+ - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
Every couple of intersection points is placed on the angular interval $[0,2\pi]$
in a counterclockwise manner, leading to a partitioning of the interval.
Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
-sensor $0$ and figure~\ref{expcm} gives the position of the corresponding arcs
+sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs
in the interval $[0,2\pi]$. More precisely, we can see that the points are
ordered according to the measures of the angles defined by their respective
positions. The intersection points are then visited one after another, starting
-from first intersection point after point~zero, and the maximum level of
+from the first intersection point after point~zero, and the maximum level of
coverage is determined for each interval defined by two successive points. The
maximum level of coverage is equal to the number of overlapping arcs. For
example,
between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
-(the value is highlighted in yellow at the bottom of figure~\ref{expcm}), which
-means that at most 2~neighbors can cover the perimeter in addition to node $0$.
+(the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which
+means that at most 2~neighbors can cover the perimeter in addition to node $0$.
Table~\ref{my-label} summarizes for each coverage interval the maximum level of
coverage and the sensor nodes covering the perimeter. The example discussed
above is thus given by the sixth line of the table.
%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
% to determine the level of the perimeter coverage for each left and right point of a segment.
-\begin{figure*}[ht!]
+\begin{figure*}[t!]
\centering
-\includegraphics[width=137.5mm]{expcm2.jpg}
+\includegraphics[width=127.5mm]{expcm2.jpg}
\caption{Maximum coverage levels for perimeter of sensor node $0$.}
\label{expcm}
\end{figure*}
\fi
- \begin{table}[h]
+ \begin{table}[h!]
\caption{Coverage intervals and contributing sensors for sensor node 0.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
-In LiCO protocol, scheduling of sensor nodes' activities is formulated with an
+In the LiCO protocol, scheduling of sensor nodes' activities is formulated with an
integer program based on coverage intervals. The formulation of the coverage
optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
node has a part of its sensing range outside the WSN sensing field, as in
-figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
+Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
and the corresponding interval will not be taken into account by the
optimization algorithm.
-\begin{figure}[t!]
+\begin{figure}[h!]
\centering
\includegraphics[width=62.5mm]{ex4pcm.jpg}
\caption{Sensing range outside the WSN's area of interest.}
our protocol will be executed in a distributed way in each subregion
simultaneously to schedule nodes' activities for one sensing period.
-As shown in figure~\ref{fig2}, node activity scheduling is produced by our
+As shown in Figure~\ref{fig2}, node activity scheduling is produced by our
protocol in a periodic manner. Each period is divided into 4 stages: Information
(INFO) Exchange, Leader Election, Decision (the result of an optimization
problem), and Sensing. For each period there is exactly one set cover
responsible for the sensing task. Protocols based on a periodic scheme, like
LiCO, are more robust against an unexpected node failure. On the one hand, if
-node failure is discovered before taking the decision, the corresponding sensor
-node will not be considered by the optimization algorithm, and, on the other
+a node failure is discovered before taking the decision, the corresponding sensor
+node will not be considered by the optimization algorithm. On the other
hand, if the sensor failure happens 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
}
\emph{$s_k.status$ = COMMUNICATION}\;
- \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \;
+ \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;
\emph{Update $RE_k $}\;
}
\Else{
\label{alg:LiCO}
\end{algorithm}
-In this algorithm, K.CurrentSize and K.PreviousSize refer to the current size
-and the previous size of the subnetwork in the subregion respectively. That
-means the number of sensor nodes which are still alive. Initially, the sensor
-node checks its remaining energy $RE_k$, which must be greater than a threshold
-$E_{th}$ in order to participate in the current period. Each sensor node
-determines its position and its subregion using an embedded GPS or a location
-discovery algorithm. After that, all the sensors collect position coordinates,
-remaining energy, sensor node ID, and the number of their one-hop live neighbors
-during the information exchange. The sensors inside a same region cooperate to
-elect a leader. The selection criteria for the leader, in order of priority,
-are: larger number of neighbors, larger remaining energy, and then in case of
-equality, larger index. Once chosen, the leader collects information to
-formulate and solve the integer program which allows to construct the set of
-active sensors in the sensing stage.
+In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
+current number and the previous number of alive nodes in the subnetwork of the
+subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
+must be greater than a threshold $E_{th}$ in order to participate in the current
+period. Each sensor node determines its position and its subregion using an
+embedded GPS or a location discovery algorithm. After that, all the sensors
+collect position coordinates, remaining energy, sensor node ID, and the number
+of their one-hop live neighbors during the information exchange. The sensors
+inside a same region cooperate to elect a leader. The selection criteria for the
+leader, in order of priority, are: larger number of neighbors, larger remaining
+energy, and then in case of equality, larger index. Once chosen, the leader
+collects information to formulate and solve the integer program which allows to
+construct the set of active sensors in the sensing stage.
%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
\end{itemize}
$I_j$ refers to the set of coverage intervals which have been defined according
to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
-let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved
+let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
in coverage interval~$i$ of sensor~$j$, that is:
\begin{equation}
a^j_{ik} = \left \{
$\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
relative importance of satisfying the associated level of coverage. For example,
weights associated with coverage intervals of a specified part of a region may
-be given a relatively larger magnitude than weights associated with another
+be given by a relatively larger magnitude than weights associated with another
region. This kind of integer program is inspired from the model developed for
brachytherapy treatment planning for optimizing dose distribution
\cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
20.16 \% active nodes during the same time interval. As the number of periods
increases, LiCO protocol has a lower number of active nodes in comparison with
the three other approaches, while keeping a greater coverage ratio as shown in
-figure \ref{fig333}.
+Figure \ref{fig333}.
\begin{figure}[h!]
\centering
We observe the superiority of LiCO and DiLCO protocols in comparison against the
two other approaches in prolonging the network lifetime. In
-figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
+Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
different network sizes. As highlighted by these figures, the lifetime
increases with the size of the network, and it is clearly the larger for DiLCO
and LiCO protocols. For instance, for a network of 300~sensors and coverage
-ratio greater than 50\%, we can see on figure~\ref{fig3LT}(b) that the lifetime
+ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime
is about two times longer with LiCO compared to DESK protocol. The performance
-difference is more obvious in figure~\ref{fig3LT}(b) than in
-figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
+difference is more obvious in Figure~\ref{fig3LT}(b) than in
+Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
the time, and the lifetime with a coverage of 50\% is far more longer than with
95\%.
