From e8beaffc3d795b3bf326898f4c0df08d8eaea6c1 Mon Sep 17 00:00:00 2001 From: ali Date: Fri, 26 Jun 2015 17:41:20 +0200 Subject: [PATCH] Update by Ali --- Abstruct.tex | 4 +- CHAPITRE_04.tex | 41 +++----- CHAPITRE_06.tex | 273 ++++++++++++++++++------------------------------ Resume.tex | 10 +- Thesis.toc | 5 +- bib.bib | 8 ++ 6 files changed, 134 insertions(+), 207 deletions(-) diff --git a/Abstruct.tex b/Abstruct.tex index 5ef2405..a5bc5b5 100644 --- a/Abstruct.tex +++ b/Abstruct.tex @@ -22,7 +22,7 @@ %Wireless sensor networks (WSNs) have recently received a great deal of research attention due to their wide range of potential applications. Many important characteristics provided by the WSNs make them different from other wireless ad-hoc networks. Furthermore, these characteristics impose lots of limitations that lead to several challenges in the network. These challenges include coverage, topology control, routing, data fusion, security, and many others. One of the main research challenges faced in wireless sensor networks is to preserve continuously and effectively the coverage of an area of interest to be monitored, while simultaneously preventing as much as possible a network failure due to battery-depleted nodes. In this dissertation, we highly focus on the area coverage problem, energy-efficiency is also the foremost requirement. We have considered distributed optimization protocols with the ultimate objective of prolonging the network lifetime. The proposed distributed optimization protocols (including algorithms, models, and solving integer programs) should be energy-efficient protocols. To address this problem, this dissertation proposes two-step approaches. Firstly, the sensing field is divided into smaller subregions using the concept of divide-and-conquer method. Secondly, one of our proposed distributed optimization protocols is distributed and applied on the -sensor nodes in each subregion so as to optimize the coverage and the lifetime performances. In this dissertation, three coverage optimization protocols are proposed. These protocols combine two efficient techniques: leader election for each subregion, followed by an optimization-based planning of sensor activity scheduling decisions for each subregion. +sensor nodes in each subregion so as to optimize the coverage and the lifetime performances. In this dissertation, three coverage optimization protocols are proposed. These protocols combine two efficient techniques: leader election for each subregion, followed by an optimization-based scheduling of sensor activity for each subregion. First, we propose a protocol called Distributed Lifetime Coverage Optimization (DiLCO). In this protocol, the lifetime is divided into periods. Each period consists of 4 phases: information exchange, leader election, decision, and sensing. The decision process is carried out by a leader node, which solves an integer program in order to provide only one cover set of active sensor nodes to ensure coverage during the sensing phase of the current period. @@ -32,7 +32,7 @@ during which sets of sensor nodes are scheduled to remain active for a number of -Last but not least, we propose a Perimeter-based Coverage Optimization (PeCO) protocol which is also distributed among sensor nodes in each subregion. The novelty of our approach lies essentially in the formulation of a new mathematical optimization model based on a perimeter coverage level to schedule sensors' activities, whereas we used primary points coverage model in the two previous models. A new integer program coverage model is solved by the leader during the decision phase so as to provide only one cover set of sensors for the sensing phase. +Last but not least, we propose a Perimeter-based Coverage Optimization (PeCO) protocol which is also distributed among sensor nodes in each subregion. The novelty of our approach lies essentially in the formulation of a new mathematical optimization model based on a perimeter coverage level to schedule sensors' activities, whereas we use primary points coverage model in the two previous models. A new integer program coverage model is solved by the leader during the decision phase so as to provide only one cover set of sensors for the sensing phase. Extensive simulations are conducted using the discrete event simulator OMNeT++ to validate the efficiency of each of our proposed protocols. We refer to the characteristics of a Medusa II sensor for the energy consumption and the time computation. In comparison with two other existing methods, our protocols are able to increase the WSN lifetime and provide improved coverage performance. diff --git a/CHAPITRE_04.tex b/CHAPITRE_04.tex index 3e691b7..09b6595 100644 --- a/CHAPITRE_04.tex +++ b/CHAPITRE_04.tex @@ -344,38 +344,27 @@ The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employ \indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmel's AVR ATmega103L microcontroller~\cite{ref112}. The typical architecture of a sensor is composed of four subsystems: the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for transmitting/receiving messages, the sensing subsystem that collects data, and the power supply which powers the complete sensor node \cite{ref112}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table1}. -\begin{table}[ht] -\caption{Energy Consumption Model} -% title of Table +\begin{table}[h] \centering -% used