receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
will be executed by each node at the beginning of a period, explains how the
-Active-Sleep packet is obtained. In this way a multiround optimization process is performed during each
+Active-Sleep packet is obtained. In this way, a multiround optimization process is performed during each
period after Information~Exchange and Leader~Election phases, in order to
produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
\begin{figure}[ht!]
This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods.
-On the one hand, if a node failure is detected before making the decision, the node will not participate to this phase, and, on the other hand, if the node failure occurs after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts.
+On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase, and, on the other hand, if the node failure occurs after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts.
-The energy consumption and some other constraints can easily be taken into account, since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period. However, the pre-sensing phases (Information Exchange, Leader Election, and Decision) are energy consuming for some nodes, even when they do not join the network to monitor the area.
+The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period. However, the pre-sensing phases (Information Exchange, Leader Election, and Decision) are energy consuming for some nodes, even when they do not join the network to monitor the area.
For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
-whether the point $p$ is covered, that is:
+whether the point $p$ is covered, that is
\begin{equation}
\alpha_{j,p} = \left \{
\begin{array}{l l}
%\label{eq12}
\end{equation}
The number of active sensors that cover the primary point $p$ during
-round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
+round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where
\begin{equation}
X_{t,j} = \left \{
\begin{array}{l l}
\end{array} \right.
%\label{eq11}
\end{equation}
-We define the Overcoverage variable $\Theta_{t,p}$ as:
+We define the Overcoverage variable $\Theta_{t,p}$ as
\begin{equation}
\Theta_{t,p} = \left \{
\begin{array}{l l}
More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
minus one that cover the primary point $p$ during round $t$. The
Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
-defined by:
+defined by
\begin{equation}
U_{t,p} = \left \{
\begin{array}{l l}
\label{eq14}
\end{equation}
-Our coverage optimization problem can then be formulated as follows:
+Our coverage optimization problem can then be formulated as follows
\begin{equation}
\min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
\end{equation}
undercoverage. The weights $W_\theta$ and $W_U$ must be properly chosen so as
to guarantee that the maximum number of points are covered during each round.
%% MS W_theta is smaller than W_u => problem with the following sentence
-In our simulations priority is given to the coverage by choosing $W_{U}$ very
+In our simulations, priority is given to the coverage by choosing $W_{U}$ very
large compared to $W_{\theta}$.
% is used to refer this table in the text
\end{table}
-Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5,
-and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of
-rounds in one sensing period). In the following, we will make comparisons with
-two other methods. The first method, called DESK and proposed by \cite{DESK},
-is a full distributed coverage algorithm. The second method, called
+Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5, and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of rounds in one sensing period). In the following, we will make comparisons with two other methods. The first method, called DESK and proposed by \cite{DESK}, is a fully distributed coverage algorithm. The second method is called
GAF~\cite{GAF}, consists in dividing the region into fixed squares.
-During the decision phase, in each square, one sensor is then chosen to remain
-active during the sensing phase time.
+During the decision phase, in each square, one sensor is then chosen to remain active during the sensing phase time.
-Some preliminary experiments were performed in chapter 4 to study the choice of the number of
-subregions which subdivides the sensing field, considering different network
+Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions which subdivides the sensing field, considering different network
sizes. They show that as the number of subregions increases, so does the network
lifetime. Moreover, it makes the MuDiLCO protocol more robust against random
network disconnection due to node failures. However, too many subdivisions
This is due to the fact that, in comparison with MuDiLCO which uses optimization
to put in SLEEP status redundant sensors, more sensor nodes remain active with
-DESK and GAF. As a consequence, when the number of rounds increases, a larger
+DESK and GAF. As a consequence, when the number of rounds increases, a larger
number of node failures can be observed in DESK and GAF, resulting in a faster
decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
coverage ratio greater than 50\% for far more rounds. Overall, the proposed
sensor activity scheduling based on optimization in MuDiLCO maintains higher
coverage ratios of the area of interest for a larger number of rounds. It also
-means that MuDiLCO saves more energy, with less dead nodes, at most for several
+means that MuDiLCO saves more energy, with fewer dead nodes, at most for several
rounds, and thus should extend the network lifetime.
\begin{figure}[ht!]
MuDiLCO clearly outperforms them with only 24.8\% of active nodes. After the
thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
with the dual observation of higher level of coverage made previously.
-Obviously, in that case DESK and GAF have less active nodes, since they have
-activated many nodes at the beginning. Anyway, MuDiLCO activates the available
-nodes in a more efficient manner.
+Obviously, in that case, DESK and GAF have fewer active nodes since they have activated many nodes in the beginning. Anyway, MuDiLCO activates the available nodes in a more efficient manner.
\begin{figure}[ht!]
\centering
\end{figure}
-The results show that MuDiLCO is the most competitive from the energy
-consumption point of view. The other approaches have a high energy consumption
-due to activating a larger number of redundant nodes as well as the energy
-consumed during the different status of the sensor node. Among the different
-versions of our protocol, the MuDiLCO-7 one consumes more energy than the other
-versions. This is easy to understand since the bigger the number of rounds and
-the number of sensors involved in the integer program are, the larger the time
-computation to solve the optimization problem is. To improve the performances of
-MuDiLCO-7, we should increase the number of subregions in order to have less
-sensors to consider in the integer program.
