X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/ThesisAli.git/blobdiff_plain/ea03ef6a15b12c2b2cd5cdee7f72ca18a520c387..39f66164c5b581dc95a199af18b58643b7c7a11b:/CHAPITRE_06.tex

diff --git a/CHAPITRE_06.tex b/CHAPITRE_06.tex
index 31e696c..f4e8bb0 100644
--- a/CHAPITRE_06.tex
+++ b/CHAPITRE_06.tex
@@ -3,47 +3,21 @@
 %%       CHAPTER 06        %%
 %%                          %%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\chapter{Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}
+ \chapter{ Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}
 \label{ch6}
 
-\iffalse
-
-\section{Summary}
-\label{ch6:sec:01}
-
-The most important problem in a Wireless Sensor Network (WSN) is to optimize the
-use of its limited energy provision so that it can fulfill its monitoring task
-as long as  possible. Among  known  available approaches  that can  be used  to
-improve  power  management,  lifetime coverage  optimization  provides  activity
-scheduling which ensures sensing coverage while minimizing the energy cost. In
-this paper,  we propose such an approach called Perimeter-based Coverage Optimization
-protocol (PeCO). It is a  hybrid of centralized and distributed methods: the
-region of interest is first subdivided into subregions and our protocol is then
-distributed among sensor nodes in each  subregion.
-The novelty of our approach lies essentially in the formulation of a new
-mathematical optimization  model based on the  perimeter coverage level  to schedule
-sensors' activities.  Extensive simulation experiments have been performed using
-OMNeT++, the  discrete event simulator, to  demonstrate that PeCO  can
-offer longer lifetime coverage for WSNs in comparison with some other protocols.
-
-
-\fi
-
 
 \section{Introduction}
 \label{ch6:sec:01}
 
-The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
-wireless communication hardware  has given rise to the opportunity to use large
-networks of tiny sensors, called Wireless Sensor Networks (WSN)~\cite{ref1,ref223}, to fulfill monitoring tasks. The features of a WSN made it suitable for a wide
-range of application  in areas such as business,  environment, health, industry,
-military, and so on~\cite{ref4}. These large number of applications have led to different design, management, and operational challenges in WSNs. The challenges become harder with considering into account the main limited capabilities of the sensor nodes such memory, processing, battery life,  bandwidth, and short radio ranges. One important feature that distinguish the WSN from the other types of wireless networks is the provision of the sensing capability for the sensor nodes \cite{ref224}.
+%The continuous progress in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware  has given rise to the opportunity to use large networks of tiny sensors, called Wireless Sensor Networks (WSN)~\cite{ref1,ref223}, to fulfill monitoring tasks. The features of a WSN made it suitable for a wide range of application  in areas such as business,  environment, health, industry, military, and so on~\cite{ref4}. These large number of applications have led to different design, management, and operational challenges in WSNs. The challenges become harder with considering into account the main limited capabilities of the sensor nodes such memory, processing, battery life,  bandwidth, and short radio ranges. One important feature that distinguish the WSN from the other types of wireless networks is the provision of the sensing capability for the sensor nodes \cite{ref224}.
 
-The sensor node consumes some energy both in performing the sensing task and in transmitting the sensed data to the sink. Therefore, it is required to activate as less number as possible of sensor nodes that can monitor the whole area of interest so as to reduce the data volume and extend the network lifetime. The sensing coverage is the most important task of the WSNs since sensing unit of the sensor node is responsible for measuring physical,  chemical, or  biological  phenomena in the sensing field. The main challenge of any sensing coverage problem is to discover the redundant sensor node and turn off those nodes in WSN \cite{ref225}. The redundant sensor node is a node whose sensing area is covered by its active neighbors. In previous works, several approaches are used to find out the redundant node such as Voronoi diagram method, sponsored sector, crossing coverage, and perimeter coverage. 
+%The sensor node consumes some energy both in performing the sensing task and in transmitting the sensed data to the sink. Therefore, it is required to activate as less number as possible of sensor nodes that can monitor the whole area of interest so as to reduce the data volume and extend the network lifetime. The sensing coverage is the most important task of the WSNs since sensing unit of the sensor node is responsible for measuring physical,  chemical, or  biological  phenomena in the sensing field. The main challenge of any sensing coverage problem is to discover the redundant sensor node and turn off those nodes in WSN \cite{ref225}. The redundant sensor node is a node whose sensing area is covered by its active neighbors. In previous works, several approaches are used to find out the redundant node such as Voronoi diagram method, sponsored sector, crossing coverage, and perimeter coverage. 
 
