From: ali Date: Thu, 11 Jun 2015 09:09:25 +0000 (+0200) Subject: Chapter 4 is finished X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/ThesisAli.git/commitdiff_plain/32808ea756588e2c67d047ff4e644c9aeeeee844 Chapter 4 is finished --- diff --git a/CHAPITRE_04.tex b/CHAPITRE_04.tex index 3cc5877..cb2c91f 100644 --- a/CHAPITRE_04.tex +++ b/CHAPITRE_04.tex @@ -483,7 +483,7 @@ The results presented in the figure show that increasing the number of subregion %\subsubsection{The percentage of stopped simulation runs} Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes. DiLCO-2 is the approach which stops first because it applies the optimization on only two subregions and the high energy consumption accelerate the network disconnection. Thus, as explained previously, in case of DiLCO-16 and DiLCO-32 which have many subregions, the optimization effectively continues as long as a subnetwork in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime. -\begin{figure}[h!] +\begin{figure}[t] \centering \includegraphics[scale=0.8]{Figures/ch4/R1/SR.pdf} \caption{Percentage of stopped simulation runs for 150 deployed nodes } @@ -495,61 +495,58 @@ Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation \item {{\bf Energy Consumption}} %\subsubsection{The Energy Consumption} -We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different subregions. Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50} illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node. +We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different subregions. Figures~\ref{Figures/ch4/R1/EC}(a) and~\ref{Figures/ch4/R1/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node. \begin{figure}[h!] \centering -\includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf} -\caption{Energy Consumption for $Lifetime_{95}$} -\label{Figures/ch4/R1/EC95} -\end{figure} - -As shown in Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50}, 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 computation time to solve the optimization problem, as well as the higher energy consumed during the communication. -\begin{figure}[h!] + %\begin{multicols}{1} \centering -\includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf} -\caption{Energy Consumption for $Lifetime_{50}$} -\label{Figures/ch4/R1/EC50} -\end{figure} -In fact, the distribution of the computation over many subregions greatly reduces the number of communications, the time of listening and computation. +\includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\ +%\vfill +\includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf}\\~ ~ ~ ~ ~(b) + +%\end{multicols} +\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} +\label{Figures/ch4/R1/EC} +\end{figure} + +As shown in Figures~\ref{Figures/ch4/R1/EC}(a) and~\ref{Figures/ch4/R1/EC}(b), 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 computation time to solve the optimization problem, as well as the higher energy consumed during the communication. In fact, the distribution of the computation over many subregions greatly reduces the number of communications, the time of listening and computation. \item {{\bf Execution Time}} %\subsubsection{Execution Time} -In this experiment, the execution time of the distributed optimization approach has been studied. Figure~\ref{Figures/ch4/R1/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one period. They are given for the different approaches and various numbers of sensors. The original execution time is computed as described in section \ref{ch4:sec:04:04}. +In this experiment, the execution time of the distributed optimization approach has been studied. Figure~\ref{Figures/ch4/R1/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one period. They are given for the different approaches and various numbers of sensors. The original execution time is computed as described in section \ref{ch4:sec:04:04}. \\ \\ \\ \\ -We can see from Figure~\ref{Figures/ch4/R1/T} that DiLCO-32 has very low execution times in comparison with other DiLCO versions because it is distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion and thus presents high execution times. Overall, to be able to deal with very large networks, a distributed method is clearly required. -\begin{figure}[h!] + +\begin{figure}[h!t] \centering \includegraphics[scale=0.8]{Figures/ch4/R1/T.pdf} \caption{Execution Time (in seconds)} \label{Figures/ch4/R1/T} \end{figure} - +We can see from Figure~\ref{Figures/ch4/R1/T} that DiLCO-32 has very low execution times in comparison with other DiLCO versions because it is distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion and thus presents high execution times. Overall, to