Update by Ali

[ThesisAli.git] / CHAPITRE_04.tex

diff --git a/CHAPITRE_04.tex b/CHAPITRE_04.tex
old mode 100755 (executable)
new mode 100644 (file)
index 603c6dd..07788db
--- a/CHAPITRE_04.tex
+++ b/CHAPITRE_04.tex
@@ -9,22 +9,20 @@
 
 
 
 
 
 

-\section{Summary}
+\section{Introduction}

 \label{ch4:sec:01}
 \label{ch4:sec:01}

-In this chapter, a Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
-the coverage and to improve  the  lifetime  in  wireless sensor  networks  is
-proposed.   The  area of  interest  is first  divided  into  subregions using  a
-divide-and-conquer  method and  then the  DiLCO protocol  is distributed  on the
-sensor nodes  in each  subregion. The DiLCO  combines two  efficient techniques:
-leader election  for each subregion, followed by  an optimization-based planning
-of activity  scheduling decisions for  each subregion. The proposed  DiLCO works
-into rounds during which a small  number of nodes, remaining active for sensing,
-is selected to ensure coverage so as to maximize the lifetime of wireless sensor
-network.   Each  round  consists   of  four  phases:  (i)~Information  Exchange,
-(ii)~Leader Election, (iii)~Decision, and (iv)~Sensing.  The decision process is
-carried out  by a leader node,  which solves an integer  program.  Compared with
-some existing protocols, simulation results  show that the proposed protocol can
-prolong the network lifetime and improve the coverage performance effectively.
+Energy efficiency is  a crucial issue in wireless  sensor networks since the sensory consumption, in  order to  maximize the network  lifetime, represents  the major difficulty when designing WSNs. As a consequence, one of the scientific research challenges in  WSNs, which has  been addressed by  a large amount  of literature
+during the  last few  years, is  the design of  energy efficient  approaches for coverage and connectivity~\cite{ref94}.   Coverage reflects how well a sensor  field is  monitored. On  the one  hand, we  want to  monitor the  area of interest in the most efficient way~\cite{ref95}.  On the other hand, we want to use  as little energy  as possible.   Sensor nodes  are battery-powered  with no means  of recharging  or replacing,  usually  due to  environmental (hostile  or
+unpractical environments)  or cost reasons.   Therefore, it is desired  that the WSNs are deployed  with high densities so as to  exploit the overlapping sensing regions of some sensor  nodes to save energy by turning off  some of them during the sensing phase to prolong the network lifetime.
+
+In this chapter, we design  a protocol that focuses on the area  coverage problem with  the objective  of maximizing  the network  lifetime. Our  proposition, the Distributed  Lifetime  Coverage  Optimization  (DiLCO) protocol,  maintains  the coverage  and improves  the lifetime  in  WSNs. The  area of  interest is  first
+divided  into subregions using  a divide-and-conquer  algorithm and  an activity scheduling  for sensor  nodes is  then  planned by  the elected  leader in  each subregion. In fact, the nodes in a subregion can be seen as a cluster where each node sends sensing data to the  cluster head or the sink node.  Furthermore, the activities in a subregion/cluster can continue even if another cluster stops due
+to too many node failures.  Our DiLCO protocol considers periods, where a period starts with  a discovery  phase to exchange  information between sensors  of the same  subregion, in order  to choose  in a  suitable manner  a sensor  node (the leader) to carry out the coverage  strategy. In each subregion, the activation of the sensors for  the sensing phase of the current period  is obtained by solving
+an integer program.  The resulting activation vector is  broadcast by a leader to every node of its subregion.
+
+The remainder of this chapter is organized as follows. The next section is devoted to the DiLCO protocol description. Section \ref{ch4:sec:03} gives the primary points based coverage problem formulation which is used to schedule the activation of sensors. Section \ref{ch4:sec:04} shows the simulation
+results obtained using the discrete event simulator OMNeT++ \cite{ref158}. They fully demonstrate the usefulness of the proposed approach. Finally, we give concluding remarks in section \ref{ch4:sec:05}.
+

 
 
 \section{Description of the DiLCO Protocol}
 
 
 \section{Description of the DiLCO Protocol}


@@ -112,9 +110,7 @@ $X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $.
 
