From: Karine Deschinkel Date: Fri, 5 Jun 2015 14:18:31 +0000 (+0200) Subject: super modifs X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/commitdiff_plain/74ea4422621d70b313f60f78c80a29abe506d6b4 super modifs --- diff --git a/PeCO-EO/articleeo.log b/PeCO-EO/articleeo.log index f0d9217..7e6f3a7 100644 --- a/PeCO-EO/articleeo.log +++ b/PeCO-EO/articleeo.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2014.3.11) 10 MAY 2015 00:35 +This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2013.9.3) 15 MAY 2015 13:26 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -506,10 +506,10 @@ LaTeX Font Warning: Font shape `OT1/cmr/bx/sc' undefined (Font) using `OT1/cmr/bx/n' instead on input line 200. 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Package epstopdf Info: Source file: -(epstopdf) date: 2015-05-08 17:47:31 +(epstopdf) date: 2015-02-06 11:42:03 (epstopdf) size: 24855 bytes (epstopdf) Output file: -(epstopdf) date: 2015-05-09 17:25:31 +(epstopdf) date: 2015-02-20 10:12:47 (epstopdf) size: 8466 bytes (epstopdf) Command: @@ -976,10 +976,10 @@ Overfull \vbox (701.0pt too high) has occurred while \output is active [] [13 <./figure6-eps-converted-to.pdf>] Package epstopdf Info: Source file: -(epstopdf) date: 2015-05-08 17:47:31 +(epstopdf) date: 2015-02-06 11:42:03 (epstopdf) size: 27000 bytes (epstopdf) Output file: -(epstopdf) date: 2015-05-09 17:25:32 +(epstopdf) date: 2015-02-20 10:12:48 (epstopdf) size: 7927 bytes (epstopdf) Command: @@ -1142,7 +1142,7 @@ LaTeX Font Warning: Some font shapes were not available, defaults substituted. ) Here is how much of TeX's memory you used: 3708 strings out of 495059 - 48092 string characters out of 3182030 + 48092 string characters out of 3182031 116289 words of memory out of 3000000 6816 multiletter control sequences out of 15000+200000 14560 words of font info for 56 fonts, out of 3000000 for 9000 @@ -1167,7 +1167,7 @@ st/fonts/type1/public/amsfonts/cm/cmsy7.pfb> -Output written on articleeo.pdf (17 pages, 734629 bytes). +Output written on articleeo.pdf (17 pages, 734558 bytes). PDF statistics: 202 PDF objects out of 1000 (max. 8388607) 137 compressed objects within 2 object streams diff --git a/PeCO-EO/articleeo.pdf b/PeCO-EO/articleeo.pdf index bc80ba6..796a15b 100644 Binary files a/PeCO-EO/articleeo.pdf and b/PeCO-EO/articleeo.pdf differ diff --git a/PeCO-EO/articleeo.tex b/PeCO-EO/articleeo.tex index 40af2f4..1dbc9e0 100644 --- a/PeCO-EO/articleeo.tex +++ b/PeCO-EO/articleeo.tex @@ -27,7 +27,7 @@ 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. 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 +region of interest is first subdivided into subregions and the 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 @@ -100,8 +100,8 @@ This paper makes the following contributions. -The rest of the paper is organized as follows. In the next section we review -some related work in the field. Section~\ref{sec:The PeCO Protocol Description} +The rest of the paper is organized as follows. In the next section +some related work in the field is reviewed. Section~\ref{sec:The PeCO Protocol Description} is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the coverage model formulation which is used to schedule the activation of sensor nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations @@ -112,9 +112,9 @@ Section~\ref{sec:Conclusion and Future Works}. \section{Related Literature} \label{sec:Literature Review} -In this section, we summarize some related works regarding the -coverage problem and distinguish our PeCO protocol from the works presented in -the literature. +In this section, some related works regarding the +coverage problem is summarized, and specific aspects of the PeCO protocol from the works presented in +the literature are presented. The most discussed coverage problems in literature can be classified in three categories~\citep{li2013survey} according to their respective monitoring @@ -129,8 +129,8 @@ nodes or between disk of sensor nodes and boundaries. In \citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered it will be the case for the whole area. They provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of -each sensor, where $d$ denotes the maximum number of sensors that are -neighbors to a sensor and $n$ is the total number of sensors in the +each sensor. $d$ denotes the maximum number of sensors that are +neighbors to a sensor, and $n$ is the total number of sensors in the network. {\it In PeCO protocol, instead of determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.} @@ -200,8 +200,8 @@ used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012col \section{ The P{\scshape e}CO Protocol Description} \label{sec:The PeCO Protocol Description} -In this section, we describe in details our Perimeter-based Coverage -Optimization protocol. First we present the assumptions we made and the models +In this section, the Perimeter-based Coverage +Optimization protocol is decribed in details. First we present the assumptions we made and the models we considered (in particular the perimeter coverage one), second we describe the background idea of our protocol, and third we give the outline of the algorithm executed by each node. @@ -217,11 +217,7 @@ of interest. We assume that all the sensor nodes are homogeneous in terms of communication, sensing, and processing capabilities and heterogeneous from the energy provision point of view. The location information is available to a sensor node either through hardware such as embedded GPS or location discovery -algorithms. We assume that each sensor node can directly transmit its -measurements to a mobile sink node. For example, a sink can be an unmanned -aerial vehicle (UAV) flying regularly over the sensor field to collect -measurements from sensor nodes. A mobile sink node collects the measurements and -transmits them to the base station. We consider a Boolean disk coverage model, +algorithms. We consider a Boolean disk coverage model, which is the most widely used sensor coverage model in the literature, and all sensor nodes have a constant sensing range $R_s$. Thus, all the space points within a disk centered at a sensor with a radius equal to the sensing range are @@ -232,11 +228,11 @@ complete coverage of a convex area implies connectivity among active nodes. The PeCO protocol uses the same perimeter-coverage model as \citet{huang2005coverage}. It can be expressed as follows: a sensor is said to be perimeter covered if all the points on its perimeter are covered by -at least one sensor other than itself. They proved that a network area is -$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). +at least one sensor other than itself. Authors \citet{huang2005coverage} proved that a network area is +$k$-covered (every point in the area covered by at least k sensors) if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this -figure, we can see that sensor~$0$ has nine neighbors and we have reported on +figure, sensor~$0$ has nine neighbors and we have reported on its perimeter (the perimeter of the disk covered by the sensor) for each neighbor the two points resulting from the intersection of the two sensing areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively @@ -259,8 +255,8 @@ Figure~\ref{figure1}(b) describes the geometric information used to find the locations of the left and right points of an arc on the perimeter of a sensor node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the west side of sensor~$u$, with the following respective coordinates in the -sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can -compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert +sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates +the euclidean distance between nodes~$u$ and $v$ is computed: $Dist(u,v)=\sqrt{\vert u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is obtained through the formula: \[ @@ -274,7 +270,7 @@ 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{figure1}(a) illustrates the arcs for the nine neighbors of sensor $0$ and Figure~\ref{figure2} gives the position of the corresponding arcs -in the interval $[0,2\pi)$. More precisely, we can see that the points are +in the interval $[0,2\pi)$. More precisely, 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 from the first intersection point after point~zero, and the maximum level of @@ -471,10 +467,10 @@ construct the set of active sensors in the sensing stage. \section{Perimeter-based Coverage Problem Formulation} \label{cp} -In this section, the coverage model is mathematically formulated. We -start with a description of the notations that will be used throughout the +In this section, the coverage model is mathematically formulated. The following +notations are used throughout the section.\\ -First, we have the following sets: +First, the following sets: \begin{itemize} \item $S$ represents the set of WSN sensor nodes; \item $A \subseteq S $ is the subset of alive sensors; @@ -495,7 +491,7 @@ a^j_{ik} = \left \{ \end{equation} Note that $a^k_{ik}=1$ by definition of the interval. -Second, we define several binary and integer variables. Hence, each binary +Second, several binary and integer variables are defined. Hence, each binary variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer variable which measures the undercoverage for the coverage interval $i$ @@ -510,7 +506,7 @@ sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network lifetime, the objective is to activate a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to reach the desired level of coverage for all -coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure +coverage intervals. Therefore variables $M^j_i$ and $V^j_i$ are introduced as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the @@ -527,8 +523,8 @@ Our coverage optimization problem can then be mathematically expressed as follow \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 )&\\ \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}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\ +\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i = l \quad \forall i \in I_j, \forall j \in S\\ +\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i = l \quad \forall i \in I_j, \forall j \in S\\ X_{k} \in \{0,1\}, \forall k \in A \end{array} \right. @@ -544,9 +540,9 @@ brachytherapy treatment planning for optimizing dose distribution each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all -sensors), whereas the number of variables $X_k$ decreases over periods, since we -consider only alive sensors (sensors with enough energy to be alive during one -sensing phase) in the model. +sensors), whereas the number of variables $X_k$ decreases over periods, since +only alive sensors (sensors with enough energy to be alive during one +sensing phase) are considered in the model. \section{Performance Evaluation and Analysis} \label{sec:Simulation Results and Analysis} @@ -580,7 +576,7 @@ Initial energy & in range 500-700~Joules \\ Sensing period & duration of 60 minutes \\ $E_{th}$ & 36~Joules\\ $R_s$ & 5~m \\ - +$R_c$ & 10~m \\ $\alpha^j_i$ & 0.6 \\ $\beta^j_i$ & 0.4 @@ -604,14 +600,14 @@ 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 +network coverage and a longer WSN lifetime. Higher priority is given to 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 +sensor~$j$. On the other hand, +$\beta^j_i$ is assigned to a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval. -We introduce the following performance metrics to evaluate the efficiency of our +The following performance metrics are used to evaluate the efficiency of the approach. @@ -625,7 +621,7 @@ approach. because without network connectivity a sensor may not be able to send to a base station an event it has sensed. \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to - observe the area of interest. In our case, we discretized the sensor field as + observe the area of interest. In our case, the sensor field is discretized as a regular grid, which yields the following equation: @@ -637,8 +633,8 @@ approach. where $n$ is the number of covered grid points by active sensors of every subregions during the current sensing phase and $N$ is total number of grid - points in the sensing field. In our simulations we have set a layout of - $N~=~51~\times~26~=~1326$~grid points. + points in the sensing field. In simulations a layout of + $N~=~51~\times~26~=~1326$~grid points is considered. \item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to activate as few nodes as possible, in order to minimize the communication overhead and maximize the WSN lifetime. The active sensors ratio is defined as diff --git a/PeCO-EO/articleeo.tex~ b/PeCO-EO/articleeo.tex~ index caeaa18..58e1e1d 100644 --- a/PeCO-EO/articleeo.tex~ +++ b/PeCO-EO/articleeo.tex~ @@ -1,867 +1,866 @@ -% gENOguide.tex -% v4.0 released April 2013 - -\documentclass{gENO2e} -%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e} -%\renewcommand{\algorithmcfname}{ALGORITHM} -\begin{document} - -%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April} - -%\articletype{GUIDE} - -\title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}} - -\author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$ -$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, - Belfort, France}};} - - -\maketitle - -\begin{abstract} -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. - -\begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling. -\end{keywords} - -\end{abstract} - - -\section{Introduction} -\label{sec:introduction} - -\noindent 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)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring -tasks. A WSN consists of small low-powered sensors working together by -communicating with one another through multi-hop radio communications. Each node -can send the data it collects in its environment, thanks to its sensor, to the -user by means of sink nodes. 