-In this chapter,  we propose such an approach called Perimeter-based Coverage Optimization
-protocol (PeCO). The PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages. An energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. 
+In this chapter,  we propose an approach called Perimeter-based Coverage Optimization
+protocol (PeCO). 
+%The PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages. An energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. 
+The framework is similar to the one described in chapter 4, section \ref{ch4:sec:02:03}, but in this approach, the optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. 
 
 
 The rest of the chapter is  organized as follows. The next section is devoted to the PeCO protocol description and section~\ref{ch6:sec:03} focuses on the
@@ -109,7 +83,7 @@ obtained through  the formula: $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 Every couple of intersection points is placed on the angular interval $[0,2\pi]$
 in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
 Figure~\ref{pcm2sensors}(a)  illustrates  the arcs  for  the  nine neighbors  of
-sensor $0$ and  Figure~\ref{expcm} gives the position of  the corresponding arcs
+sensor $0$ and  Figure~\ref{expcm} gives the position of the corresponding arcs
 in  the interval  $[0,2\pi]$. More  precisely, we  can see  that the  points are
 ordered according  to the  measures of  the angles  defined by  their respective
 positions. The intersection points are  then visited one after another, starting
@@ -174,8 +148,9 @@ In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formul
 \end{figure} 
 
 
-
-
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This section deleted %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\iffalse
 
 \subsection{The Main Idea}
 \label{ch6:sec:02:02}
@@ -196,8 +171,9 @@ are energy consuming, even for nodes that will not join the set cover to monitor
 \label{fig2}
 \end{figure} 
 
-
-
+\fi
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \subsection{PeCO Protocol Algorithm}
 \label{ch6:sec:02:03}
@@ -205,7 +181,7 @@ are energy consuming, even for nodes that will not join the set cover to monitor
 
 \noindent The  pseudocode implementing the protocol on a node is  given below.
 More  precisely,  Algorithm~\ref{alg:PeCO}  gives  a brief  description  of  the
-protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
+protocol applied by a sensor node $s_j$ where $j$ is the node index in the WSN.
 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}
@@ -214,47 +190,47 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
   %\emph{Initialize the sensor node and determine it's position and subregion} \; 
   
   \If{ $RE_k \geq E_{th}$ }{
-      \emph{$s_k.status$ = COMMUNICATION}\;
+      \emph{$s_j.status$ = COMMUNICATION}\;
       \emph{Send $INFO()$ packet to other nodes in subregion}\;
       \emph{Wait $INFO()$ packet from other nodes in subregion}\; 
-      \emph{Update K.CurrentSize}\;
+      \emph{Update A.CurrentSize}\;
       \emph{LeaderID = Leader election}\;
-      \If{$ s_k.ID = LeaderID $}{
-         \emph{$s_k.status$ = COMPUTATION}\;
+      \If{$ s_j.ID = LeaderID $}{
+         \emph{$s_j.status$ = COMPUTATION}\;
          
-      \If{$ s_k.ID $ is Not previously selected as a Leader }{
+      \If{$ s_j.ID $ is Not previously selected as a Leader }{
           \emph{ Execute the perimeter coverage model}\;
          % \emph{ Determine the segment points using perimeter coverage model}\;
       }
       
-      \If{$ (s_k.ID $ is the same Previous Leader) And (K.CurrentSize = K.PreviousSize)}{
+      \If{$ (s_j.ID $ is the same Previous Leader) And (A.CurrentSize = A.PreviousSize)}{
       