 \subsection{Main Idea}
 \label{ch4:sec:02:03}
 
 \subsection{Main Idea}
 \label{ch4:sec:02:03}

-\noindent We start by applying a divide-and-conquer algorithm  to partition the
-area of interest  into smaller areas called subregions and  then our protocol is
-executed   simultaneously  in   each   subregion.
+\noindent We start by applying a divide-and-conquer algorithm  to partition the area of interest  into smaller areas called subregions and  then our protocol is executed simultaneously in each subregion.

 
 \begin{figure}[ht!]
 \centering
 
 \begin{figure}[ht!]
 \centering


@@ -123,21 +119,10 @@ executed   simultaneously  in   each   subregion.
 \label{FirstModel}
 \end{figure} 
 
 \label{FirstModel}
 \end{figure} 
 

-As shown in Figure~\ref{FirstModel}, the  proposed DiLCO protocol is a periodic
-protocol where  each period is  decomposed into 4~phases:  Information Exchange,
-Leader Election,  Decision, and Sensing. For  each period there  will be exactly
-one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
-interesting  because it  enhances the  robustness  of the  network against  node
-failures. First,  a node  that has not  enough energy  to complete a  period, or
-which fails before  the decision is taken, will be  excluded from the scheduling
-process. Second,  if a node  fails later, whereas  it was supposed to  sense the
-region of  interest, it will only affect  the quality of the  coverage until the
-definition of  a new  cover set  in the next  period.  Constraints,  like energy
-consumption, can be easily taken into consideration since the sensors can update
-and exchange their  information during the first phase.  Let  us notice that the
-phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
-Decision) are  energy consuming for all the  nodes, even nodes that  will not be
-retained by the leader to keep watch over the corresponding area.
+As shown in Figure~\ref{FirstModel}, the  proposed DiLCO protocol is a periodic protocol where  each period is  decomposed into 4~phases:  Information Exchange, Leader Election,  Decision, and Sensing. For  each period, there  will be exactly one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is interesting  because it  enhances the  robustness  of the  network against  node failures. First,  a node  that has not  enough energy  to complete a  period, or which fails before  the decision is taken, will be  excluded from the scheduling
+process. Second,  if a node  fails later, whereas  it was supposed to sense the region of  interest, it will only affect  the quality of the  coverage until the definition of  a new  cover set  in the next  period.  Constraints,  like energy consumption, can be easily taken into consideration since the sensors can update and exchange their  information during the first phase.  Let  us notice that the
+phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and Decision) are  energy consuming for all the  nodes, even nodes that  will not be retained by the leader to keep watch over the corresponding area.
+

 
 Below, we describe each phase in more details.
 
 
 Below, we describe each phase in more details.
 


@@ -153,7 +138,7 @@ corresponds to the time that a sensor can live in the active mode.
 
 \subsubsection{Leader Election Phase}
 \label{ch4:sec:02:03:02}
 
 \subsubsection{Leader Election Phase}
 \label{ch4:sec:02:03:02}

-This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL), which  will  be  responsible  for executing  the coverage  algorithm. Each subregion in the area of interest  will select its  own  WSNL independently  for each  round.  All the  sensor  nodes cooperate  to select WSNL. The nodes in the  same subregion will  select the leader based on  the received  information from all  other nodes in  the same subregion.  The selection  criteria are,  in order  of importance: larger  number  of neighbors,  larger  remaining energy,  and  then  in case  of equality, larger index. Observations on  previous simulations suggest to use the number  of  one-hop  neighbors  as   the  primary  criterion  to  reduce  energy consumption due to the communications.  
+This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL), which  will  be  responsible  for executing  the coverage  algorithm. Each subregion in the area of interest  will select its  own  WSNL independently  for each  round.  All the  sensor  nodes cooperate  to select WSNL. The nodes in the  same subregion will  select the leader based on  the received  information from all  other nodes in  the same subregion.  The selection  criteria are,  in order  of importance: larger  number  of neighbors,  larger  remaining energy,  and  then  in case  of equality, larger index. Observations on  previous simulations suggest using the number  of  one-hop  neighbors  as   the  primary  criterion  to  reduce  energy consumption due to the communications.  

 
 
 \subsubsection{Decision phase}
 
 
 \subsubsection{Decision phase}


@@ -171,23 +156,8 @@ will receive  an Active-Sleep  packet from WSNL  informing it  to stay
 awake or to go to sleep  for a time  equal to  the period of  sensing until
 starting a new round.
 
 awake or to go to sleep  for a time  equal to  the period of  sensing until
 starting a new round.
 