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~\citep{yick2008wireless}. Typically, a sensor node contains -three main components~\citep{anastasi2009energy}: a sensing unit able to measure -physical, chemical, or biological phenomena observed in the environment; a -processing unit which will process and store the collected measurements; a radio -communication unit for data transmission and receiving. - -The energy needed by an active sensor node to perform sensing, processing, and -communication is supplied by a power supply which is a battery. This battery has -a limited energy provision and it may be unsuitable or impossible to replace or -recharge it in most applications. Therefore it is necessary to deploy WSN with -high density in order to increase reliability and to exploit node redundancy -thanks to energy-efficient activity scheduling approaches. Indeed, the overlap -of sensing areas can be exploited to schedule alternatively some sensors in a -low power sleep mode and thus save energy. Overall, the main question that must -be answered is: how to extend the lifetime coverage of a WSN as long as possible -while ensuring a high level of coverage? These past few years many -energy-efficient mechanisms have been suggested to retain energy and extend the -lifetime of the WSNs~\citep{rault2014energy}.\\\\ -This paper makes the following contributions. -\begin{enumerate} -\item We have devised a framework to schedule nodes to be activated alternatively such - that the network lifetime is prolonged while ensuring that a certain level of - coverage is preserved. A key idea in our framework is to exploit spatial and - temporal subdivision. On the one hand, the area of interest is divided into - several smaller subregions and, on the other hand, the time line is divided into - periods of equal length. In each subregion the sensor nodes will cooperatively - choose a leader which will schedule nodes' activities, and this grouping of - sensors is similar to typical cluster architecture. -\item We have proposed a new mathematical optimization model. Instead of trying to - cover a set of specified points/targets as in most of the methods proposed in - the literature, we formulate an integer program based on perimeter coverage of - each sensor. The model involves integer variables to capture the deviations - between the actual level of coverage and the required level. Hence, an - optimal scheduling will be obtained by minimizing a weighted sum of these - deviations. -\item We have conducted extensive simulation experiments, using the discrete event - simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared - our PeCO protocol to two approaches found in the literature: - DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous - work published in~\citep{Idrees2} which is based on another optimization model - for sensor scheduling. -\end{enumerate} - - - - - - -The rest of the paper is organized as follows. In the next section we review -some related work in the field. Section~\ref{sec:The PeCO Protocol Description} -is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the -coverage model formulation which is used to schedule the activation of sensor -nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations -results and discusses the comparison with other approaches. Finally, concluding -remarks are drawn and some suggestions are given for future works in -Section~\ref{sec:Conclusion and Future Works}. - -\section{Related Literature} -\label{sec:Literature Review} - -\noindent In this section, we summarize some related works regarding the -coverage problem and distinguish our PeCO protocol from the works presented in -the literature. - -The most discussed coverage problems in literature can be classified in three -categories~\citep{li2013survey} according to their respective monitoring -objective. Hence, area coverage \citep{Misra} means that every point inside a -fixed area must be monitored, while target coverage~\citep{yang2014novel} refers -to the objective of coverage for a finite number of discrete points called -targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on -preventing intruders from entering into the region of interest. In -\citep{Deng2012} authors transform the area coverage problem into the target -coverage one taking into account the intersection points among disks of sensors -nodes or between disk of sensor nodes and boundaries. In -\citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of -sensors are sufficiently covered it will be the case for the whole area. They -provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of -each sensor, where $d$ denotes the maximum number of sensors that are -neighbors to a sensor and $n$ is the total number of sensors in the -network. {\it In PeCO protocol, instead of determining the level of coverage of - a set of discrete points, our optimization model is based on checking the - perimeter-coverage of each sensor to activate a minimal number of sensors.} - -The major approach to extend network lifetime while preserving coverage is to -divide/organize the sensors into a suitable number of set covers (disjoint or -non-disjoint)\citep{wang2011coverage}, where each set completely covers a region of interest, and to -activate these set covers successively. The network activity can be planned in -advance and scheduled for the entire network lifetime or organized in periods, -and the set of active sensor nodes is decided at the beginning of each period -\citep{ling2009energy}. Active node selection is determined based on the problem -requirements (e.g. area monitoring, connectivity, or power efficiency). For -instance, \citet{jaggi2006} address the problem of maximizing -the lifetime by dividing sensors into the maximum number of disjoint subsets -such that each subset can ensure both coverage and connectivity. A greedy -algorithm is applied once to solve this problem and the computed sets are -activated in succession to achieve the desired network lifetime. -\citet{chin2007}, \citet{yan2008design}, \citet{pc10}, propose algorithms -working in a periodic fashion where a cover set is computed at the beginning of -each period. {\it Motivated by these works, PeCO protocol works in periods, - where each period contains a preliminary phase for information exchange and - decisions, followed by a sensing phase where one cover set is in charge of the - sensing task.} - -Various centralized and distributed approaches, or even a mixing of these two -concepts, have been proposed to extend the network lifetime \citep{zhou2009variable}. In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its -own activity scheduling after an information exchange with its neighbors. The -main interest of such an approach is to avoid long range communications and thus -to reduce the energy dedicated to the communications. Unfortunately, since each -node has only information on its immediate neighbors (usually the one-hop ones) -it may make a bad decision leading to a global suboptimal solution. Conversely, -centralized -algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always -provide nearly or close to optimal solution since the algorithm has a global -view of the whole network. The disadvantage of a centralized method is obviously -its high cost in communications needed to transmit to a single node, the base -station which will globally schedule nodes' activities, data from all the other -sensor nodes in the area. The price in communications can be huge since -long range communications will be needed. In fact the larger the WNS is, the -higher the communication and thus the energy cost are. {\it In order to be - suitable for large-scale networks, in the PeCO protocol, the area of interest - is divided into several smaller subregions, and in each one, a node called the - leader is in charge of selecting the active sensors for the current - period. Thus our protocol is scalable and is a globally distributed method, - whereas it is centralized in each subregion.} - -Various coverage scheduling algorithms have been developed these past few years. -Many of them, dealing with the maximization of the number of cover sets, are -heuristics. These heuristics involve the construction of a cover set by -including in priority the sensor nodes which cover critical targets, that is to -say targets that are covered by the smallest number of sensors -\citep{berman04,zorbas2010solving}. Other approaches are based on mathematical -programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014} -and dedicated techniques (solving with a branch-and-bound algorithm available in -optimization solver). The problem is formulated as an optimization problem -(maximization of the lifetime or number of cover sets) under target coverage and -energy constraints. Column generation techniques, well-known and widely -practiced techniques for solving linear programs with too many variables, have -also been -used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it In the PeCO - protocol, each leader, in charge of a subregion, solves an integer program - which has a twofold objective: minimize the overcoverage and the undercoverage - of the perimeter of each sensor.} - - - -\section{ The P{\scshape e}CO Protocol Description} -\label{sec:The PeCO Protocol Description} - -\noindent In this section, we describe in details our Perimeter-based Coverage -Optimization protocol. First we present the assumptions we made and the models -we considered (in particular the perimeter coverage one), second we describe the -background idea of our protocol, and third we give the outline of the algorithm -executed by each node. - - -\subsection{Assumptions and Models} -\label{CI} - -\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly -distributed in a bounded sensor field is considered. The wireless sensors are -deployed in high density to ensure initially a high coverage ratio of the area -of interest. We assume that all the sensor nodes are homogeneous in terms of -communication, sensing, and processing capabilities and heterogeneous from -the energy provision point of view. The location information is available to a -sensor node either through hardware such as embedded GPS or location discovery -algorithms. We assume that each sensor node can directly transmit its -measurements to a mobile sink node. For example, a sink can be an unmanned -aerial vehicle (UAV) flying regularly over the sensor field to collect -measurements from sensor nodes. A mobile sink node collects the measurements and -transmits them to the base station. We consider a Boolean disk coverage model, -which is the most widely used sensor coverage model in the literature, and all -sensor nodes have a constant sensing range $R_s$. Thus, all the space points -within a disk centered at a sensor with a radius equal to the sensing range are -said to be covered by this sensor. We also assume that the communication range -$R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, \citet{Zhang05} -proved that if the transmission range fulfills the previous hypothesis, the -complete coverage of a convex area implies connectivity among active nodes. - -The PeCO protocol uses the same perimeter-coverage model as \citet{huang2005coverage}. It can be expressed as follows: a sensor is -said to be perimeter covered if all the points on its perimeter are covered by -at least one sensor other than itself. They proved that a network area is -$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). - -Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this -figure, we can see that sensor~$0$ has nine neighbors and we have reported on -its perimeter (the perimeter of the disk covered by the sensor) for each -neighbor the two points resulting from the intersection of the two sensing -areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively -for left and right from a neighboing point of view. The resulting couples of -intersection points subdivide the perimeter of sensor~$0$ into portions called -arcs. - -\begin{figure}[ht!] - \centering - \begin{tabular}{@{}cr@{}} - \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\ - \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)} - \end{tabular} - \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of - $u$'s perimeter covered by $v$.