\section{Introduction}
\label{ch5:sec:01}
-\indent The fast developments of low-cost sensor devices and wireless
-communications have allowed the emergence of WSNs. A WSN includes a large number
-of small, limited-power sensors that can sense, process, and transmit data over
-a wireless communication. They communicate with each other by using multi-hop
-wireless communications and cooperate together to monitor the area of interest,
-so that each measured data can be reported to a monitoring center called sink
-for further analysis~\cite{ref222}. There are several fields of application
-covering a wide spectrum for a WSN, including health, home, environmental,
-military, and industrial applications~\cite{ref19}.
-
-On the one hand sensor nodes run on batteries with limited capacities, and it is
-often costly or simply impossible to replace and/or recharge batteries,
-especially in remote and hostile environments. Obviously, to achieve a long life
-of the network it is important to conserve battery power. Therefore, lifetime
-optimization is one of the most critical issues in wireless sensor networks. On
-the other hand we must guarantee coverage over the area of interest. To fulfill
-these two objectives, the main idea is to take advantage of overlapping sensing
-regions to turn-off redundant sensor nodes and thus save energy. In this paper,
-we concentrate on the area coverage problem, with the objective of maximizing
-the network lifetime by using an optimized multiround scheduling.
-
-We study the problem of designing an energy-efficient optimization algorithm that divides the sensor nodes in a WSN into multiple cover sets such that the area of interest is monitored as long as possible. Providing multiple cover sets can be used to improve the energy efficiency of WSNs. Therefore, in order to increase the longevity of the WSN and conserve the energy, it can be useful to provide multiple cover sets in one time after that schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the coverage optimization algorithm, as well as the information exchange and leader election.
+%The fast developments of low-cost sensor devices and wireless communications have allowed the emergence of WSNs. A WSN includes a large number of small, limited-power sensors that can sense, process, and transmit data over a wireless communication. They communicate with each other by using multi-hop wireless communications and cooperate together to monitor the area of interest, so that each measured data can be reported to a monitoring center called sink for further analysis~\cite{ref222}. There are several fields of application covering a wide spectrum for a WSN, including health, home, environmental, military, and industrial applications~\cite{ref19}.
+
+%On the one hand sensor nodes run on batteries with limited capacities, and it is often costly or simply impossible to replace and/or recharge batteries, especially in remote and hostile environments. Obviously, to achieve a long life of the network it is important to conserve battery power. Therefore, lifetime optimization is one of the most critical issues in wireless sensor networks. On the other hand we must guarantee coverage over the area of interest. To fulfill these two objectives, the main idea is to take advantage of overlapping sensing regions to turn-off redundant sensor nodes and thus save energy. In this paper, we concentrate on the area coverage problem, with the objective of maximizing the network lifetime by using an optimized multiround scheduling.
+We study the problem of designing an energy-efficient optimization algorithm that divides the sensor nodes in a WSN into multiple cover sets such that the area of interest is monitored as long as possible. Providing multiple cover sets can be used to improve the energy efficiency of WSNs. Therefore, in order to increase the longevity of the WSN and conserve the energy, it can be useful to provide multiple cover sets in one time and schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the coverage optimization algorithm, as well as the information exchange and leader election.
The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization protocol) presented in this chapter is an extension of the approach introduced in chapter 4. Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity. Compared to our protocol in chapter 4, in this one we study the possibility of dividing the sensing phase into multiple rounds. In fact, in this chapter we make a multiround optimization while it was a single round optimization in our protocol in chapter 4.
\section{MuDiLCO Protocol Description}
\label{ch5:sec:02}
\noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It is based on two energy-efficient
-mechanisms: subdividing the area of interest into several subregions (like cluster architecture) using divide and conquer method, where the sensor nodes cooperate within each subregion as independent group in order to achieve a network leader election; and sensor activity scheduling for maintaining the coverage and prolonging the network lifetime, which are applied periodically. MuDiLCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01} and it has been used the primary point coverage model which is described in the same chapter, section \ref{ch4:sec:02:02}.