-An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO}
-which describes the execution of a period  by a node (denoted by $s_j$  for a
-sensor  node indexed by  $j$). At  the beginning  a node  checks whether  it has
-enough energy to stay active during the next sensing phase. If yes, it exchanges
-information  with  all the  other  nodes belonging  to  the  same subregion:  it
-collects from each node its position coordinates, remaining energy ($RE_j$), ID,
-and  the number  of  one-hop neighbors  still  alive. Once  the  first phase  is
-completed, the nodes  of a subregion choose a leader to  take the decision based
-on  the  following  criteria   with  decreasing  importance:  larger  number  of
-neighbors, larger remaining energy, and  then in case of equality, larger index.
-After that,  if the sensor node is  leader, it will execute  the integer program
-algorithm (see Section~\ref{ch4:sec:03})  which provides a set of  sensors planned to be
-active in the next sensing phase. As leader, it will send an Active-Sleep packet
-to each sensor  in the same subregion to  indicate it if it has to  be active or
-not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
-Active-Sleep packet to know its state for the coming sensing phase.
-
+An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO} which describes the execution of a period  by a node (denoted by $s_j$  for a sensor  node indexed by  $j$). In  the beginning,  a node  checks whether  it has enough energy to stay active during the next sensing phase. If yes, it exchanges information  with  all the  other  nodes belonging  to  the  same subregion:  it collects from each node its position coordinates, remaining energy ($RE_j$), ID,
+and  the number  of  one-hop neighbors  still  alive. Once  the  first phase  is completed, the nodes  of a subregion choose a leader to  take the decision based on  the  following  criteria   with  decreasing  importance:  larger  number  of neighbors, larger remaining energy, and  then in case of equality, larger index. After that,  if the sensor node is  leader, it will execute  the integer program algorithm (see Section~\ref{ch4:sec:03})  which provides a set of  sensors planned to be active in the next sensing phase. As leader, it will send an Active-Sleep packet to each sensor  in the same subregion to  indicate it if it has to  be active or not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the Active-Sleep packet to know its state for the coming sensing phase.

 
 \begin{algorithm}[h!]                
 
 
 \begin{algorithm}[h!]                
 


@@ -361,7 +331,7 @@ $w_{U}$ & $|P|^2$
 % is used to refer this table in the text
 \end{table}
 
 % is used to refer this table in the text
 \end{table}
 

-Simulations with five  different node densities going from  50 to 250~nodes were
+Simulations with five different node densities going from  50 to 250~nodes were

 performed  considering  each  time  25~randomly generated  networks,  to  obtain
 experimental results  which are relevant. 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
 performed  considering  each  time  25~randomly generated  networks,  to  obtain
 experimental results  which are relevant. 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


@@ -377,7 +347,7 @@ The modeling  language for Mathematical Programming (AMPL)~\cite{AMPL} is  emplo
 
 \indent In this dissertation, we used an energy consumption model proposed by~\cite{DESK} and based on \cite{ref112} with slight  modifications.  The energy consumption for  sending/receiving the packets is added, whereas the  part related to the sensing range is removed because we consider a fixed sensing range.
 
 
 \indent In this dissertation, we used an energy consumption model proposed by~\cite{DESK} and based on \cite{ref112} with slight  modifications.  The energy consumption for  sending/receiving the packets is added, whereas the  part related to the sensing range is removed because we consider a fixed sensing range.
 

-\indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmels  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}.
+\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{The Energy Consumption Model}
 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}


@@ -413,7 +383,7 @@ COMPUTATION & on & on & on & 26.83 \\
 
 %We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}. 
 
 
 %We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}. 
 

-The initial energy of each node  is randomly set in the interval $[500;700]$.  A sensor node  will not participate in the  next round if its  remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  active state (9.72 mW) by the time in second  for one round (3600 seconds), and  adding  the energy  for  the pre-sensing  phases. According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.
+The initial energy of each node  is randomly set in the interval $[500;700]$.  A sensor node  will not participate in the  next round if its  remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  the active state (9.72 mW) by the time in second  for one round (3600 seconds), and  adding  the energy  for  the pre-sensing  phases. According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.

 
 
 \subsection{Performance Metrics}
 
 
 \subsection{Performance Metrics}


@@ -456,16 +426,8 @@ points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
       + E^{a}_m+E^{s}_m \right)}{M},
   \end{equation*}
 
       + E^{a}_m+E^{s}_m \right)}{M},
   \end{equation*}
 

-where $M$  corresponds to  the number  of periods.  The  total amount  of 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,  $E^a_{m}$ and
-$E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase
+where $M$  corresponds to  the number  of periods.  The  total amount  of 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 the 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  the period  $m$. $E^{\scriptsize \mbox{comp}}_m$  refers to the  energy needed for all  the leader nodes  to solve the  integer program  during a  period.  Finally,  $E^a_{m}$ and $E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase

 (active and sleeping nodes).
 
