%more interesting to divide the area into several subregions, given the
%computation complexity.
-\textcolor{blue}{ Compared to our previous work~\cite{idrees2015distributed},
+\textcolor{black}{ Compared to our previous work~\cite{idrees2015distributed},
in this paper we study the possibility of dividing the sensing phase into
multiple rounds. We make a multiround optimization,
while previously it was a single round optimization. The idea is to
\subsection{Assumptions and primary points}
\label{pp}
-\textcolor{blue}{The assumptions and the coverage model are identical to those presented
+\textcolor{black}{The assumptions and the coverage model are identical to those presented
in~\cite{idrees2015distributed}. We consider a scenario in which sensors are deployed in high
density to initially ensure a high coverage ratio of the interested area. Each
sensor has a predefined sensing range $R_s$, an initial energy supply
As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion,
where each period is divided into 4~phases: Information~Exchange,
-Leader~Election, Decision, and Sensing. \textcolor{blue}{Compared to
+Leader~Election, Decision, and Sensing. \textcolor{black}{Compared to
the DiLCO protocol described in~\cite{idrees2015distributed},} each sensing phase is itself
divided into $T$ rounds of equal duration and for each round a set of sensors (a
cover set) is responsible for the sensing task. In this way a multiround
optimization process is performed during each period after Information~Exchange
and Leader~Election phases, in order to produce $T$ cover sets that will take
the mission of sensing for $T$
-rounds. \textcolor{blue}{Algorithm~\ref{alg:MuDiLCO} is executed by each sensor
+rounds. \textcolor{black}{Algorithm~\ref{alg:MuDiLCO} is executed by each sensor
node~$s_j$ (with enough remaining energy) at the beginning of a period.}
\begin{figure}[t!]
\centering \includegraphics[width=125mm]{Modelgeneral.pdf} % 70mm
\label{alg:MuDiLCO}
\end{algorithm}
-\textcolor{blue}{As already described in~\cite{idrees2015distributed}}, two
+\textcolor{black}{As already described in~\cite{idrees2015distributed}}, two
types of packets are used by the proposed protocol:
\begin{enumerate}[(a)]
\item INFO packet: such a packet will be sent by each sensor node to all the
sensing phase. We also consider primary points as targets. The set of primary
points is denoted by $P$ and the set of sensors by $J$. Only sensors able to be
alive during at least one round are involved in the integer program.
-\textcolor{blue}{Note that the proposed integer program is an
+\textcolor{black}{Note that the proposed integer program is an
extension of the one formulated in~\cite{idrees2015distributed}, variables are now indexed in
addition with the number of round $t$.}
variables and $P*T$ undercoverage variables. The number of constraints is equal
to $P*T$ (for constraints (\ref{eq16})) $+$ $A$ (for constraints (\ref{eq144})).
-\iffalse
-\subsection{Sensing phase}
-
-The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
-receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
-sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
-will be executed by each sensor node~$s_j$ at the beginning of a period,
-explains how the Active-Sleep packet is obtained.
-\fi
\section{Experimental framework}
\label{exp}
network disconnection due to node failures. However, too many subdivisions
reduce the advantage of the optimization. In fact, there is a balance between
the benefit from the optimization and the execution time needed to solve it. In
-the following we have set the number of subregions to~16 \textcolor{blue}{as
+the following we have set the number of subregions to~16 \textcolor{black}{as
recommended in~\cite{idrees2015distributed}}.
\subsection{Energy model}
-\textcolor{blue}{The energy consumption model is detailed
+\textcolor{black}{The energy consumption model is detailed
in~\cite{raghunathan2002energy}. It is based on the model proposed
by~\cite{ChinhVu}. We refer to the sensor node Medusa~II which uses an Atmels
AVR ATmega103L microcontroller~\cite{raghunathan2002energy} to use numerical
values.}
-\iffalse
-\subsection{Energy model}
-
-We use an energy consumption model proposed by~\cite{ChinhVu} and based on
-\cite{raghunathan2002energy} 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.
-
-For our energy consumption model, we refer to the sensor node Medusa~II which
-uses an Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. 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{raghunathan2002energy}. 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{table4}.
-
-\begin{table}[ht]
-\caption{The Energy Consumption Model}
-\centering
-\begin{tabular}{|c|c|c|c|c|}
- \hline
-Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
-\hline
-LISTENING & on & on & on & 20.05 \\
-\hline
-ACTIVE & on & off & on & 9.72 \\
-\hline
-SLEEP & off & off & off & 0.02 \\
-\hline
-COMPUTATION & on & on & on & 26.83 \\
-\hline
-\end{tabular}
-
-\label{table4}
-\end{table}
-
-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 chosen its status), it
-can turn its radio off to save battery. MuDiLCO uses two types of packets for
-communication. The size of the INFO packet and Active-Sleep packet are 112~bits
-and 24~bits respectively. The value of energy spent to send a 1-bit-content
-message is obtained by using the equation in ~\cite{raghunathan2002energy} 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.