       	 \emph{ Use the same previous cover set for current sensing stage}\;
       }
       \Else{
             \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
-            \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
-            \emph{K.PreviousSize = K.CurrentSize}\;
+            \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{A}\right)\right\}$ = Execute Integer Program Algorithm($A$)}\;
+            \emph{A.PreviousSize = A.CurrentSize}\;
            }
       
-        \emph{$s_k.status$ = COMMUNICATION}\;
-        \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;
-        \emph{Update $RE_k $}\;
+        \emph{$s_j.status$ = COMMUNICATION}\;
+        \emph{Send $ActiveSleep()$ to each node $k$ in subregion}\;
+        \emph{Update $RE_j $}\;
       }	  
       \Else{
-        \emph{$s_k.status$ = LISTENING}\;
+        \emph{$s_j.status$ = LISTENING}\;
         \emph{Wait $ActiveSleep()$ packet from the Leader}\;
-        \emph{Update $RE_k $}\;
+        \emph{Update $RE_j $}\;
       }  
   }
-  \Else { Exclude $s_k$ from entering in the current sensing stage}
-\caption{PeCO($s_k$)}
+  \Else { Exclude $s_j$ from entering in the current sensing stage}
+\caption{PeCO($s_j$)}
 \label{alg:PeCO}
 \end{algorithm}
 
-In this  algorithm, K.CurrentSize and K.PreviousSize  respectively represent the
+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 $RE_k$, which
+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
@@ -278,8 +254,8 @@ section.
 
 First, we have the following sets:
 \begin{itemize}
-\item $S$ represents the set of WSN sensor nodes;
-\item $A \subseteq S $ is the subset of alive sensors;
+\item $J$ represents the set of WSN sensor nodes;
+\item $A \subseteq J $ is the subset of alive sensors;
 \item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
   sensor~$j$.
 \end{itemize}
@@ -326,11 +302,11 @@ Our coverage optimization problem can then be mathematically expressed as follow
 \begin{equation} %\label{eq:ip2r}
 \left \{
 \begin{array}{ll}
-\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
+\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 S\\
+\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 S\\
+\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\\
@@ -399,26 +375,18 @@ 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.
+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.  We have given a higher priority to
-the  undercoverage  (by  setting  the  $\alpha^j_i$ with  a  larger  value  than
+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.
+$\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval.
 
-We applied the performance metrics, which are described in chapter 4, section \ref{ch4:sec:04:04} in order to evaluate the efficiency of our approach. We used the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 4, section \ref{ch4:sec:04:03}.
+With the performance metrics, described in chapter 4, 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 chapter 4, section \ref{ch4:sec:04:02}. In addition, we use the same energy consumption model, presented in chapter 4, section \ref{ch4:sec:04:03}.
 
 
 \subsection{Simulation Results}
@@ -517,9 +485,9 @@ is about twice longer with  PeCO compared to DESK protocol.  The performance
 difference    is    more    obvious   in    Figure~\ref{fig3LT}(b)    than    in
 Figure~\ref{fig3LT}(a) because the gain induced  by our protocols increases with
  time, and the lifetime with a coverage  of 50\% is far  longer than with
-95\%.
+95\%. 
 
-\begin{figure}[h!]
+\begin{figure} [p]
   \centering
   \begin{tabular}{@{}cr@{}}
     \includegraphics[scale=0.8]{Figures/ch6/R/LT95.eps} & \raisebox{4cm}{(a)} \\  
@@ -541,15 +509,15 @@ 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}[h!]
+\begin{figure} [p]
 \centering \includegraphics[scale=0.8]{Figures/ch6/R/LTa.eps}
 \caption{Network lifetime for different coverage ratios.}
 \label{figLTALL}
-\end{figure} 
-
+\end{figure}
 
 
-\section{Conclusion}
+ %\FloatBarrier
+\section{Conclusion} 
 \label{ch6:sec:05}
 
 In this chapter, we have studied the problem of  Perimeter-based Coverage Optimization in