 \item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
 (active and sleeping nodes).
 
 \item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,


@@ -477,7 +439,7 @@ network lifetime. The Active Sensors Ratio is defined as follows:
 \end{equation*}
 Where: $A_r$ is the number of active sensors in the subregion $r$ during current period, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
 
 \end{equation*}
 Where: $A_r$ is the number of active sensors in the subregion $r$ during current period, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
 

-\item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power, therefore it is important that the proposed algorithm has the shortest possible execution  time. The energy of  a sensor node  must be mainly used   for  the  sensing   phase,  not   for  the   pre-sensing  ones. In this dissertation, 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   $\left( \frac{35330}{2} \times  \frac{1}{6} \right)$.  
+\item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power, therefore it is important that the proposed algorithm has the shortest possible execution  time. The energy of  a sensor node  must be mainly used   for  the  sensing   phase,  not   for  the   pre-sensing  ones. In this dissertation, 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 Atmel's AVR ATmega103L  microcontroller (6 MHz) and  a MIPS rate  equal to 6 to  run the optimization   resolution,   this  time   is   multiplied   by  2944.2   $\left( \frac{35330}{2} \times  \frac{1}{6} \right)$.  

   
 \item {{\bf Stopped simulation runs}:} A simulation ends  when the  sensor network becomes disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs ( in chapter 3, period consists of one round).
 
   
 \item {{\bf Stopped simulation runs}:} A simulation ends  when the  sensor network becomes disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs ( in chapter 3, period consists of one round).
 


@@ -489,7 +451,7 @@ Where: $A_r$ is the number of active sensors in the subregion $r$ during current
 \label{ch4:sec:04:05}
   
 In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).
 \label{ch4:sec:04:05}
   
 In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).

-The DiLCO-1 protocol is a centralized approach on all the area of the interest, while  DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We did not take the DiLCO-1 protocol in our simulation results because it need high execution time to give the decision leading to consume all it's energy before producing the solution for optimization problem.
+The DiLCO-1 protocol is a centralized approach to all the area of the interest, while  DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We did not take the DiLCO-1 protocol in our simulation results because it needs a high execution time to give the decision leading to consume all its energy before producing the solution for the optimization problem.

 
 \begin{enumerate}[i)]
 \item {{\bf Coverage Ratio}}
 
 \begin{enumerate}[i)]
 \item {{\bf Coverage Ratio}}


@@ -505,7 +467,7 @@ In this experiment, Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ra
 \end{figure} 
 It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty rounds.  
 DiLCO-2 protocol gives near similar coverage ratio with other ones for first 10 rounds and then decreased until the died of the network in the round $18^{th}$ because it consumes more energy with the effect of the network disconnection. 
 \end{figure} 
 It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty rounds.  
 DiLCO-2 protocol gives near similar coverage ratio with other ones for first 10 rounds and then decreased until the died of the network in the round $18^{th}$ because it consumes more energy with the effect of the network disconnection. 

-As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases,  the coverage preservation for area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to  DiLCO-8,  DiLCO-16 and  DiLCO-32 protocols,  other nodes are  preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the  coverage for a larger number of rounds. DiLCO-8,  DiLCO-16 and  DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
+As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases,  the coverage preservation for the area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to  DiLCO-8,  DiLCO-16, and  DiLCO-32 protocols,  other nodes are  preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the  coverage for a larger number of rounds. DiLCO-8,  DiLCO-16, and  DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.

 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 
 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 


@@ -516,7 +478,8 @@ As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions inc
 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R1/ASR}
 \end{figure} 
 \caption{Active sensors ratio for 150 deployed nodes }
 \label{Figures/ch4/R1/ASR}
 \end{figure} 

-The results presented in figure~\ref{Figures/ch4/R1/ASR} show the increase in the number of subregions led to increase in the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes but it preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.
+
+The results presented in figure~\ref{Figures/ch4/R1/ASR} show the increase in the number of subregions led to increasing in the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but it preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.