-
-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 $E_{R}=36~\mbox{Joules}$, the minimum energy needed for the node to
-stay alive during one round. This value has been computed by multiplying the
-energy consumed in active state (9.72 mW) by the time in second for one round
-(3600 seconds). According to the interval of initial energy, a sensor may be
-alive during at most 20 rounds.
-\fi
-
\subsection{Metrics}
-\textcolor{blue}{To evaluate our approach we consider the performance metrics
+\textcolor{black}{To evaluate our approach we consider the performance metrics
detailed in~\cite{idrees2015distributed}, which are: Coverage Ratio, Network
Lifetime and Energy Consumption. Compared to the previous definitions,
formulations of Coverage Ratio and Energy Consumption are enriched with the
%nodes have been drained of their energy or each sensor network monitoring an area has become disconnected.
\end{enumerate}
-\iffalse
-\begin{enumerate}
- \setcounter{5}
-\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.
-
-\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.
-\end{enumerate}
-\fi
\section{Experimental results and analysis}
\label{analysis}
primary points to be used by a MuDiLCO protocol. In this comparison, MuDiLCO-1
protocol is used with five primary point models, each model corresponding to a
number of primary points, which are called Model-5 (it uses 5 primary points),
-Model-9, Model-13, Model-17, and Model-21. \textcolor{blue}{Note
+Model-9, Model-13, Model-17, and Model-21. \textcolor{black}{Note
that the results
presented in~\cite{idrees2015distributed} correspond to Model-13 (13 primary
points)}.
\begin{figure}[t!]
\centering
- \includegraphics[scale=0.5] {R2/CR.pdf}
+ \includegraphics[scale=0.5] {R2CR.pdf}
\caption{Coverage ratio for 150 deployed nodes}
\label{Figures/ch4/R2/CR}
\end{figure}
\begin{figure}[h!]
\centering
\centering
-\includegraphics[scale=0.5]{R2/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
+\includegraphics[scale=0.5]{R2LT95.pdf}\\~ ~ ~ ~ ~(a) \\
-\includegraphics[scale=0.5]{R2/LT50.pdf}\\~ ~ ~ ~ ~(b)
+\includegraphics[scale=0.5]{R2LT50.pdf}\\~ ~ ~ ~ ~(b)
\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
\label{Figures/ch4/R2/LT}
\begin{figure}[ht!]
\centering
- \includegraphics[scale=0.5] {F/CR.pdf}
+ \includegraphics[scale=0.5] {FCR.pdf}
\caption{Average coverage ratio for 150 deployed nodes}
\label{fig3}
\end{figure}
\begin{figure}[ht!]
\centering
-\includegraphics[scale=0.5]{F/ASR.pdf}
+\includegraphics[scale=0.5]{FASR.pdf}
\caption{Active sensors ratio for 150 deployed nodes}
\label{fig4}
\end{figure}
\begin{figure}[ht!]
\centering
-\includegraphics[scale=0.5]{F/SR.pdf}
+\includegraphics[scale=0.5]{FSR.pdf}
\caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes}
\label{fig6}
\end{figure}
\begin{figure}[h!]
\centering
\begin{tabular}{cl}
- \parbox{9.5cm}{\includegraphics[scale=0.5]{F/EC95.pdf}} & (a) \\
+ \parbox{9.5cm}{\includegraphics[scale=0.5]{FEC95.pdf}} & (a) \\
\verb+ + \\
- \parbox{9.5cm}{\includegraphics[scale=0.5]{F/EC50.pdf}} & (b)
+ \parbox{9.5cm}{\includegraphics[scale=0.5]{FEC50.pdf}} & (b)
\end{tabular}
\caption{Energy consumption for (a) $Lifetime_{95}$ and
(b) $Lifetime_{50}$}
\begin{figure}[ht!]
\centering
-\includegraphics[scale=0.5]{F/T.pdf}
+\includegraphics[scale=0.5]{FT.pdf}
\caption{Execution Time (in seconds)}
\label{fig77}
\end{figure}
\begin{figure}[t!]
\centering
\begin{tabular}{cl}
- \parbox{9.5cm}{\includegraphics[scale=0.5125]{F/LT95.pdf}} & (a) \\
+ \parbox{9.5cm}{\includegraphics[scale=0.5125]{FLT95.pdf}} & (a) \\
\verb+ + \\
- \parbox{9.5cm}{\includegraphics[scale=0.5125]{F/LT50.pdf}} & (b)
+ \parbox{9.5cm}{\includegraphics[scale=0.5125]{FLT50.pdf}} & (b)
\end{tabular}
\caption{Network lifetime for (a) $Lifetime_{95}$ and
(b) $Lifetime_{50}$}