} - \label{figure1} -\end{figure} - -Figure~\ref{figure1}(b) describes the geometric information used to find the -locations of the left and right points of an arc on the perimeter of a sensor -node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the -west side of sensor~$u$, with the following respective coordinates in the -sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can -compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert - u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is -obtained through the formula: - \[ -\alpha = \arccos \left(\frac{Dist(u,v)}{2R_s} -\right). -\] -The arc on the perimeter of~$u$ defined by the angular interval $[\pi - - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$. - -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{figure1}(a) illustrates the arcs for the nine neighbors of -sensor $0$ and figure~\ref{figure2} 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 -from the first intersection point after point~zero, and the maximum level of -coverage is determined for each interval defined by two successive points. The -maximum level of coverage is equal to the number of overlapping arcs. For -example, -between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$ -(the value is highlighted in yellow at the bottom of figure~\ref{figure2}), which -means that at most 2~neighbors can cover the perimeter in addition to node $0$. -Table~\ref{my-label} summarizes for each coverage interval the maximum level of -coverage and the sensor nodes covering the perimeter. The example discussed -above is thus given by the sixth line of the table. - - -\begin{figure*}[t!] -\centering -\includegraphics[width=127.5mm]{figure2.eps} -\caption{Maximum coverage levels for perimeter of sensor node $0$.} -\label{figure2} -\end{figure*} - - - - - \begin{table} - \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}} -{\begin{tabular}{|c|c|c|c|c|c|c|c|c|} -\hline -\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline -0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline -0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline -0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline -0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline -1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline -1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline -2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline -2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline -2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline -2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline -2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline -3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline -3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline -4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline -4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline -4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline -5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline -5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline -\end{tabular}} - - -\end{table} - - - - -In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an -integer program based on coverage intervals. The formulation of the coverage -optimization problem is detailed in~section~\ref{cp}. Note that when a sensor -node has a part of its sensing range outside the WSN sensing field, as in -figure~\ref{figure3}, the maximum coverage level for this arc is set to $\infty$ -and the corresponding interval will not be taken into account by the -optimization algorithm. - - \newpage -\begin{figure}[h!] -\centering -\includegraphics[width=62.5mm]{figure3.eps} -\caption{Sensing range outside the WSN's area of interest.} -\label{figure3} -\end{figure} - - -\subsection{The Main Idea} - -\noindent The WSN area of interest is, in a first step, divided into regular -homogeneous subregions using a divide-and-conquer algorithm. In a second step -our protocol will be executed in a distributed way in each subregion -simultaneously to schedule nodes' activities for one sensing period. - -As shown in figure~\ref{figure4}, node activity scheduling is produced by our -protocol in a periodic manner. Each period is divided into 4 stages: Information -(INFO) Exchange, Leader Election, Decision (the result of an optimization -problem), and Sensing. For each period there is exactly one set cover -responsible for the sensing task. Protocols based on a periodic scheme, like -PeCO, are more robust against an unexpected node failure. On the one hand, if -a node failure is discovered before taking the decision, the corresponding sensor -node will not be considered by the optimization algorithm. On the other -hand, if the sensor failure happens after the decision, the sensing task of the -network will be temporarily affected: only during the period of sensing until a -new period starts, since a new set cover will take charge of the sensing task in -the next period. The energy consumption and some other constraints can easily be -taken into account since the sensors can update and then exchange their -information (including their residual energy) at the beginning of each period. -However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision) -are energy consuming, even for nodes that will not join the set cover to monitor -the area. - -\begin{figure}[t!] -\centering -\includegraphics[width=80mm]{figure4.eps} -\caption{PeCO protocol.} -\label{figure4} -\end{figure} - -We define two types of packets to be used by PeCO protocol: - -\begin{itemize} -\item INFO packet: sent by each sensor node to all the nodes inside a same - subregion for information exchange. -\item ActiveSleep packet: sent by the leader to all the nodes in its subregion - to transmit to them their respective status (stay Active or go Sleep) during - sensing phase. -\end{itemize} - - -Five status are possible for a sensor node in the network: - -\begin{itemize} -\item LISTENING: waits for a decision (to be active or not); -\item COMPUTATION: executes the optimization algorithm as leader to - determine the activities scheduling; -\item ACTIVE: node is sensing; -\item SLEEP: node is turned off; -\item COMMUNICATION: transmits or receives packets. -\end{itemize} - - -\subsection{PeCO Protocol Algorithm} - -\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. - - - -\begin{algorithm} - % \KwIn{all the parameters related to information exchange} -% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)} -% \BlankLine - %\emph{Initialize the sensor node and determine it's position and subregion} \; - -\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\ -\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\ -\hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\ -\hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\ -\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\ -\hspace*{0.6cm} \emph{LeaderID = Leader election;}\\ -\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\ -\hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\ -\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\ -\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\ -\hspace*{1.2cm} {\bf end}\\ -\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\ -\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\ -\hspace*{1.2cm} {\bf end}\\ -\hspace*{1.2cm} {\bf else}\\ -\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\ -\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\ -\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\ -\hspace*{1.2cm} {\bf end}\\ -\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\ -\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\ -\hspace*{1.2cm}\emph{Update $RE_k $;}\\ -\hspace*{0.6cm} {\bf end}\\ -\hspace*{0.6cm} {\bf else}\\ -\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\ -\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\ -\hspace*{1.2cm}\emph{Update $RE_k $;}\\ -\hspace*{0.6cm} {\bf end}\\ -{\bf end}\\ -{\bf else}\\ -\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\ -{\bf end}\\ -\label{alg:PeCO} -\end{algorithm} - - - -In this algorithm, K.CurrentSize and K.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 -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 -collect position coordinates, remaining energy, sensor node ID, and the number -of their one-hop live neighbors during the information exchange. The sensors -inside a same region cooperate to elect a leader. The selection criteria for the -leader, in order of priority, are: larger numbers of neighbors, larger remaining -energy, and then in case of equality, larger index. Once chosen, the leader -collects information to formulate and solve the integer program which allows to -construct the set of active sensors in the sensing stage. - - -\section{Perimeter-based Coverage Problem Formulation} -\label{cp} - -\noindent In this section, the coverage model is mathematically formulated. We -start with a description of the notations that will be used throughout the -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 $I_j$ designates the set of coverage intervals (CI) obtained for - sensor~$j$. -\end{itemize} -$I_j$ refers to the set of coverage intervals which have been defined according -to the method introduced in subsection~\ref{CI}. For a coverage interval $i$, -let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved -in coverage interval~$i$ of sensor~$j$, that is: -\begin{equation} -a^j_{ik} = \left \{ -\begin{array}{lll} - 1 & \mbox{if sensor $k$ is involved in the } \\ - & \mbox{coverage interval $i$ of sensor $j$}, \\ - 0 & \mbox{otherwise.}\\ -\end{array} \right. -\end{equation} -Note that $a^k_{ik}=1$ by definition of the interval. - -Second, we define several binary and integer variables. Hence, each binary -variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase -($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer -variable which measures the undercoverage for the coverage interval $i$ -corresponding to sensor~$j$. In the same way, the overcoverage for the same -coverage interval is given by the variable $V^j_i$. - -If we decide to sustain a level of coverage equal to $l$ all along the perimeter -of sensor $j$, we have to ensure that at least $l$ sensors involved in each -coverage interval $i \in I_j$ of sensor $j$ are active. According to the -previous notations, the number of active sensors in the coverage interval $i$ of -sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network -lifetime, the objective is to activate a minimal number of sensors in each -period to ensure the desired coverage level. As the number of alive sensors -decreases, it becomes impossible to reach the desired level of coverage for all -coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure -of the deviation between the desired number of active sensors in a coverage -interval and the effective number. And we try to minimize these deviations, -first to force the activation of a minimal number of sensors to ensure the -desired coverage level, and if the desired level cannot be completely satisfied, -to reach a coverage level as close as possible to the desired one. - - - - -Our coverage optimization problem can then be mathematically expressed as follows: - -\begin{equation} -\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 )&\\ -\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}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\ -X_{k} \in \{0,1\}, \forall k \in A -\end{array} -\right. -\end{equation} - -$\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the -relative importance of satisfying the associated level of coverage. For example, -weights associated with coverage intervals of a specified part of a region may -be given by a relatively larger magnitude than weights associated with another -region. This kind of integer program is inspired from the model developed for -brachytherapy treatment planning for optimizing dose distribution -\citep{0031-9155-44-1-012}. The integer program must be solved by the leader in -each subregion at the beginning of each sensing phase, whenever the environment -has changed (new leader, death of some sensors). Note that the number of -constraints in the model is constant (constraints of coverage expressed for all -sensors), whereas the number of variables $X_k$ decreases over periods, since we -consider only alive sensors (sensors with enough energy to be alive during one -sensing phase) in the model. - -\section{Performance Evaluation and Analysis} -\label{sec:Simulation Results and Analysis} - - -\subsection{Simulation Settings} - - -The WSN area of interest is supposed to be divided into 16~regular subregions -and we use the same energy consumption than in our previous work~\citep{Idrees2}. -Table~\ref{table3} gives the chosen parameters settings. - -\begin{table}[ht] -\tbl{Relevant parameters for network initialization \label{table3}}{ - -\centering - -\begin{tabular}{c|c} - -\hline -Parameter & Value \\ [0.5ex] - -\hline -% inserts single horizontal line -Sensing field & $(50 \times 25)~m^2 $ \\ - -WSN size & 100, 150, 200, 250, and 300~nodes \\ - -Initial energy & in range 500-700~Joules \\ - -Sensing period & duration of 60 minutes \\ -$E_{th}$ & 36~Joules\\ -$R_s$ & 5~m \\ - -$\alpha^j_i$ & 0.6 \\ - -$\beta^j_i$ & 0.4 - -\end{tabular}} - - -\end{table} -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. - -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 -$\beta^j_i$) 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. - -We introduce the following performance metrics to evaluate the efficiency of our -approach. - - -\begin{itemize} -\item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until - the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and - $Lifetime_{50}$ denote, respectively, the amount of time during which is - guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can - fulfill the expected monitoring task until all its nodes have depleted their - energy or if the network is no more connected. This last condition is crucial - because without network connectivity a sensor may not be able to send to a - base station an event it has sensed. -\item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to - observe the area of interest. In our case, we discretized the sensor field as - a regular grid, which yields the following equation: - - -\[ - \scriptsize - \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100 -\] - - - where $n$ is the number of covered grid points by active sensors of every - subregions during the current sensing phase and $N$ is total number of grid - points in the sensing field. In our simulations we have set a layout of - $N~=~51~\times~26~=~1326$~grid points. -\item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to - activate as few nodes as possible, in order to minimize the communication - overhead and maximize the WSN lifetime. The active sensors ratio is defined as - follows: - -\[ - \scriptsize - \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100 -\] - - where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the - current sensing period~$p$, $|S|$ is the number of sensors in the network, and - $R$ is the number of subregions. -\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total - energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$, - divided by the number of periods. The value of EC is computed according to - this formula: - -\[ - \scriptsize - \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p - + E^{a}_p+E^{s}_p \right)}{P}, -\] - - where $P$ corresponds to the number of periods. The total energy consumed by - the sensors comes through taking into consideration four main energy - factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the - energy consumption spent by all the nodes for wireless communications during - period $p$. $E^{\scriptsize \mbox{list}}_p$, 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 $p$. $E^{\scriptsize \mbox{comp}}_p$ - refers to the energy needed by all the leader nodes to solve the integer - program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy - consumed by the WSN during the sensing phase (active and sleeping nodes). -\end{itemize} - - -\subsection{Simulation Results} - -In order to assess and analyze the performance of our protocol we have -implemented PeCO protocol in OMNeT++~\citep{varga} simulator. Besides PeCO, two -other protocols, described in the next paragraph, will be evaluated for -comparison purposes. The simulations were run on a DELL laptop with an Intel -Core~i3~2370~M (1.8~GHz) processor (2 cores) whose MIPS (Million Instructions -Per Second) rate is equal to 35330. To be consistent with the use of a sensor -node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate -equal to 6, the original execution time on the laptop is multiplied by 2944.2 -$\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for -Mathematical Programming (AMPL)~\citep{AMPL} is employed to generate the integer -program instance in a standard format, which is then read and solved by the -optimization solver GLPK (GNU linear Programming Kit available in the public -domain) \citep{glpk} through a Branch-and-Bound method. - -As said previously, the PeCO is compared to three other approaches. The first -one, called DESK, is a fully distributed coverage algorithm proposed by -\citep{ChinhVu}. The second one, called GAF~\citep{xu2001geography}, consists in -dividing the monitoring area into fixed squares. Then, during the decision -phase, in each square, one sensor is chosen to remain active during the sensing -phase. The last one, the DiLCO protocol~\citep{Idrees2}, is an improved version -of a research work we presented in~\citep{idrees2014coverage}. Let us notice that -PeCO and DiLCO protocols are based on the same framework. In particular, the -choice for the simulations of a partitioning in 16~subregions was made because -it corresponds to the configuration producing the best results for DiLCO. The -protocols are distinguished from one another by the formulation of the integer -program providing the set of sensors which have to be activated in each sensing -phase. DiLCO protocol tries to satisfy the coverage of a set of primary points, -whereas the PeCO protocol objective is to reach a desired level of coverage for each -sensor perimeter. In our experimentations, we chose a level of coverage equal to -one ($l=1$). - -\subsubsection{\bf Coverage Ratio} - -Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes -obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better -coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\% -produced by PeCO for the first periods. This is due to the fact that at the -beginning the DiLCO protocol puts to sleep status more redundant sensors (which -slightly decreases the coverage ratio), while the three other protocols activate -more sensor nodes. Later, when the number of periods is beyond~70, it clearly -appears that PeCO provides a better coverage ratio and keeps a coverage ratio -greater than 50\% for longer periods (15 more compared to DiLCO, 40 more -compared to DESK). The energy saved by PeCO in the early periods allows later a -substantial increase of the coverage performance. - -\parskip 0pt -\begin{figure}[h!] -\centering - \includegraphics[scale=0.5] {figure5.eps} -\caption{Coverage ratio for 200 deployed nodes.} -\label{figure5} -\end{figure} - - - - -\subsubsection{\bf Active Sensors Ratio} - -Having the less active sensor nodes in each period is essential to minimize the -energy consumption and thus to maximize the network lifetime. Figure~\ref{figure6} -shows the average active nodes ratio for 200 deployed nodes. We observe that -DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen -rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and -20.16~\% active nodes during the same time interval. As the number of periods -increases, PeCO protocol has a lower number of active nodes in comparison with -the three other approaches, while keeping a greater coverage ratio as shown in -figure \ref{figure5}. - -\begin{figure}[h!] -\centering -\includegraphics[scale=0.5]{figure6.eps} -\caption{Active sensors ratio for 200 deployed nodes.} -\label{figure6} -\end{figure} - -\subsubsection{\bf Energy Consumption} - -We studied the effect of the energy consumed by the WSN during the communication, -computation, listening, active, and sleep status for different network densities -and compared it for the four approaches. Figures~\ref{figure7}(a) and (b) -illustrate the energy consumption for different network sizes and for -$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the -most competitive from the energy consumption point of view. As shown in both -figures, PeCO consumes much less energy than the three other methods. One might -think that the resolution of the integer program is too costly in energy, but -the results show that it is very beneficial to lose a bit of time in the -selection of sensors to activate. Indeed the optimization program allows to -reduce significantly the number of active sensors and so the energy consumption -while keeping a good coverage level. - -\begin{figure}[h!] - \centering - \begin{tabular}{@{}cr@{}} - \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\ - \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)} - \end{tabular} - \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.} - \label{figure7} -\end{figure} - - - -\subsubsection{\bf Network Lifetime} - -We observe the superiority of PeCO and DiLCO protocols in comparison with the -two other approaches in prolonging the network lifetime. In -Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for -different network sizes. As highlighted by these figures, the lifetime -increases with the size of the network, and it is clearly largest for DiLCO -and PeCO protocols. For instance, for a network of 300~sensors and coverage -ratio greater than 50\%, we can see on figure~\ref{figure8}(b) that the lifetime -is about twice longer with PeCO compared to DESK protocol. The performance -difference is more obvious in figure~\ref{figure8}(b) than in -figure~\ref{figure8}(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\%. - -\begin{figure}[h!] - \centering - \begin{tabular}{@{}cr@{}} - \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\ - \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)} - \end{tabular} - \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\ - and (b)~$Lifetime_{50}$.} - \label{figure8} -\end{figure} - - - -Figure~\ref{figure9} compares the lifetime coverage of our protocols for -different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85, -Protocol/90, and Protocol/95 the amount of time during which the network can -satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ -respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications -that do not require a 100\% coverage of the area to be monitored. PeCO might be -an interesting method since it achieves a good balance between a high level -coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three -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!] -\centering \includegraphics[scale=0.5]{figure9.eps} -\caption{Network lifetime for different coverage ratios.} -\label{figure9} -\end{figure} - - - - -\section{Conclusion and Future Works} -\label{sec:Conclusion and Future Works} - -In this paper we have studied the problem of Perimeter-based Coverage Optimization in -WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which -schedules nodes' activities (wake up and sleep stages) with the objective of -maintaining a good coverage ratio while maximizing the network lifetime. This -protocol is applied in a distributed way in regular subregions obtained after -partitioning the area of interest in a preliminary step. It works in periods and -is based on the resolution of an integer program to select the subset of sensors -operating in active status for each period. Our work is original in so far as it -proposes for the first time an integer program scheduling the activation of -sensors based on their perimeter coverage level, instead of using a set of -targets/points to be covered. - - -We have carried out several simulations to evaluate the proposed protocol. The -simulation results show that PeCO is more energy-efficient than other -approaches, with respect to lifetime, coverage ratio, active sensors ratio, and -energy consumption. - -We plan to extend our framework so that the schedules are planned for multiple -sensing periods. - -We also want to improve our integer program to take into account heterogeneous -sensors from both energy and node characteristics point of views. - -Finally, it would be interesting to implement our protocol using a -sensor-testbed to evaluate it in real world applications. - -\bibliographystyle{gENO} -\bibliography{biblio} - - -\end{document} +% gENOguide.tex +% v4.0 released April 2013 + +\documentclass{gENO2e} +%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e} +%\renewcommand{\algorithmcfname}{ALGORITHM} +\usepackage{indentfirst} +\begin{document} + +%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April} + +%\articletype{GUIDE} + +\title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}} + +\author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$ +$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, + Belfort, France}};} + + +\maketitle + +\begin{abstract} +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. 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 the 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 demonstrate that PeCO can +offer longer lifetime coverage for WSNs in comparison with some other protocols. + +\begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling. +\end{keywords} + +\end{abstract} + + +\section{Introduction} +\label{sec:introduction} + +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)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring +tasks. A WSN consists of small low-powered sensors working together by +communicating with one another through multi-hop radio communications. Each node +can send the data it collects in its environment, thanks to its sensor, to the +user by means of sink nodes. 