be able to deal with very large networks, a distributed method is clearly required. \item {{\bf Network Lifetime}} %\subsubsection{The Network Lifetime} -In Figure~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, network lifetime, $Lifetime_{95}$ and $Lifetime_{50}$ respectively, are illustrated for different network sizes. +In Figures~\ref{Figures/ch4/R1/LT}(a) and \ref{Figures/ch4/R1/LT}(b), network lifetime, $Lifetime_{95}$ and $Lifetime_{50}$ respectively, are illustrated for different network sizes. + \begin{figure}[h!] \centering -\includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf} -\caption{Network Lifetime for $Lifetime_{95}$} -\label{Figures/ch4/R1/LT95} -\end{figure} -For DiLCO-2 protocol, execution times quickly become unsuitable for a sensor network, and the energy consumed during the communication, seems to be huge because it is distributed over only two subregions. +\centering +\includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\ -As highlighted by figures~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases. The network lifetime also increases with the number of subregions, but only up to a given number. Thus we can see that DiLCO-16 leads to the larger lifetime improvement and not DiLCO-32. In fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions. It means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is a relevant way to maximize the lifetime of a network. +\includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}\\~ ~ ~ ~ ~(b) + +\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} + \label{Figures/ch4/R1/LT} +\end{figure} + +For DiLCO-2 protocol, execution times quickly become unsuitable for a sensor network, and the energy consumed during the communication, seems to be huge because it is distributed over only two subregions. As highlighted by Figures~\ref{Figures/ch4/R1/LT}(a) and \ref{Figures/ch4/R1/LT}(b), the network lifetime obviously increases when the size of the network increases. The network lifetime also increases with the number of subregions, but only up to a given number. Thus we can see that DiLCO-16 leads to the larger lifetime improvement and not DiLCO-32. In fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions. It means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is a relevant way to maximize the lifetime of a network. -\begin{figure}[h!] -\centering -\includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf} -\caption{Network Lifetime for $Lifetime_{50}$} -\label{Figures/ch4/R1/LT50} -\end{figure} \end{enumerate} @@ -610,20 +607,20 @@ When the number of primary points is increased, the percentage of the stopped si \item {{\bf Energy Consumption}} %\subsubsection{The Energy Consumption} -In this experiment, we study the effect of increasing the primary points to represent the area of the sensor on the energy consumed by the wireless sensor network for different network densities. Figures~\ref{Figures/ch4/R2/EC95} and ~\ref{Figures/ch4/R2/EC50} illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. +In this experiment, we study the effect of increasing the primary points to represent the area of the sensor on the energy consumed by the wireless sensor network for different network densities. Figures~\ref{Figures/ch4/R2/EC}(a) and~\ref{Figures/ch4/R2/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. + \begin{figure}[h!] \centering -\includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf} -\caption{Energy Consumption with $Lifetime_{95}$} -\label{Figures/ch4/R2/EC95} -\end{figure} - -\begin{figure}[h!] + %\begin{multicols}{1} \centering -\includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf} -\caption{Energy Consumption with $Lifetime_{50}$} -\label{Figures/ch4/R2/EC50} -\end{figure} +\includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf}\\~ ~ ~ ~ ~(a) \\ +%\vfill +\includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf}\\~ ~ ~ ~ ~(b) + +%\end{multicols} +\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} +\label{Figures/ch4/R2/EC} +\end{figure} We see from the results presented in both figures that the energy consumed by the network for each period increases when the number of primary points increases. Indeed, the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model-5 is the most competitive from the energy consumption point of view and the coverage ratio point of view. The other models have a high energy consumption due to the increase in the primary points. In fact, Model-5 is a good candidate to be used by wireless sensor network because it preserves a good coverage ratio with a suitable energy consumption in comparison with other models. @@ -635,7 +632,7 @@ In this