+mechanisms: subdividing the area of interest into several subregions (like cluster architecture) using divide and conquer method, where the sensor nodes cooperate within each subregion as independent group in order to achieve a network leader election; and sensor activity scheduling for maintaining the coverage and prolonging the network lifetime, which are applied periodically. MuDiLCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01} and it uses the primary point coverage model which is described in the same chapter, section \ref{ch4:sec:02:02}.
\subsection{Background Idea and Algorithm}
where each is divided into 4 phases: Information~Exchange, Leader~Election,
Decision, and Sensing. The information exchange among wireless sensor nodes is described in chapter 4, section \ref{ch4:sec:02:03:01}. The leader election in each subregion is explained in chapter 4, section \ref{ch4:sec:02:03:02}, but the difference in that the elected leader in each subregion is for each period. In decision phase, each WSNL will solve an integer program to select which cover sets will be
activated in the following sensing phase to cover the subregion to which it belongs. The integer program will produce $T$ cover sets, one for each round. The WSNL will send an Active-Sleep packet to each sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in
-each round of the sensing phase. Each sensing phase may be itself divided into $T$ rounds
+each round of the sensing phase. Each sensing phase is itself divided into $T$ rounds
and for each round a set of sensors (a cover set) is responsible for the sensing
task. Each sensor node in the subregion will
receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
and undercoverage variables help balancing the restriction equations by taking
positive values. The constraint given by equation~(\ref{eq144}) guarantees that
the sensor has enough energy ($RE_j$ corresponds to its remaining energy) to be
-alive during the selected rounds knowing that $E_{th}$ is the amount of energy
+alive during the selected rounds knowing that $E_{th}$ is the amount of energy
required to be alive during one round.
There are two main objectives. First, we limit the overcoverage of primary
\subsection{Simulation Setup}
\label{ch5:sec:04:01}
-We conducted a series of simulations to evaluate the efficiency and the
+We conducted a series of simulations to evaluate the efficiency and the
relevance of our approach, using the discrete event simulator OMNeT++
-\cite{ref158}. The simulation parameters are summarized in Table~\ref{table3}. Each experiment for a network is run over 25~different random topologies and the results presented hereafter are the average of these 25 runs.
-%Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions.
+\cite{ref158}. The simulation parameters are summarized in chapter 4, Table~\ref{tablech4}. Each experiment for a network is run over 25~different random topologies and the results presented hereafter are the average of these 25 runs.
We performed simulations for five different densities varying from 50 to
250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
precisely, the deployment is controlled at a coarse scale in order to ensure
that the deployed nodes can cover the sensing field with the given sensing
range.
-%%RC these parameters are realistic?
-%% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
-
-\begin{table}[ht]
-\caption{Relevant parameters for network initializing.}
-% title of Table
-\centering
-% used for centering table
-\begin{tabular}{c|c}
-% centered columns (4 columns)
- \hline
-%inserts double horizontal lines
-Parameter & Value \\ [0.5ex]
-
-%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
-% inserts table
-%heading
-\hline
-% inserts single horizontal line
-Sensing field size & $(50 \times 25)~m^2 $ \\
-% inserting body of the table
-%\hline
-Network size & 50, 100, 150, 200 and 250~nodes \\
-%\hline
-Initial energy & 500-700~joules \\
-%\hline
-Sensing time for one round & 60 Minutes \\
-$E_{th}$ & 36 Joules\\
-$R_s$ & 5~m \\
-%\hline
-$W_{\Theta}$ & 1 \\
-% [1ex] adds vertical space
-%\hline
-$W_{U}$ & $|P|^2$
-%inserts single line
-\end{tabular}
-\label{table3}
-% 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 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.
-
-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
-reduce the advantage of the optimization. In fact, there is a balance between
-the benefit from the optimization and the execution time needed to solve
-it. Therefore, we have set the number of subregions to 16 rather than 32.