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~\citep{yick2008wireless}. Typically, a sensor node contains +three main components~\citep{anastasi2009energy}: a sensing unit able to measure +physical, chemical, or biological phenomena observed in the environment; a +processing unit which will process and store the collected measurements; a radio +communication unit for data transmission and receiving. + +The energy needed by an active sensor node to perform sensing, processing, and +communication is supplied by a power supply which is a battery. This battery has +a limited energy provision and it may be unsuitable or impossible to replace or +recharge it in most applications. Therefore it is necessary to deploy WSN with +high density in order to increase reliability and to exploit node redundancy +thanks to energy-efficient activity scheduling approaches. Indeed, the overlap +of sensing areas can be exploited to schedule alternatively some sensors in a +low power sleep mode and thus save energy. Overall, the main question that must +be answered is: how to extend the lifetime coverage of a WSN as long as possible +while ensuring a high level of coverage? These past few years many +energy-efficient mechanisms have been suggested to retain energy and extend the +lifetime of the WSNs~\citep{rault2014energy}.\\\\ +This paper makes the following contributions. +\begin{enumerate} +\item We have devised a framework to schedule nodes to be activated alternatively such + that the network lifetime is prolonged while ensuring that a certain level of + coverage is preserved. A key idea in our framework is to exploit spatial and + temporal subdivision. On the one hand, the area of interest is divided into + several smaller subregions and, on the other hand, the time line is divided into + periods of equal length. In each subregion the sensor nodes will cooperatively + choose a leader which will schedule nodes' activities, and this grouping of + sensors is similar to typical cluster architecture. +\item We have proposed a new mathematical optimization model. Instead of trying to + cover a set of specified points/targets as in most of the methods proposed in + the literature, we formulate an integer program based on perimeter coverage of + each sensor. The model involves integer variables to capture the deviations + between the actual level of coverage and the required level. Hence, an + optimal schedule will be obtained by minimizing a weighted sum of these + deviations. +\item We have conducted extensive simulation experiments, using the discrete event + simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared + our PeCO protocol to two approaches found in the literature: + DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous + work published in~\citep{Idrees2} which is based on another optimization model + for sensor scheduling. +\end{enumerate} + + + + + + +The rest of the paper is organized as follows. In the next section +some related work in the field is reviewed. Section~\ref{sec:The PeCO Protocol Description} +is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the +coverage model formulation which is used to schedule the activation of sensor +nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations +results and discusses the comparison with other approaches. Finally, concluding +remarks are drawn and some suggestions are given for future works in +Section~\ref{sec:Conclusion and Future Works}. + +\section{Related Literature} +\label{sec:Literature Review} + +In this section, some related works regarding the +coverage problem is summarized, and specific aspects of the PeCO protocol from the works presented in +the literature are presented. + +The most discussed coverage problems in literature can be classified in three +categories~\citep{li2013survey} according to their respective monitoring +objective. Hence, area coverage \citep{Misra} means that every point inside a +fixed area must be monitored, while target coverage~\citep{yang2014novel} refers +to the objective of coverage for a finite number of discrete points called +targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on +preventing intruders from entering into the region of interest. In +\citep{Deng2012} authors transform the area coverage problem into the target +coverage one taking into account the intersection points among disks of sensors +nodes or between disk of sensor nodes and boundaries. In +\citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of +sensors are sufficiently covered it will be the case for the whole area. They +provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of +each sensor. $d$ denotes the maximum number of sensors that are +neighbors to a sensor, and $n$ is the total number of sensors in the +network. {\it In PeCO protocol, instead of determining the level of coverage of + a set of discrete points, our optimization model is based on checking the + perimeter-coverage of each sensor to activate a minimal number of sensors.} + +The major approach to extend network lifetime while preserving coverage is to +divide/organize the sensors into a suitable number of set covers (disjoint or +non-disjoint)\citep{wang2011coverage}, where each set completely covers a region of interest, and to +activate these set covers successively. The network activity can be planned in +advance and scheduled for the entire network lifetime or organized in periods, +and the set of active sensor nodes is decided at the beginning of each period +\citep{ling2009energy}. Active node selection is determined based on the problem +requirements (e.g. area monitoring, connectivity, or power efficiency). For +instance, \citet{jaggi2006} address the problem of maximizing +the lifetime by dividing sensors into the maximum number of disjoint subsets +such that each subset can ensure both coverage and connectivity. A greedy +algorithm is applied once to solve this problem and the computed sets are +activated in succession to achieve the desired network lifetime. +\citet{chin2007}, \citet{yan2008design}, \citet{pc10}, propose algorithms +working in a periodic fashion where a cover set is computed at the beginning of +each period. {\it Motivated by these works, PeCO protocol works in periods, + where each period contains a preliminary phase for information exchange and + decisions, followed by a sensing phase where one cover set is in charge of the + sensing task.} + +Various centralized and distributed approaches, or even a mixing of these two +concepts, have been proposed to extend the network lifetime \citep{zhou2009variable}. In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its +own activity scheduling after an information exchange with its neighbors. The +main interest of such an approach is to avoid long range communications and thus +to reduce the energy dedicated to the communications. Unfortunately, since each +node has only information on its immediate neighbors (usually the one-hop ones) +it may make a bad decision leading to a global suboptimal solution. Conversely, +centralized +algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always +provide nearly or close to optimal solution since the algorithm has a global +view of the whole network. The disadvantage of a centralized method is obviously +its high cost in communications needed to transmit to a single node, the base +station which will globally schedule nodes' activities, and data from all the other +sensor nodes in the area. The price in communications can be huge since +long range communications will be needed. In fact the larger the WNS is, the +higher the communication and thus the energy cost are. {\it In order to be + suitable for large-scale networks, in the PeCO protocol, the area of interest + is divided into several smaller subregions, and in each one, a node called the + leader is in charge of selecting the active sensors for the current + period. Thus our protocol is scalable and is a globally distributed method, + whereas it is centralized in each subregion.} + +Various coverage scheduling algorithms have been developed these past few years. +Many of them, dealing with the maximization of the number of cover sets, are +heuristics. These heuristics involve the construction of a cover set by +including in priority the sensor nodes which cover critical targets, that is to +say targets that are covered by the smallest number of sensors +\citep{berman04,zorbas2010solving}. Other approaches are based on mathematical +programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014} +and dedicated techniques (solving with a branch-and-bound algorithm available in +optimization solver). The problem is formulated as an optimization problem +(maximization of the lifetime or number of cover sets) under target coverage and +energy constraints. Column generation techniques, well-known and widely +practiced techniques for solving linear programs with too many variables, have +also been +used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it In the PeCO + protocol, each leader, in charge of a subregion, solves an integer program + which has a twofold objective: minimize the overcoverage and the undercoverage + of the perimeter of each sensor.} + + + +\section{ The P{\scshape e}CO Protocol Description} +\label{sec:The PeCO Protocol Description} + +In this section, the Perimeter-based Coverage +Optimization protocol is decribed in details. First we present the assumptions we made and the models +we considered (in particular the perimeter coverage one), second we describe the +background idea of our protocol, and third we give the outline of the algorithm +executed by each node. + + +\subsection{Assumptions and Models} +\label{CI} + +A WSN consisting of $J$ stationary sensor nodes randomly and uniformly +distributed in a bounded sensor field is considered. The wireless sensors are +deployed in high density to ensure initially a high coverage ratio of the area +of interest. We assume that all the sensor nodes are homogeneous in terms of +communication, sensing, and processing capabilities and heterogeneous from +the energy provision point of view. The location information is available to a +sensor node either through hardware such as embedded GPS or location discovery +algorithms. We assume that each sensor node can directly transmit its +measurements to a mobile sink node. For example, a sink can be an unmanned +aerial vehicle (UAV) flying regularly over the sensor field to collect +measurements from sensor nodes. A mobile sink node collects the measurements and +transmits them to the base station. We consider a Boolean disk coverage model, +which is the most widely used sensor coverage model in the literature, and all +sensor nodes have a constant sensing range $R_s$. Thus, all the space points +within a disk centered at a sensor with a radius equal to the sensing range are +said to be covered by this sensor. We also assume that the communication range +$R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, \citet{Zhang05} +proved that if the transmission range fulfills the previous hypothesis, the +complete coverage of a convex area implies connectivity among active nodes. + +The PeCO protocol uses the same perimeter-coverage model as \citet{huang2005coverage}. It can be expressed as follows: a sensor is +said to be perimeter covered if all the points on its perimeter are covered by +at least one sensor other than itself. Authors \citet{huang2005coverage} proved that a network area is +$k$-covered (every point in the area covered by at least k sensors) if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). + +Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this +figure, sensor~$0$ has nine neighbors and we have reported on +its perimeter (the perimeter of the disk covered by the sensor) for each +neighbor the two points resulting from the intersection of the two sensing +areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively +for left and right from a neighboing point of view. The resulting couples of +intersection points subdivide the perimeter of sensor~$0$ into portions called +arcs. + +\begin{figure}[ht!] + \centering + \begin{tabular}{@{}cr@{}} + \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\ + \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)} + \end{tabular} + \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of + $u$'s perimeter covered by $v$.