for centering table -\begin{tabular}{|c|c|c|c|c|} -% centered columns (4 columns) - \hline -%inserts double horizontal lines -Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex] -\hline -% inserts single horizontal line -LISTENING & on & on & on & 20.05 \\ -% inserting body of the table -\hline -ACTIVE & on & off & on & 9.72 \\ -\hline -SLEEP & off & off & off & 0.02 \\ -\hline -COMPUTATION & on & on & on & 26.83 \\ -%\hline -%\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\ - \hline +\caption{Power consumption values} +\label{tab:EC} +\begin{tabular}{|l||cccc|} + \hline + {\bf Sensor status} & MCU & Radio & Sensor & {\it Power (mW)} \\ + \hline + LISTENING & On & On & On & 20.05 \\ + ACTIVE & On & Off & On & 9.72 \\ + SLEEP & Off & Off & Off & 0.02 \\ + COMPUTATION & On & On & On & 26.83 \\ + \hline + \multicolumn{4}{|l}{Energy needed to send or receive a 2-bit content message} & 0.515 \\ + \hline \end{tabular} - -\label{table1} -% is used to refer this table in the text \end{table} \indent For the sake of simplicity we ignore the energy needed to turn on the radio, to start up the sensor node, to move from one status to another, etc. Thus, when a sensor becomes active (i.e., it has already received its status from leader), it can turn its radio off to save battery. DiLCO uses two types of packets for communication. The size of the INFO packet and ActiveSleep packet -are 112 bits and 16 bits respectively. The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{ref112} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets. The energy needed to send or receive a 1-bit packet is equal to $0.2575~mW$. +are 112 bits and 16 bits respectively. The value of energy spent to send a 2-bit-content message is obtained by using the equation in ~\cite{ref112} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets. The energy needed to send or receive a 1-bit packet is equal to $0.2575~mW$. %We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}. diff --git a/CHAPITRE_06.tex b/CHAPITRE_06.tex index dc74d83..aeb9ffa 100644 --- a/CHAPITRE_06.tex +++ b/CHAPITRE_06.tex @@ -1,6 +1,6 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% -%% CHAPTER 06 %% +%% CHAPTER 06 %% %% %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{ Perimeter-based Coverage Optimization to Improve Lifetime in WSNs} @@ -36,8 +36,9 @@ we considered (in particular the perimeter coverage one), second we describe the \subsection{Assumptions and Models} \label{ch6:sec:02:01} The PeCO protocol uses the same assumptions and network model than both the DiLCO and the MuDiLCO protocols. All the hypotheses can be found in section \ref{ch4:sec:02:01}. -The PeCO protocol uses the same perimeter-coverage model as Huang and Tseng in~\cite{ref133}. It can be expressed as follows: a sensor is said to be a 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 -$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). +The PeCO protocol uses the same perimeter-coverage model as Huang and Tseng in~\cite{ref133}. It can be expressed as follows: a sensor is said to be a 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 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). +Authors \cite{ref133} proved that a network area is $k$-covered (every point in the area is covered by at least $k$~sensors) if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this figure, we can see that sensor~$0$ has nine neighbors and we have reported on its perimeter (the perimeter of the disk covered by the sensor) for each neighbor the two points resulting from intersection of the two sensing @@ -56,18 +57,21 @@ arcs. \end{figure} Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the locations of the left and right points of an arc on the perimeter of a sensor node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the -west side of sensor~$u$, with the following respective coordinates in the 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: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s} -\right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi - - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$. +west side of sensor~$u$, with the following respective coordinates in the sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates, the euclidean distance between nodes~$u$ and $v$ is computed as follow: $Dist(u,v)=\sqrt{\vert + u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, + +while the angle~$\alpha$ is obtained through the formula: + + $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s} +\right).$$ + +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 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 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 $0$. -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. - +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. \begin{figure*}[t!] \centering @@ -107,7 +111,8 @@ above is thus given by the sixth line of the table. \end{table} -In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated as an integer program based on coverage intervals. The formulation of the coverage optimization problem is detailed in~section~\ref{ch6:sec:03}. 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 $\infty$ and the corresponding interval will not be taken into account by the optimization algorithm. +%In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated as an integer program based on coverage intervals. +In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an mixed-integer program based on coverage intervals~\cite{ref239}. The formulation of the coverage optimization problem is detailed in~section~\ref{ch6:sec:03}. 