 
 \item {{\bf The percentage of stopped simulation runs}}
 %\subsubsection{The percentage of stopped simulation runs}
 
 \item {{\bf The percentage of stopped simulation runs}}
 %\subsubsection{The percentage of stopped simulation runs}


@@ -544,7 +507,7 @@ We measure the energy consumed by the sensors during the communication, listenin
 
 The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view but as the network size increase the energy consumption increase compared with DiLCO-2,  DiLCO-4, and DiLCO-8. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.\\
  
 
 The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view but as the network size increase the energy consumption increase compared with DiLCO-2,  DiLCO-4, and DiLCO-8. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.\\
  

-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 time computation to solve the optimization problem as well as the higher energy consumed during the communication.  
+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 time computation to solve the optimization problem, as well as the higher energy consumed during the communication.  

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf} 


@@ -565,9 +528,9 @@ In this experiment, the execution time of the our distributed optimization appro
 \label{Figures/ch4/R1/T}
 \end{figure} 
 
 \label{Figures/ch4/R1/T}
 \end{figure} 
 

-We can see from figure~\ref{Figures/ch4/R1/T}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions, because it distributed on larger number of small subregions.  Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.
+We can see from figure~\ref{Figures/ch4/R1/T}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions because it distributed on larger number of small subregions.  Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.

 
 

-The DiLCO-32 protocol has more suitable times at the same time it turn on redundant nodes more.  We think that in distributed fashion the solving of the  optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks,  a distributed method is clearly required.
+The DiLCO-32 protocol has more suitable times at the same time it turns on redundant nodes more.  We think that in distributed fashion the solving of the  optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks,  a distributed method is clearly required.

 
 \item {{\bf The Network Lifetime}}
 %\subsubsection{The Network Lifetime}
 
 \item {{\bf The Network Lifetime}}
 %\subsubsection{The Network Lifetime}


@@ -579,12 +542,13 @@ In figure~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, network lifet
 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R1/LT95}
 \end{figure} 
 \caption{Network Lifetime for $Lifetime95$}
 \label{Figures/ch4/R1/LT95}
 \end{figure} 

-We see that DiLCO-2 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumed during the communication seems to be huge because it is distributed over only two subregions.
+We see that DiLCO-2 protocol results in execution times that quickly become unsuitable for a sensor network, as well as 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/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol that leads to the larger lifetime improvement. By choosing the best suited nodes, for each round, to cover the area of interest and by
-letting the other ones sleep in order to be used later in next rounds, DiLCO-16 protocol efficiently extends the network lifetime because the benefit from the optimization with 16 subregions is better than DiLCO-32 protocol with 32 subregion. DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.
+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, with DiLCO-16 protocol that leads to the larger lifetime improvement. By choosing the best-suited nodes, for each round, to cover the area of interest and by
+letting the other ones sleep in order to be used later in next rounds, DiLCO-16 protocol efficiently extends the network lifetime because the benefit from the optimization with 16 subregions is better than DiLCO-32 protocol with 32 subregions. DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.

 
 Comparison shows that DiLCO-16 protocol, which uses 16 leaders, is the best one because it is used less number of active nodes during the network lifetime compared with DiLCO-32 protocol. It also means that distributing the protocol 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.
 
 Comparison shows that DiLCO-16 protocol, which uses 16 leaders, is the best one because it is used less number of active nodes during the network lifetime compared with DiLCO-32 protocol. It also means that distributing the protocol 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.

+

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}  
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}  


@@ -614,6 +578,7 @@ In this experiment, we Figure~\ref{Figures/ch4/R2/CR} shows the average coverage
 \caption{Coverage ratio for 150 deployed nodes}
 \label{Figures/ch4/R2/CR}
 \end{figure} 
 \caption{Coverage ratio for 150 deployed nodes}
 \label{Figures/ch4/R2/CR}
 \end{figure} 

+

 It is shown that all models provide a very near coverage ratios during the network lifetime, with very small superiority for the models with higher number of primary points. Moreover, when the number of rounds increases, coverage ratio produced by Model~3, Model~4, and Model~5 decreases in comparison with Model~1 and Model~2 due to the high energy consumption during the listening to take the decision after finishing optimization process for larger number of primary points. As shown in figure ~\ref{Figures/ch4/R2/CR}, Coverage ratio decreases when the number of rounds increases due to dead nodes. Although  some nodes are dead,
 thanks to  Model~2, which is slightly more efficient than other Models, because it is balanced between the number of rounds and the better coverage ratio in comparison with other Models.
 