} + \label{figure1} +\end{figure} + +Figure~\ref{figure1}(b) describes the geometric information used to find the +locations of the left and right points of an arc on the perimeter of a sensor +node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the +west side of sensor~$u$, with the following respective coordinates in the +sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates +the euclidean distance between nodes~$u$ and $v$ is computed: $Dist(u,v)=\sqrt{\vert + u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is +obtained through the formula: + \[ +\alpha = \arccos \left(\frac{Dist(u,v)}{2R_s} +\right). +\] +The arc on the perimeter of~$u$ defined by the angular interval $[\pi + - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$. + +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{figure1}(a) illustrates the arcs for the nine neighbors of +sensor $0$ and Figure~\ref{figure2} gives the position of the corresponding arcs +in the interval $[0,2\pi)$. More precisely, 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 +from the first intersection point after point~zero, and the maximum level of +coverage is determined for each interval defined by two successive points. The +maximum level of coverage is equal to the number of overlapping arcs. For +example, +between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$ +(the value is highlighted in yellow at the bottom of Figure~\ref{figure2}), which +means that at most 2~neighbors can cover the perimeter in addition to node $0$. +Table~\ref{my-label} summarizes for each coverage interval the maximum level of +coverage and the sensor nodes covering the perimeter. The example discussed +above is thus given by the sixth line of the table. + + +\begin{figure*}[t!] +\centering +\includegraphics[width=127.5mm]{figure2.eps} +\caption{Maximum coverage levels for perimeter of sensor node $0$.} +\label{figure2} +\end{figure*} + + + + + \begin{table} + \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}} +{\begin{tabular}{|c|c|c|c|c|c|c|c|c|} +\hline +\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline +0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline +0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline +0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline +0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline +1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline +1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline +2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline +2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline +2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline +2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline +2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline +3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline +3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline +4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline +4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline +4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline +5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline +5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline +\end{tabular}} + + +\end{table} + + + + +In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an +integer program based on coverage intervals. The formulation of the coverage +optimization problem is detailed in~Section~\ref{cp}. Note that when a sensor +node has a part of its sensing range outside the WSN sensing field, as in +Figure~\ref{figure3}, the maximum coverage level for this arc is set to $\infty$ +and the corresponding interval will not be taken into account by the +optimization algorithm. + + \newpage +\begin{figure}[h!] +\centering +\includegraphics[width=62.5mm]{figure3.eps} +\caption{Sensing range outside the WSN's area of interest.} +\label{figure3} +\end{figure} + + +\subsection{The Main Idea} + +The WSN area of interest is, in a first step, divided into regular +homogeneous subregions using a divide-and-conquer algorithm. In a second step +our protocol will be executed in a distributed way in each subregion +simultaneously to schedule nodes' activities for one sensing period. + +As shown in Figure~\ref{figure4}, node activity scheduling is produced by our +protocol in a periodic manner. Each period is divided into 4 stages: Information +(INFO) Exchange, Leader Election, Decision (the result of an optimization +problem), and Sensing. For each period there is exactly one set cover +responsible for the sensing task. Protocols based on a periodic scheme, like +PeCO, are more robust against an unexpected node failure. On the one hand, if +a node failure is discovered before taking the decision, the corresponding sensor +node will not be considered by the optimization algorithm. On the other +hand, if the sensor failure happens after the decision, the sensing task of the +network will be temporarily affected: only during the period of sensing until a +new period starts, since a new set cover will take charge of the sensing task in +the next period. The energy consumption and some other constraints can easily be +taken into account since the sensors can update and then exchange their +information (including their residual energy) at the beginning of each period. +However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision) +are energy consuming, even for nodes that will not join the set cover to monitor +the area. + +\begin{figure}[t!] +\centering +\includegraphics[width=80mm]{figure4.eps} +\caption{PeCO protocol.} +\label{figure4} +\end{figure} + +We define two types of packets to be used by PeCO protocol: + +\begin{itemize} +\item INFO packet: sent by each sensor node to all the nodes inside a same + subregion for information exchange. +\item ActiveSleep packet: sent by the leader to all the nodes in its subregion + to transmit to them their respective status (stay Active or go Sleep) during + sensing phase. +\end{itemize} + + +Five statuses are possible for a sensor node in the network: + +\begin{itemize} +\item LISTENING: waits for a decision (to be active or not); +\item COMPUTATION: executes the optimization algorithm as leader to + determine the activities scheduling; +\item ACTIVE: node is sensing; +\item SLEEP: node is turned off; +\item COMMUNICATION: transmits or receives packets. +\end{itemize} + + +\subsection{PeCO Protocol Algorithm} + +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. + + + +\begin{algorithm} + % \KwIn{all the parameters related to information exchange} +% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)} +% \BlankLine + %\emph{Initialize the sensor node and determine it's position and subregion} \; + +\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\ +\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\ +\hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\ +\hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\ +\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\ +\hspace*{0.6cm} \emph{LeaderID = Leader election;}\\ +\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\ +\hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\ +\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\ +\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\ +\hspace*{1.2cm} {\bf end}\\ +\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\ +\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\ +\hspace*{1.2cm} {\bf end}\\ +\hspace*{1.2cm} {\bf else}\\ +\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\ +\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\ +\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\ +\hspace*{1.2cm} {\bf end}\\ +\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\ +\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\ +\hspace*{1.2cm}\emph{Update $RE_k $;}\\ +\hspace*{0.6cm} {\bf end}\\ +\hspace*{0.6cm} {\bf else}\\ +\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\ +\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\ +\hspace*{1.2cm}\emph{Update $RE_k $;}\\ +\hspace*{0.6cm} {\bf end}\\ +{\bf end}\\ +{\bf else}\\ +\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\ +{\bf end}\\ +\label{alg:PeCO} +\end{algorithm} + + + +In this algorithm, K.CurrentSize and K.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 +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 +collect position coordinates, remaining energy, sensor node ID, and the number +of their one-hop live neighbors during the information exchange. The sensors +inside a same region cooperate to elect a leader. The selection criteria for the +leader, in order of priority, are: larger numbers of neighbors, larger remaining +energy, and then in case of equality, larger index. Once chosen, the leader +collects information to formulate and solve the integer program which allows to +construct the set of active sensors in the sensing stage. + + +\section{Perimeter-based Coverage Problem Formulation} +\label{cp} + +In this section, the coverage model is mathematically formulated. The following +notations are used throughout the +section.\\ +First, 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 $I_j$ designates the set of coverage intervals (CI) obtained for + sensor~$j$. +\end{itemize} +$I_j$ refers to the set of coverage intervals which have been defined according +to the method introduced in subsection~\ref{CI}. For a coverage interval $i$, +let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved +in coverage interval~$i$ of sensor~$j$, that is: +\begin{equation} +a^j_{ik} = \left \{ +\begin{array}{lll} + 1 & \mbox{if sensor $k$ is involved in the } \\ + & \mbox{coverage interval $i$ of sensor $j$}, \\ + 0 & \mbox{otherwise.}\\ +\end{array} \right. +\end{equation} +Note that $a^k_{ik}=1$ by definition of the interval. + +Second, several binary and integer variables are defined. Hence, each binary +variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase +($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer +variable which measures the undercoverage for the coverage interval $i$ +corresponding to sensor~$j$. In the same way, the overcoverage for the same +coverage interval is given by the variable $V^j_i$. + +If we decide to sustain a level of coverage equal to $l$ all along the perimeter +of sensor $j$, we have to ensure that at least $l$ sensors involved in each +coverage interval $i \in I_j$ of sensor $j$ are active. According to the +previous notations, the number of active sensors in the coverage interval $i$ of +sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network +lifetime, the objective is to activate a minimal number of sensors in each +period to ensure the desired coverage level. As the number of alive sensors +decreases, it becomes impossible to reach the desired level of coverage for all +coverage intervals. Therefore variables $M^j_i$ and $V^j_i$ are introduced as a measure +of the deviation between the desired number of active sensors in a coverage +interval and the effective number. And we try to minimize these deviations, +first to force the activation of a minimal number of sensors to ensure the +desired coverage level, and if the desired level cannot be completely satisfied, +to reach a coverage level as close as possible to the desired one. + + + + +Our coverage optimization problem can then be mathematically expressed as follows: + +\begin{equation} +\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 )&\\ +\textrm{subject to :}&\\ +\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i = l \quad \forall i \in I_j, \forall j \in S\\ +\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i = l \quad \forall i \in I_j, \forall j \in S\\ +X_{k} \in \{0,1\}, \forall k \in A +\end{array} +\right. +\end{equation} + +$\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the +relative importance of satisfying the associated level of coverage. For example, +weights associated with coverage intervals of a specified part of a region may +be given by a relatively larger magnitude than weights associated with another +region. This kind of integer program is inspired from the model developed for +brachytherapy treatment planning for optimizing dose distribution +\citep{0031-9155-44-1-012}. The integer program must be solved by the leader in +each subregion at the beginning of each sensing phase, whenever the environment +has changed (new leader, death of some sensors). Note that the number of +constraints in the model is constant (constraints of coverage expressed for all +sensors), whereas the number of variables $X_k$ decreases over periods, since +only alive sensors (sensors with enough energy to be alive during one +sensing phase) are considered in the model. + +\section{Performance Evaluation and Analysis} +\label{sec:Simulation Results and Analysis} + + +\subsection{Simulation Settings} + + +The WSN area of interest is supposed to be divided into 16~regular subregions +and we use the same energy consumption model as in our previous work~\citep{Idrees2}. +Table~\ref{table3} gives the chosen parameters settings. + +\begin{table}[ht] +\tbl{Relevant parameters for network initialization \label{table3}}{ + +\centering + +\begin{tabular}{c|c} + +\hline +Parameter & Value \\ [0.5ex] + +\hline +% inserts single horizontal line +Sensing field & $(50 \times 25)~m^2 $ \\ + +WSN size & 100, 150, 200, 250, and 300~nodes \\ + +Initial