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 $\infty$ and the corresponding interval will not be taken into account by the optimization algorithm. \begin{figure}[h!] @@ -125,10 +130,7 @@ In the PeCO protocol, the scheduling of the sensor nodes' activities is formul \subsection{The Main Idea} \label{ch6:sec:02:02} -\noindent The WSN area of interest is, in a first step, divided into regular -homogeneous subregions using a divide-and-conquer algorithm. In a second step -our protocol will be executed in a distributed way in each subregion -simultaneously to schedule nodes' activities for one sensing period. +\noindent The WSN area of interest is, in a first step, divided into regular homogeneous subregions using a divide-and-conquer algorithm. In a second step our protocol will be executed in a distributed way in each subregion simultaneously to schedule nodes' activities for one sensing period. Sensor nodes are assumed to be deployed almost uniformly over the region. The regular subdivision is made such that the number of hops between any pairs of sensors inside a subregion is less than or equal to 3. 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 PeCO, are more robust against an unexpected node failure. On the one hand, if 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 the next period. 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 (INFO Exchange, Leader Election, and Decision) @@ -198,39 +200,34 @@ protocol applied by a sensor node $s_j$ where $j$ is the node index in the WSN. \label{alg:PeCO} \end{algorithm} -In this algorithm, A.CurrentSize and A.PreviousSize respectively represent the -current number and the previous number of living nodes in the subnetwork of the -subregion. Initially, the sensor node checks its remaining energy $RE_j$, 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 numbers 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, A.CurrentSize and A.PreviousSize respectively represent the current number and the previous number of living nodes in the subnetwork of the subregion. Initially, the sensor node checks its remaining energy $RE_j$, 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 numbers 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. +The sensors inside a same region cooperate to elect a leader. The selection criteria for the leader are (in order of priority): +\begin{enumerate} +\item larger number of neighbors; +\item larger remaining energy; +\item and then in case of equality, larger index. +\end{enumerate} +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. \section{Perimeter-based Coverage Problem Formulation} \label{ch6:sec:03} -\noindent In this section, the coverage model is mathematically formulated. We -start with a description of the notations that will be used throughout the -section. +\noindent In this section, the perimeter-based coverage problem is mathematically formulated. It has been proved to be a NP-hard problem by \cite{ref239}. Authors study the coverage of the perimeter of a large object requiring to be monitored. For the proposed formulation in this chapter, the large object to be monitored is the sensor itself (or more precisely its sensing area). + +The following notations are used throughout the section. -First, we have the following sets: +First, the following sets: \begin{itemize} -\item $J$ represents the set of sensor nodes; -\item $A \subseteq J $ is the subset of alive sensors; +\item $S$ represents the set of sensor nodes; +\item $A \subseteq S $ is the subset of alive sensors; \item $I_j$ designates the set of coverage intervals (CI) obtained for - sensor~$j$, which have been defined according to the method introduced in section~\ref{ch6:sec:02:01}. + sensor~$j$. \end{itemize} -First, for a coverage interval $i$, let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved -in coverage interval~$i$ of sensor~$j$, that is: +$I_j$ refers to the set of coverage intervals which have been defined according to the method introduced in subsection~\ref{ch6:sec:02:01}. For a coverage interval $i$, let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved in coverage interval~$i$ of sensor~$j$, that is: \begin{equation} a^j_{ik} = \left \{ \begin{array}{lll} @@ -238,64 +235,32 @@ a^j_{ik} = \left \{ & \mbox{coverage interval $i$ of sensor $j$}, \\ 0 & \mbox{otherwise.}\\ \end{array} \right. -%\label{eq12} -\notag \end{equation} Note that $a^k_{ik}=1$ by definition of the interval. -Second, we define several binary and integer variables. Hence, each binary -variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase -($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer -variable which measures the undercoverage for the coverage interval $i$ -corresponding to sensor~$j$. In the same way, the overcoverage for the same -coverage interval is given by the variable $V^j_i$. - -If we decide to sustain a level of coverage equal to $l$ all along the perimeter -of sensor $j$, we have to ensure that at least $l$ sensors involved in each -coverage interval $i \in I_j$ of sensor $j$ are active. According to the -previous notations, the number of active sensors in the coverage interval $i$ of -sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network -lifetime, the objective is to activate a minimal number of sensors in each -period to ensure the desired coverage level. As the number of alive sensors -decreases, it becomes impossible to reach the desired level of coverage for all -coverage intervals. Therefore, we use variables $M^j_i$ and $V^j_i$ as a measure -of the deviation between the desired number of active sensors in a coverage -interval and the effective number. And we try to minimize these deviations, -first to force the activation of a minimal number of sensors to ensure the -desired coverage level, and if the desired level cannot be completely satisfied, -to reach a coverage level as close as possible to the desired one. - -Our coverage optimization problem can then be mathematically expressed as follows: -%Objective: -\begin{equation} %\label{eq:ip2r} -\left \{ -\begin{array}{ll} -\min \sum_{j \in J} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\ -\textrm{subject to :}&\\ -\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in J\\ -%\label{c1} -\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in J\\ -% \label{c2} -% \Theta_{p}\in \mathbb{N}, &\forall p \in P\\ -% U_{p} \in \{0,1\}, &\forall p \in P\\ -X_{k} \in \{0,1\}, \forall k \in A -\end{array} -\right. -\notag +Second, several variables are defined. Hence, each binary variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is a variable which measures the undercoverage for the coverage interval $i$ corresponding to sensor~$j$. In the same way, the overcoverage for the same coverage interval is given by the variable $V^j_i$. + +To sustain a level of coverage equal to $l$ all along the perimeter of sensor $j$, at least $l$ sensors involved in each coverage interval $i \in I_j$ of sensor $j$ have to be active. According to the previous notations, the number of active sensors in the coverage interval $i$ of sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network lifetime, the objective is to activate a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to reach the desired level of coverage for all coverage intervals. Therefore +variables $M^j_i$ and $V^j_i$ are introduced as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the desired coverage level, and if the desired level cannot be completely satisfied, to reach a coverage level as close as possible to the desired one. + +The coverage optimization problem can then be mathematically expressed as follows: +\begin{equation} + \begin{aligned} + \text{Minimize } & \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) \\ + \text{Subject to:} & \\ + & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S \\ + & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S \\ + & X_{k} \in \{0,1\}, \forall k \in A \\ + & M^j_i, V^j_i \in \mathbb{R}^{+} + \end{aligned} \end{equation} -$\alpha^j_i$ 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 by a relatively larger magnitude than weights associated with another -region. This kind of an 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 -each subregion at the beginning of each sensing phase, whenever the environment -has changed (new leader, death of some sensors). Note that the number of -constraints in the model is constant (constraints of coverage expressed for all -sensors), whereas the number of variables $X_k$ decreases over periods, since we -consider only alive sensors (sensors with enough energy to be alive during one -sensing phase) in the model. + +If a given level of coverage $l$ is required for one sensor, the sensor is said to be undercovered (respectively overcovered) if the level of coverage of one of its CI is less (respectively greater) than $l$. If the sensor $j$ is undercovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. Conversely, if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is greater than $l$ and in this case: $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$. + +$\alpha^j_i$ 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 by a relatively larger magnitude than weights associated with another region. This kind of mixed-integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \cite{0031-9155-44-1-012}. The choice of the values for variables $\alpha$ and $\beta$ should be made according to the needs of the application. $\alpha$ should be large enough to prevent undercoverage and so to reach the highest +possible coverage ratio. $\beta$ should be large enough to prevent overcoverage and so to activate a minimum number of sensors. The mixed-integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since only alive sensors (sensors with enough energy to be alive during one sensing phase) are considered in the model. + + \section{Performance Evaluation and Analysis} \label{ch6:sec:04} @@ -303,54 +268,15 @@ sensing phase) in the model. \subsection{Simulation Settings} \label{ch6:sec:04:01} -The WSN area of interest is supposed to be divided into 16~regular subregions. The simulation parameters are summarized in Table~\ref{tablech4}. -%Table~\ref{table3} gives the chosen parameters settings. -%\begin{table}[ht] -%\caption{Relevant parameters for network initialization.