 It is shown that all models provide a very near coverage ratios during the network lifetime, with very small superiority for the models with higher number of primary points. Moreover, when the number of rounds increases, coverage ratio produced by Model~3, Model~4, and Model~5 decreases in comparison with Model~1 and Model~2 due to the high energy consumption during the listening to take the decision after finishing optimization process for larger number of primary points. As shown in figure ~\ref{Figures/ch4/R2/CR}, Coverage ratio decreases when the number of rounds increases due to dead nodes. Although  some nodes are dead,
 thanks to  Model~2, which is slightly more efficient than other Models, because it is balanced between the number of rounds and the better coverage ratio in comparison with other Models.
 


@@ -627,8 +592,7 @@ thanks to  Model~2, which is slightly more efficient than other Models, because
 \label{Figures/ch4/R2/ASR}
 \end{figure} 
 
 \label{Figures/ch4/R2/ASR}
 \end{figure} 
 

-The results presented in figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed  Model 1, in comparison with the other Models. The
-model with less number of primary points uses less active nodes than the other models, which uses a more number of primary points to represent the area of the sensor. According to the results that presented in figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model~1 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model~2 approach is to use less number of active nodes for each round compared with Model~3,  Model~4, and Model~5; and this led to continue for a larger number of rounds with extending the network lifetime. Model~2 has a better coverage ratio compared to Model~1 and acceptable number of rounds.
+The results presented in figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed  Model 1, in comparison with the other Models. The model with fewer number of primary points uses fewer active nodes than the other models, which uses larger number of primary points to represent the area of the sensor. According to the results that presented in figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model~1 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model~2 approach is to use fewer number of active nodes for each round compared with Model~3,  Model~4, and Model~5. This led to continuing for a larger number of rounds with extending the network lifetime. Model~2 has a better coverage ratio compared to Model~1 and acceptable number of rounds.

 
 
 \item {{\bf he percentage of stopped simulation runs}}
 
 
 \item {{\bf he percentage of stopped simulation runs}}


@@ -642,7 +606,7 @@ In this study, we want to show the effect of increasing the primary points on th
 \label{Figures/ch4/R2/SR}
 \end{figure} 
 
 \label{Figures/ch4/R2/SR}
 \end{figure} 
 

-As shown in Figure~\ref{Figures/ch4/R2/SR}, when the number of primary points are increased, the percentage of the stopped simulation runs per round is increased. The reason behind the increase is the increase in the sensors dead when the primary points increases. We are observed that the Model~1 is a better than other models because it conserve more energy by turn on less number of sensors during the sensing phase, but in the same time it preserve the coverage with a less coverage ratio in comparison with other models. Model~2 seems to be more suitable to be used in wireless sensor networks.
+As shown in Figure~\ref{Figures/ch4/R2/SR}, when the number of primary points is increased, the percentage of the stopped simulation runs per round is increased. The reason behind the increase is the increase in the sensors dead when the primary points increase. We are observed that the Model~1 is a better than other models because it conserve more energy by turn on less number of sensors during the sensing phase, but in the same time it preserve the coverage with a less coverage ratio in comparison with other models. Model~2 seems to be more suitable to be used in wireless sensor networks.

 
 
 \item {{\bf The Energy Consumption}}
 
 
 \item {{\bf The Energy Consumption}}


@@ -662,7 +626,7 @@ In this experiment, we study the effect of increasing the primary points to repr
 \label{Figures/ch4/R2/EC50}
 \end{figure} 
 
 \label{Figures/ch4/R2/EC50}
 \end{figure} 
 

-We see from the results presented in Figures~\ref{Figures/ch4/R2/EC95} and \ref{Figures/ch4/R2/EC50}, The energy consumed by the network for each round increases when the primary points increases, because the decision for optimization process will takes more time leads to consume more energy during the listening mode. The results show that Model~1 is the most competitive from the energy consumption point of view but the worst one from coverage ratio point of view. The other Models have a high energy consumption  due  to the increase in the primary points, which are led to increase the energy consumption during the listening mode before producing the solution by solving the optimization process. In fact, we see that Model~2 is a good candidate to be used by wireless sensor network because it preserve a good coverage ratio and a suitable energy consumption in comparison with other models. 
+ We see from the results presented in Figures~\ref{Figures/ch4/R2/EC95} and \ref{Figures/ch4/R2/EC50}, The energy consumed by the network for each round increases when the primary points increases, because the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model~1 is the most competitive from the energy consumption point of view, but the worst one from coverage ratio point of view. The other Models have a high energy consumption  due to the increase in the primary points, which are led to increase the energy consumption during the listening mode before producing the solution by solving the optimization process. In fact, we see that Model~2 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. 