energy & in range 500-700~Joules \\ + +Sensing period & duration of 60 minutes \\ +$E_{th}$ & 36~Joules\\ +$R_s$ & 5~m \\ +$R_c$ & 10~m \\ +$\alpha^j_i$ & 0.6 \\ + +$\beta^j_i$ & 0.4 + +\end{tabular}} + + +\end{table} +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 longer participate in the +coverage task. This value corresponds to the energy needed by the sensing phase, +obtained by multiplying the energy consumed in the 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. Higher priority is given to +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, +$\beta^j_i$ is assigned to a value which is slightly lower so as to minimize the number of active sensor nodes which contribute +in covering the interval. + +The following performance metrics are used to evaluate the efficiency of the +approach. + + +\begin{itemize} +\item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until + the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and + $Lifetime_{50}$ denote, respectively, the amount of time during which is + guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can + fulfill the expected monitoring task until all its nodes have depleted their + energy or if the network is no more connected. This last condition is crucial + because without network connectivity a sensor may not be able to send to a + base station an event it has sensed. +\item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to + observe the area of interest. In our case, the sensor field is discretized as + a regular grid, which yields the following equation: + + +\[ + \scriptsize + \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100 +\] + + + where $n$ is the number of covered grid points by active sensors of every + subregions during the current sensing phase and $N$ is total number of grid + points in the sensing field. In simulations a layout of + $N~=~51~\times~26~=~1326$~grid points is considered. +\item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to + activate as few nodes as possible, in order to minimize the communication + overhead and maximize the WSN lifetime. The active sensors ratio is defined as + follows: + +\[ + \scriptsize + \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100 +\] + + where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the + current sensing period~$p$, $|J|$ is the number of sensors in the network, and + $R$ is the number of subregions. +\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total + energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$, + divided by the number of periods. The value of EC is computed according to + this formula: + +\[ + \scriptsize + \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p + + E^{a}_p+E^{s}_p \right)}{P}, +\] + + where $P$ corresponds to the number of periods. The total energy consumed by + the sensors comes through taking into consideration four main energy + factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the + energy consumption spent by all the nodes for wireless communications during + period $p$. $E^{\scriptsize \mbox{list}}_p$, 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 $p$. $E^{\scriptsize \mbox{comp}}_p$ + refers to the energy needed by all the leader nodes to solve the integer + program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy + consumed by the WSN during the sensing phase (active and sleeping nodes). +\end{itemize} + + +\subsection{Simulation Results} + +In order to assess and analyze the performance of our protocol we have +implemented PeCO protocol in OMNeT++~\citep{varga} simulator. Besides PeCO, two +other protocols, described in the next paragraph, will be evaluated for +comparison purposes. The simulations were run on a DELL laptop with an Intel +Core~i3~2370~M (1.8~GHz) processor (2 cores) whose MIPS (Million Instructions +Per Second) rate is equal to 35330. To be consistent with the use of a sensor +node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate +equal to 6, the original execution time on the laptop is multiplied by 2944.2 +$\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for +Mathematical Programming (AMPL)~\citep{AMPL} is employed to generate the integer +program instance in a standard format, which is then read and solved by the +optimization solver GLPK (GNU linear Programming Kit available in the public +domain) \citep{glpk} through a Branch-and-Bound method. + +As said previously, the PeCO is compared to three other approaches. The first +one, called DESK, is a fully distributed coverage algorithm proposed by +\citep{ChinhVu}. The second one, called GAF~\citep{xu2001geography}, consists in +dividing the monitoring area into fixed squares. Then, during the decision +phase, in each square, one sensor is chosen to remain active during the sensing +phase. The last one, the DiLCO protocol~\citep{Idrees2}, is an improved version +of a research work we presented in~\citep{idrees2014coverage}. Let us notice that +PeCO and DiLCO protocols are based on the same framework. In particular, the +choice for the simulations of a partitioning in 16~subregions was made because +it corresponds to the configuration producing the best results for DiLCO. The +protocols are distinguished from one another by the formulation of the integer +program providing the set of sensors which have to be activated in each sensing +phase. DiLCO protocol tries to satisfy the coverage of a set of primary points, +whereas the PeCO protocol objective is to reach a desired level of coverage for each +sensor perimeter. In our experimentations, we chose a level of coverage equal to +one ($l=1$). + +\subsubsection{\bf Coverage Ratio} + +Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes +obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better +coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\% +produced by PeCO for the first periods. This is due to the fact that at the +beginning the DiLCO protocol puts to sleep status more redundant sensors (which +slightly decreases the coverage ratio), while the three other protocols activate +more sensor nodes. Later, when the number of periods is beyond~70, it clearly +appears that PeCO provides a better coverage ratio and keeps a coverage ratio +greater than 50\% for longer periods (15 more compared to DiLCO, 40 more +compared to DESK). The energy saved by PeCO in the early periods allows later a +substantial increase of the coverage performance. + +\parskip 0pt +\begin{figure}[h!] +\centering + \includegraphics[scale=0.5] {figure5.eps} +\caption{Coverage ratio for 200 deployed nodes.} +\label{figure5} +\end{figure} + + + + +\subsubsection{\bf Active Sensors Ratio} + +Having the less active sensor nodes in each period is essential to minimize the +energy consumption and thus to maximize the network lifetime. Figure~\ref{figure6} +shows the average active nodes ratio for 200 deployed nodes. We observe that +DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen +rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and +20.16~\% active nodes during the same time interval. As the number of periods +increases, PeCO protocol has a lower number of active nodes in comparison with +the three other approaches, while keeping a greater coverage ratio as shown in +Figure \ref{figure5}. + +\begin{figure}[h!] +\centering +\includegraphics[scale=0.5]{figure6.eps} +\caption{Active sensors ratio for 200 deployed nodes.} +\label{figure6} +\end{figure} + +\subsubsection{\bf Energy Consumption} + +We studied the effect of the energy consumed by the WSN during the communication, +computation, listening, active, and sleep status for different network densities +and compared it for the four approaches. Figures~\ref{figure7}(a) and (b) +illustrate the energy consumption for different network sizes and for +$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the +most competitive from the energy consumption point of view. As shown in both +figures, PeCO consumes much less energy than the three other methods. One might +think that the resolution of the integer program is too costly in energy, but +the results show that it is very beneficial to lose a bit of time in the +selection of sensors to activate. Indeed the optimization program allows to +reduce significantly the number of active sensors and so the energy consumption +while keeping a good coverage level. + +\begin{figure}[h!] + \centering + \begin{tabular}{@{}cr@{}} + \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\ + \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)} + \end{tabular} + \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.} + \label{figure7} +\end{figure} + + + +\subsubsection{\bf Network Lifetime} + +We observe the superiority of PeCO and DiLCO protocols in comparison with the +two other approaches in prolonging the network lifetime. In +Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for +different network sizes. As highlighted by these figures, the lifetime +increases with the size of the network, and it is clearly largest for DiLCO +and PeCO protocols. For instance, for a network of 300~sensors and coverage +ratio greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime +is about twice longer with PeCO compared to DESK protocol. The performance +difference is more obvious in Figure~\ref{figure8}(b) than in +Figure~\ref{figure8}(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\%. + +\begin{figure}[h!] + \centering + \begin{tabular}{@{}cr@{}} + \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\ + \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)} + \end{tabular} + \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\ + and (b)~$Lifetime_{50}$.} + \label{figure8} +\end{figure} + + + +Figure~\ref{figure9} compares the lifetime coverage of our protocols for +different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85, +Protocol/90, and Protocol/95 the amount of time during which the network can +satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ +respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications +that do not require a 100\% coverage of the area to be monitored. PeCO might be +an interesting method since it achieves a good balance between a high level +coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three +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!] +\centering \includegraphics[scale=0.5]{figure9.eps} +\caption{Network lifetime for different coverage ratios.} +\label{figure9} +\end{figure} + + + + +\section{Conclusion and Future Works} +\label{sec:Conclusion and Future Works} + +In this paper we have studied the problem of Perimeter-based Coverage Optimization in +WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which +schedules nodes' activities (wake up and sleep stages) with the objective of +maintaining a good coverage ratio while maximizing the network lifetime. This +protocol is applied in a distributed way in regular subregions obtained after +partitioning the area of interest in a preliminary step. It works in periods and +is based on the resolution of an integer program to select the subset of sensors +operating in active status for each period. Our work is original in so far as it +proposes for the first time an integer program scheduling the activation of +sensors based on their perimeter coverage level, instead of using a set of +targets/points to be covered. + + +We have carried out several simulations to evaluate the proposed protocol. The +simulation results show that PeCO is more energy-efficient than other +approaches, with respect to lifetime, coverage ratio, active sensors ratio, and +energy consumption. + +We plan to extend our framework so that the schedules are planned for multiple +sensing periods. + +We also want to improve our integer program to take into account heterogeneous +sensors from both energy and node characteristics point of views. + +Finally, it would be interesting to implement our protocol using a +sensor-testbed to evaluate it in real world applications. + +\bibliographystyle{gENO} +\bibliography{biblio} + + +\end{document} diff --git a/PeCO-EO/reponse.tex b/PeCO-EO/reponse.tex index b10b1d9..1b8643c 100644 --- a/PeCO-EO/reponse.tex +++ b/PeCO-EO/reponse.tex @@ -56,32 +56,33 @@ This paper proposes a scheduling technique for WSN to maximize coverage and netw \noindent {\bf 1.} The paper makes use of the existing integer optimization model to govern the state of each sensor node within the WSN to maximize coverage and network lifetime. This formulation of the coverage problem is different from the literature in the sense that they use the perimeter coverage measures to optimize coverage as opposed to the targets/points coverage. The methodology uses existing methods and the original contribution lies only in the application of these methods for the coverage scheduling problem.