} -%\centering -%\begin{tabular}{c|c} -%\hline -%Parameter & Value \\ [0.5ex] -%\hline -%Sensing field & $(50 \times 25)~m^2 $ \\ -%WSN size & 100, 150, 200, 250, and 300~nodes \\ -%Initial energy & in range 500-700~Joules \\ -%Sensing period & duration of 60 minutes \\ -%$E_{th}$ & 36~Joules\\ -%$R_s$ & 5~m \\ -%$\alpha^j_i$ & 0.6 \\ -%$\beta^j_i$ & 0.4 -%\end{tabular} -%\label{table3} -%\end{table} -To obtain experimental results which are relevant, simulations with five different node densities going from 100 to 300~nodes were performed considering each time 25~randomly generated networks. The nodes are deployed on a field of +The WSN area of interest is supposed to be divided into 16~regular subregions. The simulation parameters are summarized in Table~\ref{tablech4}. To obtain experimental results which are relevant, simulations with five different node densities going from 100 to 300~nodes were performed considering each time 25~randomly generated networks. The nodes are deployed on a field of interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a high coverage ratio. %Each node has an initial energy level, in Joules, which is randomly drawn in the interval $[500-700]$. If its energy provision reaches a value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a node to stay active during one period, it will no more participate in the coverage task. This value corresponds to the energy needed by the sensing phase, obtained by multiplying the energy consumed in active state (9.72 mW) with the time in seconds for one period (3600 seconds), and adding the energy for the pre-sensing phases. According to the interval of initial energy, a sensor may be active during at most 20 periods. +%The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good network coverage and a longer WSN lifetime as shown in Table \ref{my-beta-alfa}. We set the values of $\alpha^j_i$ and $\beta^j_i$ to 0.6 and 0.4 respectively. We have given a higher priority to the undercoverage (by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the sensor~$j$. On the other hand, we have assigned to $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval. -The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good network coverage and a longer WSN lifetime as shown in Table \ref{my-beta-alfa}. We set the values of $\alpha^j_i$ and $\beta^j_i$ to 0.6 and 0.4 respectively. We have given a higher priority to the undercoverage (by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the sensor~$j$. On the other hand, we have assigned to -$\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval. +The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good network coverage and a longer WSN lifetime. Higher priority is given to the undercoverage (by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the sensor~$j$. On the other hand, $\beta^j_i$ is assigned to a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval. Section~\ref{sec:Impact} investigates more deeply how the values of +both parameters affect the performance of PeCO protocol. -\begin{table}[h] -\centering -\caption{The impact of $\alpha^j_i$ and $\beta^j_i$ on PeCO's performance for 200 deployed nodes} -\label{my-beta-alfa} -\begin{tabular}{|c|c|c|c|} -\hline -$\alpha^j_i$ & $\beta^j_i$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline -0.0 & 1.0 & 151 & 0 \\ \hline -0.1 & 0.9 & 145 & 0 \\ \hline -0.2 & 0.8 & 140 & 0 \\ \hline -0.3 & 0.7 & 134 & 0 \\ \hline -0.4 & 0.6 & 125 & 0 \\ \hline -0.5 & 0.5 & 118 & 30 \\ \hline -0.6 & 0.4 & 94 & 57 \\ \hline -0.7 & 0.3 & 97 & 49 \\ \hline -0.8 & 0.2 & 90 & 52 \\ \hline -0.9 & 0.1 & 77 & 50 \\ \hline -1.0 & 0.0 & 60 & 44 \\ \hline -\end{tabular} -\end{table} With the performance metrics, described in section \ref{ch4:sec:04:04}, we evaluate the efficiency of our approach. We use the modeling language and the optimization solver which are mentioned in section \ref{ch4:sec:04:02}. In addition, we use the same energy consumption model, as previously, described in section \ref{ch4:sec:04:03}. @@ -368,16 +294,8 @@ PeCO protocol is compared with three other approaches. DESK \cite{DESK}, GAF~\c \subsubsection{Coverage Ratio} \label{ch6:sec:04:02:01} -Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better -coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\% -produced by PeCO for the first periods. This is due to the fact that at the -beginning the DiLCO protocol puts to sleep status more redundant sensors (which -slightly decreases the coverage ratio), while the three other protocols activate -more sensor nodes. Later, when the number of periods is beyond~70, it clearly -appears that PeCO provides a better coverage ratio and keeps a coverage ratio -greater than 50\% for longer periods (15 more compared to DiLCO, 40 more -compared to DESK). The energy saved by PeCO in the early periods allows later a -substantial increase of the coverage performance. +Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\% produced by PeCO for the first periods. This is due to the fact that at the beginning the DiLCO and PeCO protocols put to sleep status more redundant sensors (which slightly decreases the coverage ratio), while the two other protocols activate more sensor nodes. Later, when the number of periods is beyond~70, it clearly +appears that PeCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK). The energy saved by PeCO in the early periods allows later a substantial increase of the coverage performance. \parskip 0pt \begin{figure}[h!] @@ -392,15 +310,8 @@ substantial increase of the coverage performance. \subsubsection{Active Sensors