%more interesting to divide the area into several subregions, given the
%computation complexity.
-\textcolor{blue}{ Compared to our previous paper~\cite{idrees2015distributed},
- in this one we study the possibility of dividing the sensing phase into
- multiple rounds. In fact, in this paper we make a multiround optimization,
- while it was a single round optimization in our previous work. The idea is to
+\textcolor{blue}{ 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
take advantage of the pre-sensing phase to plan the sensor's activity for
several rounds instead of one, thus saving energy. In addition, when the
optimization problem becomes more complex, its resolution is stopped after a
\subsection{Assumptions and primary points}
\label{pp}
-\textcolor{blue}{Assumptions and coverage model are identical to those presented
- in~\cite{idrees2015distributed}.}
-
-\iffalse
-We consider a randomly and uniformly deployed network consisting of static
-wireless sensors. The sensors are deployed in high density to ensure initially
-a high coverage ratio of the interested area. We assume that all nodes are
-homogeneous in terms of communication and processing capabilities, and
-heterogeneous from the point of view of energy provision. Each sensor is
-supposed to get information on its location either through hardware such as
-embedded GPS or through location discovery algorithms.
-
-To model a sensor node's coverage area, we consider the boolean disk coverage
-model which is the most widely used sensor coverage model in the
-literature. Thus, each sensor has a constant sensing range $R_s$ and all space
-points within the disk centered at the sensor with the radius of the sensing
-range is said to be covered by this sensor. We also assume that the
-communication range satisfies $R_c \geq 2R_s$. In fact, Zhang and
-Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous
-hypothesis, a complete coverage of a convex area implies connectivity among the
-active nodes.\fi
-
-\textcolor{blue}{We consider a scenario where sensors are deployed in high
- density to ensure initially a high coverage ratio of the interested area. Each
+\textcolor{blue}{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
(eventually different from each other) and is supposed to be equipped with
- module for locating its geographical positions. All space points within the
- disk centered at the sensor with the radius of the sensing range is said to be
+ a module to locate its geographical positions. All space points within the
+ disk centered at the sensor with the radius of the sensing range are said to be
covered by this sensor.}
\indent Instead of working with the coverage area, we consider for each sensor a
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 protocol
- DiLCO described in~\cite{idrees2015distributed},} each sensing phase is itself
+Leader~Election, Decision, and Sensing. \textcolor{blue}{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
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 extension of that
- formulated in~\cite{idrees2015distributed}, variables are now indexed in
+\textcolor{blue}{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 $t$.}
For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
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}
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.} \textcolor{red}{Est-ce qu'il faut en ecrire plus et redonner le
- tableau de valeurs?}
-
-\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
+ values.}
\subsection{Metrics}
%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 that results
+Model-9, Model-13, Model-17, and Model-21. \textcolor{blue}{Note
+ that the results
presented in~\cite{idrees2015distributed} correspond to Model-13 (13 primary
points)}.