experiment, we study the impact of the increase in primary points on the \begin{figure}[h!] \centering \includegraphics[scale=0.8]{Figures/ch4/R2/T.pdf} -\caption{Execution Time(s) vs The Number of Sensors } +\caption{Execution Time (in seconds)} \label{Figures/ch4/R2/T} \end{figure} @@ -647,23 +644,21 @@ Moreover, Model-5 has more suitable execution times and coverage ratio that lead Finally, we study the effect of increasing the primary points on the lifetime of the network. %In Figure~\ref{Figures/ch4/R2/LT95} and in Figure~\ref{Figures/ch4/R2/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes. -As highlighted by figures~\ref{Figures/ch4/R2/LT95} and \ref{Figures/ch4/R2/LT50}, the network lifetime obviously increases when the size of the network increases, with Model-5 that leads to the larger lifetime improvement. Comparison shows that Model-5, which uses less number of primary points, is the best one because it is less energy consuming during the network lifetime. It is also the better one from the point of view of coverage ratio. Our proposed Model-5 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models. Therefore, we have chosen Model-5 for all the experiments presented thereafter. - -\begin{figure}[h!] -\centering -\includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf} -\caption{Network Lifetime for $Lifetime_{95}$} -\label{Figures/ch4/R2/LT95} -\end{figure} +As highlighted by Figures~\ref{Figures/ch4/R2/LT}(a) and \ref{Figures/ch4/R2/LT}(b), the network lifetime obviously increases when the size of the network increases, with Model-5 that leads to the larger lifetime improvement. \\ \\ +Comparison shows that Model-5, which uses less number of primary points, is the best one because it is less energy consuming during the network lifetime. It is also the better one from the point of view of coverage ratio. Our proposed Model-5 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models. Therefore, we have chosen Model-5 for all the experiments presented thereafter. + \begin{figure}[h!] \centering -\includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf} -\caption{Network Lifetime for $Lifetime_{50}$} -\label{Figures/ch4/R2/LT50} -\end{figure} +\centering +\includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf}\\~ ~ ~ ~ ~(a) \\ +\includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf}\\~ ~ ~ ~ ~(b) + +\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} + \label{Figures/ch4/R2/LT} +\end{figure} \end{enumerate} @@ -677,7 +672,6 @@ Based on the results, conducted in the previous subsections, \ref{ch4:sec:04:02} %\subsubsection{Coverage Ratio} The average coverage ratio for 150 deployed nodes is demonstrated in Figure~\ref{Figures/ch4/R3/CR}. - \parskip 0pt \begin{figure}[h!] \centering @@ -685,8 +679,9 @@ The average coverage ratio for 150 deployed nodes is demonstrated in Figure~\ref \caption{Coverage ratio for 150 deployed nodes} \label{Figures/ch4/R3/CR} \end{figure} +DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 98.4\% and 98.9\% produced by DiLCO-16 and DiLCO-32 for the lowest number of periods. \\ \\ \\ -DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 98.4\% and 98.9\% produced by DiLCO-16 and DiLCO-32 for the lowest number of periods. This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors thanks to the optimization (which lightly decreases the coverage ratio), while there are more active nodes in the case of DESK and GAF. +This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors thanks to the optimization (which lightly decreases the coverage ratio), while there are more active nodes in the case of DESK and GAF. Moreover, when the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. %This is due to dead nodes. However, DiLCO-16 protocol and DiLCO-32 protocol maintain almost a good coverage. @@ -728,21 +723,21 @@ On the one hand, DESK is the approach which stops first because it consumes more %\subsubsection{The Energy Consumption} %In this experiment, we have studied the effect of the energy consumed by the wireless sensor network during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches. -Figures~\ref{Figures/ch4/R3/EC95} and ~\ref{Figures/ch4/R3/EC50} illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. +Figures~\ref{Figures/ch4/R3/EC}(a) and~\ref{Figures/ch4/R3/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. \begin{figure}[h!] \centering -\includegraphics[scale=0.8]{Figures/ch4/R3/EC95.eps} -\caption{Energy Consumption with $Lifetime_{95}$} -\label{Figures/ch4/R3/EC95} -\end{figure} - -\begin{figure}[h!] + %\begin{multicols}{1} \centering -\includegraphics[scale=0.8]{Figures/ch4/R3/EC50.eps} -\caption{Energy Consumption