 
 \item {{\bf Execution Time}}
 %\subsubsection{Execution Time}
 
 \item {{\bf Execution Time}}
 %\subsubsection{Execution Time}


@@ -675,7 +639,7 @@ In this experiment, we have studied the impact of the increase in primary points
 \label{Figures/ch4/R2/T}
 \end{figure} 
 
 \label{Figures/ch4/R2/T}
 \end{figure} 
 

-They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model~1 has lower execution time in comparison with other Models, because it used smaller number of primary points to represent the area of the sensor.  Conversely, the other primary point models  have been presented  a higher execution times.
+They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model~1 has lower execution time in comparison with other Models because it used smaller number of primary points to represent the area of the sensor.  Conversely, the other primary point models  have been presented  a higher execution times.

 Moreover, Model~2 has more suitable times and coverage ratio that lead to continue for a larger number of rounds extending the network lifetime. We  think that a good primary point model, this one that balances between the coverage ratio and the number of rounds during the lifetime of the network.
 
 \item {{\bf The Network Lifetime}}
 Moreover, Model~2 has more suitable times and coverage ratio that lead to continue for a larger number of rounds extending the network lifetime. We  think that a good primary point model, this one that balances between the coverage ratio and the number of rounds during the lifetime of the network.
 
 \item {{\bf The Network Lifetime}}


@@ -705,7 +669,7 @@ Comparison shows that the Model~1, which uses less number of primary points, is
 
 \subsection{Performance Comparison with other Approaches}
 \label{ch4:sec:04:07}
 
 \subsection{Performance Comparison with other Approaches}
 \label{ch4:sec:04:07}

-Based on the results, which are conducted from previous two subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are the best candidates to be compared with other two approaches. The first approach, called DESK that proposed by ~\cite{DESK}, which is a full distributed coverage algorithm. The second approach, called GAF~\cite{GAF}, consists in dividing the region into fixed squares.   During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time. 
+Based on the results, which are conducted from previous two subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are the best candidates to be compared with other two approaches. The first approach is called DESK~\cite{DESK}, which is a fully distributed coverage algorithm. The second approach is called GAF~\cite{GAF}, consists in dividing the region into fixed squares.   During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time. 

 
 \begin{enumerate}[i)]
 
 
 \begin{enumerate}[i)]
 


@@ -723,7 +687,7 @@ In this experiment, the average coverage ratio for 150 deployed nodes has been d
 
 It has been shown that DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 99.1\% and 99.2\% produced by DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more nodes are active in the case of DESK and GAF.
 
 
 It has been shown that DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 99.1\% and 99.2\% produced by DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more nodes are active in the case of DESK and GAF.
 

-Moreover, when the number of rounds 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. This is because they optimized the coverage and the lifetime in wireless sensor network by selecting the best representative sensor nodes to take the responsibility of coverage during the sensing phase and this will leads to continue for a larger number of rounds and prolonging the network lifetime; although some nodes are dead, sensor activity scheduling of our protocol chooses other nodes to ensure the coverage of the area of interest. 
+Moreover, when the number of rounds 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. This is because they optimized the coverage and the lifetime in wireless sensor network by selecting the best representative sensor nodes to take the responsibility of coverage during the sensing phase, and this will lead to continuing for a larger number of rounds and prolonging the network lifetime. Furthermore, although some nodes are dead, sensor activity scheduling of our protocol chooses other nodes to ensure the coverage of the area of interest. 

 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 
 
 \item {{\bf Active Sensors Ratio}}
 %\subsubsection{Active Sensors Ratio} 


@@ -741,16 +705,15 @@ The results presented in figure~\ref{Figures/ch4/R3/ASR} show the superiority of
 
 \item {{\bf The percentage of stopped simulation runs}}
 %\subsubsection{The percentage of stopped simulation runs}
 
 \item {{\bf The percentage of stopped simulation runs}}
 %\subsubsection{The percentage of stopped simulation runs}

-The results presented in this experiment, is to show the comparison of DiLCO-16 protocol and DiLCO-32 protocol with other two approaches from point of view of stopped simulation runs per round.
-Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation
-runs per round for 150 deployed nodes. 
+The results presented in this experiment, are to show the comparison of DiLCO-16 protocol and DiLCO-32 protocol with other two approaches from the point of view of stopped simulation runs per round.
+Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R3/SR.pdf} 
 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R3/SR}
 \end{figure} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch4/R3/SR.pdf} 
 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
 \label{Figures/ch4/R3/SR}
 \end{figure} 