-
-We used the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 4, section \ref{ch4:sec:04:03}.
-
-%The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mW) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.
+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. DESK \cite{DESK} and GAF~\cite{GAF}.
+%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 reduce the advantage of the optimization. In fact, there is a balance between the benefit from the optimization and the execution time needed to solve it. Therefore,
+we set the number of subregions to 16 rather than 32 as explained in chapter 4, section ref{ch4:sec:04:05}. We use the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, the energy consumption model is presented in chapter 4, section \ref{ch4:sec:04:03}.
\subsection{Metrics}
\label{ch5:sec:04:02}
To evaluate our approach we consider the following performance metrics:
-\begin{enumerate}[i]
+\begin{enumerate}[i)]
-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
- of a sensor field is covered. In our case, the sensing field is represented as
- a connected grid of points and we use each grid point as a sample point to
- compute the coverage. The coverage ratio can be calculated by:
+\item {{\bf Coverage Ratio (CR)}:} The coverage ratio can be calculated by:
\begin{equation*}
\scriptsize
\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
of grid points in the sensing field of the network. In our simulations $N = 51
\times 26 = 1326$ grid points.
-\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:
+\item{{\bf Number of Active Sensors Ratio (ASR)}:} The Active Sensors
+ Ratio for round t is defined as follows:
\begin{equation*}
-\scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
+\scriptsize \mbox{$ASR^t$}(\%) = \frac{\sum\limits_{r=1}^R
\mbox{$A_r^t$}}{\mbox{$|J|$}} \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, $|J|$ is the total number of sensors in the
network, and $R$ is the total number of subregions in the network.
-\item {{\bf Network Lifetime}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Network Lifetime}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
\item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
% New version with global loops on period
\begin{equation*}
\scriptsize
- \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
+ \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M} T},
\end{equation*}
-where $M_L$ is the number of periods and $T_m$ the number of rounds in a
+where $M$ is the number of periods and $T$ the number of rounds in a
period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
consumed by the sensors (EC) comes through taking into consideration four main
energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
indicate the energy consumed by the whole network in round $t$.
-\item {{\bf Execution Time}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Execution Time}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
-\item {{\bf Stopped simulation runs}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Stopped simulation runs}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
\end{enumerate}
\label{ch5:sec:04:02}
-\begin{enumerate}[(i)]
+\begin{enumerate}[i)]
\item {{\bf Coverage Ratio}}
%\subsection{Coverage ratio}
which is a little bit better than the one of MuDiLCO.
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
+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
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
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!]
+\begin{figure}[h!]
\centering
\includegraphics[scale=0.8] {Figures/ch5/R1/CR.pdf}
\caption{Average coverage ratio for 150 deployed nodes}
minimize the communication overhead and maximize the network
lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
nodes all along the network lifetime. It appears that up to round thirteen, DESK
-and GAF have respectively 37.6\% and 44.8\% of nodes in ACTIVE status, whereas
+and GAF have respectively 37.6\% and 44.8\% of nodes in active mode, whereas
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 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!]
+\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Figures/ch5/R1/ASR.pdf}
\caption{Active sensors ratio for 150 deployed nodes}
still connected.
-\begin{figure}[ht!]
+\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Figures/ch5/R1/SR.pdf}
\caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
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.
+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.
%The original execution time is computed on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6} \right)$ and reported on Figure~\ref{fig77} for different network sizes.
-\begin{figure}[ht!]
+\begin{figure}[H]
\centering
\includegraphics[scale=0.8]{Figures/ch5/R1/T.pdf}
\caption{Execution Time (in seconds)}
\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.
+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. \\
energy consumption, since network lifetime and energy consumption are directly linked.
-\begin{figure}[h!]
+\begin{figure}[hi]
\centering
% \begin{multicols}{0}
\centering
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.
+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.