with $Lifetime_{50}$} -\label{Figures/ch4/R3/EC50} -\end{figure} +\includegraphics[scale=0.8]{Figures/ch4/R3/EC95.eps}\\~ ~ ~ ~ ~(a) \\ +%\vfill +\includegraphics[scale=0.8]{Figures/ch4/R3/EC50.eps}\\~ ~ ~ ~ ~(b) + +%\end{multicols} +\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} +\label{Figures/ch4/R3/EC} +\end{figure} + DiLCO-16 protocol and DiLCO-32 protocol are 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 modes of sensor nodes. @@ -757,20 +752,18 @@ In fact, the distribution of computation over the subregions greatly reduces th \begin{figure}[h!] \centering -\includegraphics[scale=0.8]{Figures/ch4/R3/LT95.eps} -\caption{Network Lifetime for $Lifetime_{95}$} -\label{Figures/ch4/R3/LT95} -\end{figure} - - -\begin{figure}[h!] +% \begin{multicols}{0} \centering -\includegraphics[scale=0.8]{Figures/ch4/R3/LT50.eps} -\caption{Network Lifetime for $Lifetime_{50}$} -\label{Figures/ch4/R3/LT50} -\end{figure} +\includegraphics[scale=0.8]{Figures/ch4/R3/LT95.eps}\\~ ~ ~ ~ ~(a) \\ +%\hfill +\includegraphics[scale=0.8]{Figures/ch4/R3/LT50.eps}\\~ ~ ~ ~ ~(b) + +%\end{multicols} +\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} + \label{Figures/ch4/R3/LT} +\end{figure} -As highlighted by figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol and DiLCO-32 protocol which lead to maximize the lifetime of the network compared with other approaches. +As highlighted by Figures~\ref{Figures/ch4/R3/LT}(a) and \ref{Figures/ch4/R3/LT}(b), the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol and DiLCO-32 protocol which lead to maximize the lifetime of the network compared with other approaches. By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next periods, DiLCO-16 protocol and DiLCO-32 protocol efficiently prolong the network lifetime. Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which use distributed optimization over the subregions, are the best ones because they are robust to network disconnection during the network lifetime as well as they consume less energy in comparison with other approaches. %It also means that distributing the algorithm 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. diff --git a/CHAPITRE_05.tex b/CHAPITRE_05.tex index d542a14..d4ebf28 100644 --- a/CHAPITRE_05.tex +++ b/CHAPITRE_05.tex @@ -14,53 +14,46 @@ %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. +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 step and schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the presensing phases of MuDiLCO protocol. -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. +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 DiLCO 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. -The remainder of the chapter continues with section \ref{ch5:sec:02} where a detail of MuDiLCO Protocol is presented. The next section describes the Primary Points based Multiround Coverage Problem formulation which is used to schedule the activation of sensors in T cover sets. Section \ref{ch5:sec:04} shows the simulation +The remainder of this chapter continues with section \ref{ch5:sec:02} where a detailed description of MuDiLCO Protocol is given. The next section describes the primary points based multiround coverage problem formulation which is used to schedule the activation of sensors in multiple cover sets. Section \ref{ch5:sec:04} shows the simulation results. The chapter ends with a conclusion and some suggestions for further work. -\section{MuDiLCO Protocol Description} +\section{Description of the MuDiLCO Protocol } \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 uses the primary point coverage model which is described in the same chapter, section \ref{ch4:sec:02:02}. +%\noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It +Like DiLCO, the MuDiLCO protocol 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 uses the same assumptions, primary point coverage and network models, than DiLCO, given in section \ref{ch4:sec:02:01} and \ref{ch4:sec:02:02}, respectively. -\subsection{Background Idea and Algorithm} -\label{ch5:sec:02:02} -The area of interest can be divided using the divide-and-conquer strategy into -smaller areas, called subregions, and then our MuDiLCO protocol will be -implemented in each subregion in a distributed way. - -As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion, -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 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 -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 -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. +%\subsection{Background Idea and Algorithm} +%\label{ch5:sec:02:02} +%The area of interest can be divided using the divide-and-conquer strategy