+The results show that MuDiLCO is the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes, as well as the energy consumed during the different status of the sensor node. Among the different versions of our protocol, the MuDiLCO-7 one consumes more energy than the other versions. This is easy to understand since the bigger the number of rounds and
+the number of sensors involved in the integer program is the larger the time computation to solve the optimization problem is. To improve the performances of MuDiLCO-7, we should increase the number of subregions in order to have fewer sensors to consider in the integer program.
\label{fig77}
\end{figure}
-As expected, the execution time increases with the number of rounds $T$ taken
-into account to schedule the sensing phase. The times obtained for $T=1,3$
-or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor
-node, especially when the sensor network size increases. Again, we can notice
-that if we want to schedule the nodes activities for a large number of rounds,
-we need to choose a relevant number of subregions in order to avoid a complicated
-and cumbersome optimization. On the one hand, a large value for $T$ permits to
-reduce the energy-overhead due to the three pre-sensing phases, on the other
-hand a leader node may waste a considerable amount of energy to solve the
-optimization problem.
+As expected, the execution time increases with the number of rounds $T$ taken into account to schedule the sensing phase. The times obtained for $T=1,3$ or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor node, especially when the sensor network size increases. Again, we can notice that if we want to schedule the nodes activities for a large number of rounds,
+we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization. On the one hand, a large value for $T$ permits to reduce the energy overhead due to the three pre-sensing phases, on the other hand a leader node may waste a considerable amount of energy to solve the optimization problem.
%\subsection{Network lifetime}
%\label{ch5:sec:03:02:06}
-The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the
-network lifetime for different network sizes, respectively for $Lifetime_{95}$
-and $Lifetime_{50}$. Both figures show that the network lifetime increases
-together with the number of sensor nodes, whatever the protocol, thanks to the
-node density which results in more and more redundant nodes that can be
-deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
-protocol maximizes the lifetime of the network. In particular the gain in
-lifetime for a coverage over 95\% is greater than 38\% when switching from GAF
-to MuDiLCO-3. The slight decrease that can be observed for MuDiLCO-7 in case
-of $Lifetime_{95}$ with large wireless sensor networks results from the
-difficulty of the optimization problem to be solved by the integer program.
+The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the network lifetime for different network sizes, respectively for $Lifetime_{95}$ and $Lifetime_{50}$. Both figures show that the network lifetime increases together with the number of sensor nodes, whatever the protocol, thanks to the node density which results in more and more redundant nodes that can be deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
+protocol maximizes the lifetime of the network. In particular, the gain in lifetime for a coverage over 95\% is greater than 38\% when switching from GAF to MuDiLCO-3. The slight decrease that can be observed for MuDiLCO-7 in case of $Lifetime_{95}$ with large wireless sensor networks results from the difficulty of the optimization problem to be solved by the integer program.
This point was already noticed in \ref{subsec:EC} devoted to the
-energy consumption, since network lifetime and energy consumption are directly
-linked.
+energy consumption, since network lifetime and energy consumption are directly linked.
\begin{figure}[h!]
\section{Conclusion}
\label{ch5:sec:04}
-We have addressed the problem of the coverage and of 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 we propose a protocol which
-optimizes coverage and lifetime performances in each subregion. Our protocol,
-called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) combines
-two efficient techniques: network leader election and sensor activity
-scheduling.
-
-The activity scheduling in each subregion works in periods, where each period
-consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii)
-Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing
-Phase itself divided into T rounds.
-
-Simulations results show the relevance of the proposed protocol in terms of
-lifetime, coverage ratio, active sensors ratio, energy consumption, execution
-time. Indeed, when dealing with large wireless sensor networks, a distributed
-approach, like the one we propose, 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. Nevertheless, results also show that
-it is not possible to plan the activity of sensors over too many rounds, because
-the resulting optimization problem leads to too high resolution times and thus to
-an excessive energy consumption.
+We have addressed the problem of the coverage and of 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 we propose a protocol which optimizes coverage and lifetime performances in each subregion. Our protocol,
+called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) combines two efficient techniques: network leader election and sensor activity scheduling.
+
+The activity scheduling in each subregion works in periods, where each period consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii) Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing Phase itself divided into T rounds.
+
+Simulations results show the relevance of the proposed protocol in terms of lifetime, coverage ratio, active sensors ratio, energy consumption, execution time. Indeed, when dealing with large wireless sensor networks, a distributed approach, like the one we propose, allows to reduce the difficulty of a single global optimization problem by partitioning it into many smaller problems, one per subregion, that can be solved more easily. Nevertheless, results also show that it is not possible to plan the activity of sensors over too many rounds because the resulting optimization problem leads to too high-resolution times and thus to an excessive energy consumption.
