X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/f7dcdff7f2151372dfabe5d5a70f4f4e3d13324b..95a4de6bd78956216592f062ffe0337a222fa20a:/article.tex diff --git a/article.tex b/article.tex index cd6a361..b0a1878 100644 --- a/article.tex +++ b/article.tex @@ -149,10 +149,10 @@ in~\cite{idrees2015distributed}. %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 @@ -291,34 +291,13 @@ Indeed, each sensor maintains its own timer and its wake-up time is randomized \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 @@ -377,8 +356,8 @@ inside a subregion is less than or equal to 3. 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 @@ -503,8 +482,8 @@ determine the possibility of activating sensor $j$ during round $t$ of a given 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 @@ -695,8 +674,7 @@ the following we have set the number of subregions to~16 \textcolor{blue}{as 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?} + values.} \iffalse \subsection{Energy model} @@ -856,7 +834,8 @@ points. The objective of this comparison is to select the suitable number of 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)}.