into smaller areas, called subregions, and then our MuDiLCO protocol will be implemented in each subregion in a distributed way. + +As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion, 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}, +The difference with MuDiLCO in that the elected leader in each subregion is for each period. In decision phase, each leader 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 leader will send an ActiveSleep 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 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 ActiveSleep packet from leader, 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 ActiveSleep 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!] \centering \includegraphics[width=160mm]{Figures/ch5/GeneralModel.jpg} % 70mm Modelgeneral.pdf -\caption{The MuDiLCO protocol scheme executed on each node} +\caption{MuDiLCO protocol.} \label{fig2} \end{figure} -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 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. +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 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. @@ -86,7 +79,7 @@ The energy consumption and some other constraints can easily be taken into \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ = Execute Integer Program Algorithm($T,J$)}\; \emph{$s_j.status$ = COMMUNICATION}\; - \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\ + \emph{Send $ActiveSleep()$ to each node $k$ in subregion: a packet \\ with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\; \emph{Update $RE_j $}\; } @@ -113,15 +106,13 @@ The energy consumption and some other constraints can easily be taken into \label{ch5:sec:03} -According to our algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model -proposed by \cite{ref156} with some modifications, where the objective is -to find a maximum number of disjoint cover sets. To fulfill this goal, the -authors proposed an integer program which forces undercoverage and overcoverage -of targets to become minimal at the same time. They use binary variables -$x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our model, we -consider binary variables $X_{t,j}$ to determine the possibility of activating +According to Algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model +proposed by \cite{ref156} with some modifications, where the objective of our model is +to find a maximum number of non-disjoint cover sets. +%To fulfill this goal, the authors proposed an integer program which forces undercoverage and overcoverage of targets to become minimal at the same time. They use binary variables $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our model, +We consider binary variables $X_{t,j}$ to determine the possibility of activating sensor $j$ during round $t$ of a given sensing phase. We also consider primary -points as targets. The set of primary points is denoted by $P$ and the set of +points as targets. The set of primary points is denoted by $P$ and the set of sensors by $J$. Only sensors able to be alive during at least one round are involved in the integer program. @@ -237,21 +228,23 @@ large compared to $W_{\theta}$. \label{ch5:sec:04:01} 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 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. +\cite{ref158}. We performed the optimization in the same manner than in chapter 4, considering the same energy model. The simulation parameters are summarized in 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. -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}. +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 three other methods. DESK \cite{DESK}, GAF~\cite{GAF}, and DiLCO~\cite{Idrees2}, where MuDiLCO-1 is similar to DiLCO. %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}. +We set the number of subregions to 16 rather than 32 as explained in section \ref{ch4:sec:04:05}. +We use the modeling language and the optimization solver which are mentioned in 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: - +To evaluate our approach we consider the following performance metrics +\begin{frame}{} \begin{enumerate}[i)] \item {{\bf Coverage Ratio (CR)}:} The coverage ratio can be calculated by: @@ -260,9 +253,8 @@ To evaluate our approach we consider the following performance metrics: \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100, \end{equation*} where $n^t$ is the number of covered grid points by the active sensors of all -subregions during round $t$ in the current sensing phase and $N$ is the total number -of grid points in the sensing field of the network. In our simulations $N = 51 -\times 26 = 1326$ grid