-It has been observed that DESK is the approach, which stops first because it consumes more energy for communication as well as it turn on a large number of redundant nodes during the sensing phase. On the other  hand DiLCO-16 protocol and DiLCO-32 protocol have less stopped simulation runs in comparison with DESK and GAF because it distributed the optimization on several subregions in order to optimizes the coverage and the lifetime of the network by activating a less number of nodes during the sensing phase leading to extend the network lifetime and coverage preservation. The optimization effectively continues as long as a network in a subregion is still connected.
+It has been observed that DESK is the approach, which stops first because it consumes more energy for communication as well as it turns on a large number of redundant nodes during the sensing phase. On the other  hand DiLCO-16 protocol and DiLCO-32 protocol have less stopped simulation runs in comparison with DESK and GAF because it distributed the optimization on several subregions in order to optimize the coverage and the lifetime of the network by activating a less number of nodes during the sensing phase leading to extending the network lifetime and coverage preservation. The optimization effectively continues as long as a network in a subregion is still connected.

 
 
 \item {{\bf The Energy Consumption}}
 
 
 \item {{\bf The Energy Consumption}}


@@ -771,7 +734,7 @@ In this experiment, we have studied the effect of the energy consumed by the wir
 \label{Figures/ch4/R3/EC50}
 \end{figure} 
 
 \label{Figures/ch4/R3/EC50}
 \end{figure} 
 

-The results show that 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. In fact,  a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 
+The results show that 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. In fact,  a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 

 
 
 \item {{\bf The Network Lifetime}}
 
 
 \item {{\bf The Network Lifetime}}


@@ -802,11 +765,7 @@ Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which are used di
 
 \section{Conclusion}
 \label{ch4:sec:05}
 
 \section{Conclusion}
 \label{ch4:sec:05}

-A crucial problem in WSN is to schedule the sensing activities of the different nodes  in order to  ensure both  coverage of  the area  of interest  and longer
-network lifetime. The inherent limitations of sensor nodes, in energy provision, communication and computing capacities,  require protocols that optimize the use
-of the  available resources  to  fulfill the sensing  task. To address  this problem, this chapter proposes a  two-step approach. Firstly, the field of sensing
-is  divided into  smaller  subregions using  the  concept of  divide-and-conquer method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage
-Optimization is applied in each  subregion to optimize the coverage and lifetime performances. In a subregion,  our protocol  consists in  electing a  leader node
-which will then perform a sensor activity scheduling. The challenges include how to  select the most efficient leader in each  subregion and  the  best representative set of active nodes to ensure a high level of coverage. To assess the performance of our approach, we  compared it with two other approaches using many performance metrics  like coverage ratio or network  lifetime. We have also studied the  impact of the  number of subregions  chosen to subdivide the  area of interest, considering  different  network  sizes. The  experiments  show  that increasing the  number of subregions improves  the lifetime. The  more subregions there are, the  more robust the network is against random disconnection resulting from dead nodes.  However, for  a given sensing field and network size there is an optimal number of  subregions. Therefore, in case of our simulation context  a subdivision in  $16$~subregions seems to be the most relevant.
+A crucial problem in WSN is to schedule the sensing activities of the different nodes  in order to ensure both of  coverage of  the area  of interest  and longer network lifetime. The inherent limitations of sensor nodes, in energy provision, communication and computing capacities,  require protocols that optimize the use of the  available resources  to  fulfill the sensing  task. To address  this problem, this chapter proposes a  two-step approach. Firstly, the field of sensing
+is  divided into  smaller  subregions using  the  concept of  divide-and-conquer method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage Optimization is applied in each  subregion to optimize the coverage and lifetime performances. In a subregion,  our protocol  consists in  electing a  leader node, which will then perform a sensor activity scheduling. The challenges include how to  select the most efficient leader in each  subregion and  the  best representative set of active nodes to ensure a high level of coverage. To assess the performance of our approach, we  compared it with two other approaches using many performance metrics  like coverage ratio or network  lifetime. We have also studied the  impact of the  number of subregions  chosen to subdivide the  area of interest, considering  different  network  sizes. The  experiments  show  that increasing the  number of subregions improves  the lifetime. The  more subregions there are, the  more robust the network is against random disconnection resulting from dead nodes.  However, for  a given sensing field and network size there is an optimal number of  subregions. Therefore, in case of our simulation context  a subdivision in  $16$~subregions seems to be the most relevant.