Ratio} \label{ch6:sec:04:02:02} -Having the less active sensor nodes in each period is essential to minimize the -energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444} -shows the average active nodes ratio for 200 deployed nodes. We observe that -DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen -rounds and DiLCO and PeCO protocols compete perfectly with only 17.92 \% and -20.16 \% active nodes during the same time interval. As the number of periods -increases, PeCO 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}. +Having the less active sensor nodes in each period is essential to minimize the energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 200 deployed nodes. We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds, and DiLCO and PeCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, PeCO 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}. \begin{figure}[h!] \centering @@ -412,15 +323,8 @@ Figure \ref{fig333}. \subsubsection{Energy Consumption} \label{ch6:sec:04:02:03} -We studied the effect of the energy consumed by the WSN during the communication, -computation, listening, active, and sleep status for different network densities -and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b) -illustrate the energy consumption for different network sizes and for -$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the -most competitive from the energy consumption point of view. As shown in both -figures, PeCO consumes much less energy than the three other methods. \\ \\ \\ \\ \\ \\ - -One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed the optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level. +We studied the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep status for different network densities and the four approaches compared. Figures~\ref{fig3EC}(a) and (b) illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the most competitive from the energy consumption point of view. As shown by both figures, PeCO consumes much less energy than the other methods. +One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed the optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level. Let us notice that the energy overhead when increasing network size is the lowest with PeCO. \begin{figure}[h!] \centering @@ -438,10 +342,10 @@ One might think that the resolution of the integer program is too costly in e \label{ch6:sec:04:02:04} We observe the superiority of PeCO and DiLCO protocols in comparison with the two other approaches in prolonging the network lifetime. In -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 largest for the DiLCO and the PeCO 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 is about twice longer with the PeCO compared to the 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 time, and the lifetime with a coverage of 50\% is far longer than with +Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for different network sizes. As can be seen in these figures, the lifetime increases with the size of the network, and it is clearly largest for the DiLCO and the PeCO 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 is about twice longer with the PeCO compared to the 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 time, and the lifetime with a coverage of 50\% is far longer than with 95\%. -\begin{figure} [p] +\begin{figure} [h!] \centering \begin{tabular}{@{}cr@{}} \includegraphics[scale=0.8]{Figures/ch6/R/LT95.eps} & \raisebox{4cm}{(a)} \\ @@ -451,20 +355,45 @@ Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for \label{fig3LT} \end{figure} -Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for -different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85, -Protocol/90, and Protocol/95 the amount of time during which the network can -satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ -respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications that do not require a 100\% coverage of the area to be monitored. PeCO might be an interesting method since it achieves a good balance between a high level coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three lower coverage ratios, moreover the improvements grow with the network size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is not ineffective for the smallest network sizes. +Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications that do not require a 100\% coverage of the area to be monitored. PeCO might be an interesting method since it achieves a good balance between a high level coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three lower coverage ratios, moreover the improvements grow with the network size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is not ineffective for the smallest network sizes. -\begin{figure} [p] +\begin{figure} [h!] \centering \includegraphics[scale=0.8]{Figures/ch6/R/LTa.eps} \caption{Network lifetime for different coverage ratios.} \label{figLTALL} \end{figure} +\subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance} +\label{sec:Impact} + +Table~\ref{my-labelx} shows network lifetime results for different values of $\alpha$ and $\beta$, and a network size equal to 200 sensor nodes. On the one hand, the choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit the activation of a large number of sensors, but as $\alpha$ is low, some areas may be poorly covered. This explains the results obtained for {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. On the other hand, when we choose $\alpha \gg \beta$, we favor the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network +lifetime is reduced. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ +The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio. That explains why we have chosen this setting for the experiments presented in the previous subsections. + +\begin{table}[h!] +\centering +\caption{The impact of $\alpha$ and $\beta$ on PeCO's performance} +\label{my-labelx} +\begin{tabular}{|c|c|c|c|} +\hline +$\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline +0.0 & 1.0 & 151 & 0 \\ \hline +0.1 & 0.9 & 145 & 0 \\ \hline +0.2 & 0.8 & 140 & 0 \\ \hline +0.3 & 0.7 & 134 & 0 \\ \hline +0.4 & 0.6 & 125 & 0 \\ \hline +0.5 & 0.5 & 118 & 30 \\ \hline +{\bf 0.6} & {\bf 0.4} & {\bf 94} & {\bf 57} \\ \hline +0.7 & 0.3 & 97 & 49 \\ \hline +0.8 & 0.2 & 90 & 52 \\ \hline +0.9 & 0.1 & 77 & 50 \\ \hline +1.0 & 0.0 & 60 & 44 \\ \hline +\end{tabular} +\end{table} + + - %\FloatBarrier + \section{Conclusion} \label{ch6:sec:05} diff --git a/Resume.tex b/Resume.tex index 978f736..e3dbc74 100644 --- a/Resume.tex +++ b/Resume.tex @@ -19,21 +19,21 @@ Les réseaux de capteurs sans fil ont suscité beaucoup de travaux de recherche au cours des dernières années en raison de leur large gamme d'applications potentielles. Les caractéristiques des n\oe uds capteurs imposent des contraintes de consommation d'énergie et de capacité de traitement qui rendent caduque les protocoles des réseaux ad-hoc sans fil, avec de nombreux défis à résoudre. Parmi ces défis, on peut noter la préservation de la couverture, le contrôle de la topologie, le routage, la fusion de données, la sécurité, etc. La préservation de la couverture d'une région à surveiller, de manière permanente et efficace, tout en empêchant autant que possible un dysfonctionnement du réseau en raison du déchargement de la batterie de certains n\oe uds, est une des problématiques de recherche majeures. -Dans cette thèse, nous nous sommes intéressés au problème de la préservation de la couverture, ainsi qu'à l'efficatité qui est une exigence essentielle dans un réseau de capteurs sans fil. Nous avons étudié les protocoles d'optimisation distribués avec l'objectif ultime de prolonger la durée de vie opérationnelle du réseau. Les protocoles proposés doivent être efficaces en consommation énergétique induite par les calculs et les communications. Pour résoudre le problème, nous avons proposé des nouvelles approches en deux étapes. Dans un premier temps, la région à surveiller est divisée en petites sous-régions en utilisant le concept de la méthode diviser pour mieux régner. Dans un second temps, un protocole est exécuté par chacun des n\oe uds capteurs dans chaque sous-région, afin d'optimiser la couverture et la durée de vie du réseau. Nous proposons trois protocoles distribués qui combinent, chacun, deux techniques efficaces: l'élection d'un n\oe ud leader dans chaque sous-région, suivie par la mise en oeuvre par celui-ci d'un processus de décision via l'optimisation de l'ordonnancement d'activité des n\oe uds capteurs de sa sous-région. +Dans cette thèse, nous nous sommes intéressés au problème de la préservation de la couverture, ainsi qu'à efficacité qui est une exigence essentielle dans un réseau de capteurs sans fil. Nous avons étudié les protocoles d'optimisation distribués avec l'objectif de prolonger la durée de vie opérationnelle du réseau. Les protocoles proposés doivent être efficaces en consommation énergétique induite par les calculs et les communications. Pour résoudre le problème, nous avons proposé des nouvelles approches qui s'articulen autour de deux étapes. Dans un premier temps, la région à surveiller est divisée en petites sous-régions en utilisant le concept de la méthode diviser pour mieux régner. Dans un second temps, un protocole est exécuté par chacun des n\oe uds capteurs dans chaque sous-région, afin d'optimiser la couverture et la durée de vie du réseau. Nous proposons trois protocoles distribués qui combinent, chacun, deux techniques efficaces: l'élection d'un n\oe ud leader dans chaque sous-région, suivie par la mise en oeuvre par celui-ci d'un processus d'ordonnancement d'activité des n\oe uds capteurs de sa sous-région. -Le premier protocole proposé est appelé DiLCO, pour Distributed Lifetime Coverage Optimization. Dans ce protocole, la durée de vie est divisée en périodes, avec chaque période qui est composée de 4 phases: échange d'informations entre les n\oe uds d'une sous-région, élection d'un n\oe ud leader, décision et surveillance. Le processus de décision est mis en oeuvre par le n\oe ud leader en résolvant un programme linéaire en nombres entiers qui permet de définir un seul ensemble de n\oe uds de capteurs devant être actifs pour assurer la couverture durant la période courante. +Le premier protocole proposé est appelé DiLCO, pour Distributed Lifetime Coverage Optimization. Dans ce protocole, la durée de vie est divisée en périodes, avec chaque période qui est composée de 4 phases: échange d'informations entre les n\oe uds d'une sous-région, élection d'un n\oe ud leader, phase de décision et surveillance. Le processus de décision est mis en oeuvre par le n\oe ud leader en résolvant un programme linéaire en nombres entiers qui permet de définir l'ensemble des n\oe uds