points. +subregions during round $t$ in the current sensing phase. +% and $N$ is the total number 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)}:} The Active Sensors Ratio for round t is defined as follows: @@ -271,43 +263,32 @@ of grid points in the sensing field of the network. In our simulations $N = 51 \mbox{$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}:} Described in chapter 4, section \ref{ch4:sec:04:04}. +$t$ 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 Energy Consumption (EC)}:} the average energy consumption can be - seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or - $Lifetime_{50}$ divided by the number of rounds. EC can be computed as - follows: +\item {{\bf Energy Consumption (EC)}:} EC can be computed as follows: - % New version with global loops on period \begin{equation*} \scriptsize \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*} +The energy factors of above equation are described in section \ref{ch4:sec:04:04}. $E^a_t$ and $E^s_t$ +indicate the energy consumed by the whole network in round $t$ of the sensing phase. -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 $E^{\scriptsize \mbox{com}}_m$, -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, $E^a_t$ and $E^s_t$ -indicate the energy consumed by the whole network in round $t$. +%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 $E^{\scriptsize \mbox{com}}_m$, 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, $E^a_t$ and $E^s_t$ indicate the energy consumed by the whole network in round $t$. - -\item {{\bf Execution Time}:} 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}. + %$\right\}$ + +\item {{\bf Execution Time}:} +\item {{\bf Stopped simulation runs}:} \makebox(0,0){\put(0,2.2\normalbaselineskip){% + $\left.\rule{0pt}{2.3\normalbaselineskip}\right\}$ Described in section \ref{ch4:sec:04:04}.}} +\item {{\bf Network Lifetime}:} \end{enumerate} - +\end{frame} \subsection{Results Analysis and Comparison } \label{ch5:sec:04:02} @@ -351,8 +332,8 @@ 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 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 +MuDiLCO clearly outperforms them with only 23.7\% of active nodes. After the +thirty-sixth 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. @@ -412,7 +393,7 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$. 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, the larger the time computation to solve the optimization problem. 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. @@ -426,7 +407,7 @@ seconds (needed to solve optimization problem) for different values of $T$. The %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}[H] +\begin{figure}[h!] \centering \includegraphics[scale=0.8]{Figures/ch5/R1/T.pdf} \caption{Execution Time (in seconds)} @@ -448,7 +429,7 @@ This point was already noticed in \ref{subsec:EC} devoted to the energy consumption, since network lifetime and energy consumption are directly linked. -\begin{figure}[hi] +\begin{figure}[h!] \centering % \begin{multicols}{0} \centering @@ -469,12 +450,10 @@ energy consumption, since network lifetime and energy consumption are directly \section{Conclusion} \label{ch5:sec:05} -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. +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. +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. diff --git a/Thesis.toc b/Thesis.toc index deb9774..cf3c3ea 100644 --- a/Thesis.toc +++ b/Thesis.toc @@ -71,36 +71,35 @@ \contentsline {subsection}{\numberline {4.4.3}Energy Consumption Model}{81}{subsection.4.4.3} \contentsline {subsection}{\numberline {4.4.4}Performance Metrics}{81}{subsection.4.4.4} \contentsline {subsection}{\numberline {4.4.5}Performance Analysis for Different Number of Subregions}{83}{subsection.4.4.5} -\contentsline {subsection}{\numberline {4.4.6}Performance Analysis for Different Number of Primary Points}{87}{subsection.4.4.6} +\contentsline {subsection}{\numberline {4.4.6}Performance Analysis for Different Number of Primary Points}{89}{subsection.4.4.6} \contentsline {subsection}{\numberline {4.4.7}Performance Comparison with other Approaches}{93}{subsection.4.4.7} -\contentsline {section}{\numberline {4.5}Conclusion}{99}{section.4.5} +\contentsline {section}{\numberline {4.5}Conclusion}{100}{section.4.5} \contentsline {chapter}{\numberline {5}Multiround Distributed Lifetime Coverage Optimization Protocol}{101}{chapter.5} \contentsline {section}{\numberline {5.1}Introduction}{101}{section.5.1} -\contentsline {section}{\numberline {5.2}MuDiLCO Protocol Description}{101}{section.5.2} -\contentsline {subsection}{\numberline {5.2.1}Background Idea and Algorithm}{102}{subsection.5.2.1} +\contentsline {section}{\numberline {5.2}Description of the MuDiLCO Protocol }{101}{section.5.2} \contentsline {section}{\numberline {5.3}Primary Points based Multiround Coverage Problem Formulation}{103}{section.5.3} \contentsline {section}{\numberline {5.4}Experimental Study and Analysis}{105}{section.5.4} \contentsline {subsection}{\numberline {5.4.1}Simulation Setup}{105}{subsection.5.4.1} \contentsline {subsection}{\numberline {5.4.2}Metrics}{105}{subsection.5.4.2} \contentsline {subsection}{\numberline {5.4.3}Results Analysis and Comparison }{106}{subsection.5.4.3} -\contentsline {section}{\numberline {5.5}Conclusion}{113}{section.5.5} -\contentsline {chapter}{\numberline {6} Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}{115}{chapter.6} -\contentsline {section}{\numberline {6.1}Introduction}{115}{section.6.1} -\contentsline {section}{\numberline {6.2}The PeCO Protocol Description}{115}{section.6.2} -\contentsline {subsection}{\numberline {6.2.1}Assumptions and Models}{115}{subsection.6.2.1} -\contentsline {subsection}{\numberline {6.2.2}PeCO Protocol Algorithm}{118}{subsection.6.2.2} -\contentsline {section}{\numberline {6.3}Perimeter-based Coverage Problem Formulation}{120}{section.6.3} -\contentsline {section}{\numberline {6.4}Performance Evaluation and Analysis}{121}{section.6.4} -\contentsline {subsection}{\numberline {6.4.1}Simulation Settings}{121}{subsection.6.4.1} -\contentsline {subsection}{\numberline {6.4.2}Simulation Results}{122}{subsection.6.4.2} -\contentsline {subsubsection}{\numberline {6.4.2.1}Coverage Ratio}{122}{subsubsection.6.4.2.1} -\contentsline {subsubsection}{\numberline {6.4.2.2}Active Sensors Ratio}{122}{subsubsection.6.4.2.2} -\contentsline {subsubsection}{\numberline {6.4.2.3}The Energy Consumption}{122}{subsubsection.6.4.2.3} -\contentsline {subsubsection}{\numberline {6.4.2.4}The Network Lifetime}{125}{subsubsection.6.4.2.4} -\contentsline {section}{\numberline {6.5}Conclusion}{128}{section.6.5} -\contentsline {part}{III\hspace {1em}Conclusion and Perspectives}{129}{part.3} -\contentsline {chapter}{\numberline {7}Conclusion and Perspectives}{131}{chapter.7} -\contentsline {section}{\numberline {7.1}Conclusion}{131}{section.7.1} -\contentsline {section}{\numberline {7.2}Perspectives}{132}{section.7.2} -\contentsline {part}{Publications}{135}{chapter*.13} -\contentsline {part}{Bibliographie}{149}{chapter*.17} +\contentsline {section}{\numberline {5.5}Conclusion}{112}{section.5.5} +\contentsline {chapter}{\numberline {6} Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}{113}{chapter.6} +\contentsline {section}{\numberline {6.1}Introduction}{113}{section.6.1} +\contentsline {section}{\numberline {6.2}The PeCO Protocol Description}{113}{section.6.2} +\contentsline {subsection}{\numberline {6.2.1}Assumptions and Models}{113}{subsection.6.2.1} +\contentsline {subsection}{\numberline {6.2.2}PeCO Protocol Algorithm}{116}{subsection.6.2.2} +\contentsline {section}{\numberline {6.3}Perimeter-based Coverage Problem Formulation}{118}{section.6.3} +\contentsline {section}{\numberline {6.4}Performance Evaluation and Analysis}{119}{section.6.4} +\contentsline {subsection}{\numberline {6.4.1}Simulation Settings}{119}{subsection.6.4.1} +\contentsline {subsection}{\numberline {6.4.2}Simulation Results}{120}{subsection.6.4.2} +\contentsline {subsubsection}{\numberline {6.4.2.1}Coverage Ratio}{120}{subsubsection.6.4.2.1} +\contentsline {subsubsection}{\numberline {6.4.2.2}Active Sensors Ratio}{120}{subsubsection.6.4.2.2} +\contentsline {subsubsection}{\numberline {6.4.2.3}The Energy Consumption}{120}{subsubsection.6.4.2.3} +\contentsline {subsubsection}{\numberline {6.4.2.4}The Network Lifetime}{123}{subsubsection.6.4.2.4} +\contentsline {section}{\numberline {6.5}Conclusion}{126}{section.6.5} +\contentsline {part}{III\hspace {1em}Conclusion and Perspectives}{127}{part.3} +\contentsline {chapter}{\numberline {7}Conclusion and Perspectives}{129}{chapter.7} +\contentsline {section}{\numberline {7.1}Conclusion}{129}{section.7.1} +\contentsline {section}{\numberline {7.2}Perspectives}{130}{section.7.2} +\contentsline {part}{Publications}{133}{chapter*.13} +\contentsline {part}{Bibliographie}{147}{chapter*.17} diff --git a/entete.tex b/entete.tex index 61f2137..212ee36 100644 --- a/entete.tex +++ b/entete.tex @@ -30,10 +30,13 @@ %\usepackage{subfig} \usepackage{multirow} \usepackage{array} - +\usepackage{picture} \usepackage[section]{placeins} \usepackage{float} +\def\setgrouptext#1{\gdef\grouptext{#1}} +\newenvironment{groupeditems}{\begin{displaymath}\left.\vbox\bgroup\setgrouptext}{% + \egroup\right\rbrace\hbox{\grouptext}\end{displaymath}} \newcommand*\rot{\rotatebox{90}} \newcommand*\OK{\ding{51}}