de capteurs devant être actifs pour assurer la couverture durant la période courante. -Dans le second protocole, qui est une évolution de DiLCO, nous cherchons à construire simultanément plusieurs ensembles de n\oe uds de capteurs de couverture pour la phase de surveillance. Cette dernière est ainsi divisée en "rondes" de surveillance, d'où le nom Multiround DiLCO ou MuDiLCO donné à ce protocole. Le processus de décision est toujours effectué par un n\oe ud leader, qui détermine les ensembles de n\oe uds capteurs à activer successivement via la résolution d'un nouveau programme linéaire en nombres entiers. +Dans le second protocole, qui est une évolution de DiLCO, nous cherchons à construire simultanément plusieurs ensembles de n\oe uds de capteurs de couverture pour la phase de surveillance. Cette dernière est ainsi divisée en "rounds" de surveillance, d'où le nom Multiround DiLCO ou MuDiLCO donné à ce protocole. Le processus de décision est toujours effectué par un n\oe ud leader, qui détermine les ensembles de n\oe uds capteurs à activer successivement via la résolution d'un nouveau programme linéaire en nombres entiers. %Ensuite, nous avons étudié le problème de l'optimisation multi-ronde de la zone de couverture dans un réseau de capteurs sans fil. Nous avons proposé le protocole d'optimisation multi-ronde distribué de la durée de vie de couverture (MuDiLCO) pour étudier la possibilité de fournir plusieurs ensembles de n\oe uds de capteurs de couverture pour la phase de surveillance. Ce protocole travaille également en périodes pendant lesquelles les ensembles de capteurs sont programmés pour rester actifs pour un certain nombre de rondes durant la phase de surveillance, pour assurer la couverture et maximiser la durée de vie du réseau. Le processus de décision est toujours effectué par le n\oe ud leader qui résout un programme entier pour définir un meilleur ensemble de capteurs à être utilisé pendant les rondes de la phase de surveillance. -Enfin, nous avons proposé un protocole d'optimisation de la couverture basé sur le périmètre des n\oe uds de capteurs (PeCO), qui est aussi un protocole distribué sur les n\oe uds de capteurs dans chaque sous-région. Notre contribution dans ce protocole consiste essentiellement dans la proposition d'un nouveau modèle mathématique de l'optimisation basé sur le périmètre de couverture pour l'ordonnancement de l'activité des capteurs. Un nouveau programme entier du modèle de couverture est résolu par le leader durant la phase de décision pour définir un ensemble de capteurs de couverture pour la phase de surveillance. +Enfin, nous avons proposé un protocole d'optimisation de la couverture basé sur la couverture périmètre du capteurs (PeCO), qui est aussi un protocole distribué sur les n\oe uds de capteurs dans chaque sous-région. Notre contribution dans ce protocole consiste essentiellement dans la proposition d'un nouveau modèle d'optimisation basé sur le périmètre de couverture pour l'ordonnancement de l'activité des capteurs. Ce modèle de couverture est résolu par le leader durant la phase de décision pour définir un ensemble de capteurs actifs pour la phase de surveillance. -Nous avons effectué plusieurs simulations en utilisant le simulateur à évènements discrets OMNeT++ pour valider l'efficacité de nos protocoles proposés. Nous avons pris en considération les caractéristiques d'un capteur Medusa II pour la consommation d'énergie et le temps de calcul. En comparaison avec deux autres méthodes existantes, nos protocoles ont la capacité d'augmenter la durée de vie du réseau de capteurs et d'améliorer les performances de couverture. +Nous avons effectué plusieurs simulations en utilisant le simulateur à évènements discrets OMNeT++ pour valider l'efficacité de nos protocoles. Nous avons pris en considération les caractéristiques d'un capteur Medusa II pour la consommation d'énergie et le temps de calcul. En comparaison avec deux autres méthodes existantes, nos protocoles ont la capacité d'augmenter la durée de vie du réseau de capteurs et d'améliorer les performances de couverture. \textbf{MOTS-CLÉS:} Réseaux de capteurs sans fil, Zone de couverture, Durée de vie du réseau, Optimisation Distribué, Ordonnancement. diff --git a/Thesis.toc b/Thesis.toc index 44067d7..5d6f069 100644 --- a/Thesis.toc +++ b/Thesis.toc @@ -94,8 +94,9 @@ \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}Energy Consumption}{120}{subsubsection.6.4.2.3} -\contentsline {subsubsection}{\numberline {6.4.2.4}Network Lifetime}{122}{subsubsection.6.4.2.4} +\contentsline {subsubsection}{\numberline {6.4.2.3}Energy Consumption}{121}{subsubsection.6.4.2.3} +\contentsline {subsubsection}{\numberline {6.4.2.4}Network Lifetime}{121}{subsubsection.6.4.2.4} +\contentsline {subsubsection}{\numberline {6.4.2.5}Impact of $\alpha $ and $\beta $ on PeCO's performance}{122}{subsubsection.6.4.2.5} \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} diff --git a/bib.bib b/bib.bib index 1dada04..24ed356 100644 --- a/bib.bib +++ b/bib.bib @@ -2257,3 +2257,11 @@ pages={1-6} year={2009}, publisher={Wiley} } + +@article{ref239, +author = {Hung, Ka-Shun and Lui, King-Shan}, +title = {Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors with a Single Continuous Cover Range}, +journal = {EURASIP Journal on Wireless Communications and Networking }, +volume = {2010}, +year = {2010} +} \ No newline at end of file -- 2.39.5