\\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} To the best of our knowledge, no integer linear programming based on perimeter coverage has been already proposed in the literature. As specified in the paper, in section 4, it is inspired from one model developed for brachytherapy treatment planning for optimizing dose distribution. In this model the deviation between an actual dose distribution and a required dose distribution in each organ is minimized. In WSN the deviations between the actual level of coverage and the required level are minimized. Outside this parallel between these two applications the mathematical formulation is completly different. }}\\ \noindent {\bf 2.} The theory seems mathematically sound. However, the assumption made on the selection criteria for the leader seems too vague. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} The selection criteria for the leader inside each subregion is explained in page 8, lines 50-51. After information exchange among the sensor nodes in the subregion, each node will have all required information to decide if it is a leader or not. The decision is based on selecting the sensor node that have a larger number of one-hop neighbors. If there is more than one sensor node has the same number of one-hop neighbors, the node that has larger remaining energy will be selected as a leader. If there is more than one sensor node with the same number of neighbors and remaining energy, the sensor node that has larger index will be selected as a leader. In fact, we gave a high priority to the number of neighbors to reduce the communication energy consumption }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The selection criteria for the leader inside each subregion is explained in page 8, lines 50-51. After information exchange among the sensor nodes in the subregion, each node will have all required information to decide if it is a leader or not. The decision is based on selecting the sensor node that has a larger number of one-hop neighbors. If this value is the same for many sensors, the node that has the largest remaining energy will be selected as a leader. If there exists sensors with the same number of neighbors and the same value for the remaining energy, the sensor node that has the largest index will be selected as a leader. }}\\ +%{\bf In fact, we gave a high priority to the number of neighbors to reduce the communication energy consumption - PAS CLAIR }}.\\ \noindent {\bf 3.} The communication and information sharing required to cooperate and make these decisions was not discussed. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} The communication and information sharing required to cooperate and make these decisions was discussed in page 8, lines 48-49}}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The communication and information sharing required to cooperate and make these decisions was discussed in page 8, lines 48-49. Position coordinates, remaining energy, sensor node ID and number of one-hop neighbors are exchanged.}}\\ \noindent {\bf 4.} The definitions of the undercoverage and overcoverage variables are not clear. I suggest adding some information about these values, since without it, you cannot understand how M and V are computed for the optimization problem. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The perimeter of each sensor may be cut in parts called coverage intervals (CI). The level of coverage of one CI is defined as the number of active sensors neighbours covering this part of the perimeter. If a given level of coverage $l$ is required for one sensor, the sensor is said to be undercovered (respectively overcovered) if the level of coverage of one of its CI is less (respectively greater) than $l$. In other terms, we define undercoverage and overcoverage through the use of variables $M_{i}^{j}$ and $V_{i}^{j}$ for one sensor $j$ and its coverage interval $i$. If the sensor $j$ is undercovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In the contrary, if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is greater than $l$ and in this case : $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$. }}\\ \noindent {\bf 5.} Can you mathematically justify how you chose the values of alpha and beta? This is not very clear. I would suggest possibly adding more results showing how the algorithm performs with different alphas and betas. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The choice of alpha and beta should be made according to the needs of the application. alpha should be enough large to prevent undercoverage and so to reach the highest possible coverage ratio. beta should be enough large to prevent overcoverage and so to activate a minimum number of sensors. The values of $\alpha_{i}^{j}$ can be identical for all coverage intervals $i$ of one sensor $j$ in order to express that the perimeter of each sensor should be uniformly covered, but $\alpha_{i}^{j}$ values can be differenciated between sensors to force some regions to be better covered than others. The choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit the activation of a large number of sensors, but as $\alpha$ is low, some areas may be poorly covered. This explains the results obtained for {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. With $\alpha \gg \beta$, we priviligie the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio. }}\\ @@ -89,18 +90,18 @@ very clear. I would suggest possibly adding more results showing how the algorit However, the clarity in the literature review is a little off. Some of the descriptions of the method s used are very vague and do not bring out their key contributions. Some references are not consistent and I suggest using the journals template to adjust them for overall consistency. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} }}\\ \noindent {\bf 7.} The methodology is implemented in OMNeT++ (network simulator) and tested against 2 existing algorithms and a previously developed method by the authors. The simulation results are thorough and show that the proposed method improves the coverage and network lifetime compared with the 3 existing methods. The results are similar to previous work done by their team. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Although the study conducted in this paper reuses the same protocol presented in our previous work, we focus in this paper on the mathematical optimization model developed to schedule nodes activities. We deliberately chose to keep the same performance indicators to compare the results obtained with this new formulation with other existing algorithms. }}\\ \noindent {\bf 8.} Since this paper is attacking the coverage problem, I would like to see more information on the amount of coverage the algorithm is achieving. It seems that there is a tradeoff in this algorithm that allows the network to increase its lifetime but does not improve the coverage ratio. This may be an issue if this approach is used in an application that requires high coverage ratio. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Your remark is interesting. Indeed, figures 8(a) and (b) highlight this result. PeCO methods allows to achieve a coverage ratio greater than $50\%$ for many more periods than the others three methods, but for applications requiring an high level of coverage (greater than $95\%$), DilCO method is more efficient. }}\\ %%%%%%%%%%%%%%%%%%%%%% ENGLISH and GRAMMER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -108,77 +109,78 @@ s used are very vague and do not bring out their key contributions. Some referen \noindent {\ding{90} The first paragraph of every section is not indented. } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected. The first paragraph of every section is indented in the new version. }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed. The first paragraph of every section is indented in the new version. }}\\ \noindent {\ding{90} You seem to be writing in the first person. I suggest rewriting sentences that include “we” “our” or “I” in the third person. (There are too many instances to list them all. They are easily found using the find tool.) } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} It is very common to find sentences with "we" and "our" in scientific papers to explain the work made by the authors. Nevertheless we agree with the reviewer and we reformulated some sentences in the paper to avoid too many uses of the first person. }}\\ \noindent {\ding{90} Run-on sentence: Page 2 lines 43-48} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} We rewrote this sentence in two separated sentences. }}\\ \noindent {\ding{90} Add an “and” after the comma on page 3 line 34.} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected. }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\ \noindent {\ding{90} “model as” instead of “Than” on page 10 line 12.} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected. }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\ \noindent {\ding{90} “no longer” instead of “no more” on page 10 line 31.} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\ \noindent {\ding{90} “in the active state” add the on page 10 line 34. } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\ \noindent { \ding{90} Lots of English and grammar mistakes. I recommend rereading the paper line by line and adjusting the sentences that do not make sense.} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} ?????? relecture par Ingrid }}.\\ \section*{Response to Reviewer No. 2 Comments} -The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks", by Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier proposes a new protocol for Wireless Sensor Networks called PeCO (Perimeter-based Coverage Optimization protocol) that aims at optimizing the use of energy by conjointly exploiting a spatial and temporal subdivision. The protocol is based on solving a Mixed Integer Linear Program at each leader node, and at each iteration of the protocol. The results obtained by PeCO are compared with three other competitors. +The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks", by Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier proposes a new protocol for Wireless Sensor Networks called PeCO (Perimeter-based Coverage Optimization protocol) that aims at optimizing the use of energy by conjointly exploiting a spatial and temporal subdivision. The protocol is based on solving a Mixed Integer Linear Program at each leader node, and at each iteration of the protocol. The results obtained by PeCO are compared with three other competitors.\\ -\noindent\textcolor{black}{\textbf{\Large MAJOR COMMENTS:}} \\ +\noindent\textcolor{black}{\textbf{MAJOR COMMENTS:}} \\ -\noindent {\ding{90} The protocol framework is not described in details. In particular, the spatial and temporal subdivision (page 2, line 11) that is at the core of PeCO, is not described nor justified in much detail. How to implement an efficient spatial subdivision? On page 10, line 11, the number of subdivisions is said to be equal to 16, but the clustering algorithm used is not mentioned. Is this number dependent of the size of the sensing area? Of the number of sensors? Of the sensing range? The proposed protocol cannot be adopted by practitioners if such an important step is not documented. Temporal subdivision suffers from the same lack of description and justification: why should time intervals have the same duration? If they have the same duration, how should this common duration should be chosen? } \\ +\noindent {\bf 1.} The protocol framework is not described in details. In particular, the spatial and temporal subdivision (page 2, line 11) that is at the core of PeCO, is not described nor justified in much detail. How to implement an efficient spatial subdivision? On page 10, line 11, the number of subdivisions is said to be equal to 16, but the clustering algorithm used is not mentioned. Is this number dependent of the size of the sensing area? Of the number of sensors? Of the sensing range? The proposed protocol cannot be adopted by practitioners if such an important step is not documented. Temporal subdivision suffers from the same lack of description and justification: why should time intervals have the same duration? If they have the same duration, how should this common duration should be chosen? \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Spatial and temporal choices of subdivision are not the topics of the paper. In the study, we assume that the deployment of sensors is almost uniformly over the region. So we only need to fix a regular division of the region into subregions to make the problem tractable. The subdivision is made such that the number of hops between any pairs of sensors inside a subregion is less than or equal to 3. Concerning the choice of the sensing period duration, it is correlated with the types of applications, with the amount of initial energy in sensors batteries and also with the duration of the exchange phase. All applications do not have the same requirements of Quality of Service. Here information exchange is executed every hour but the length of the sensing period could be reduced and adapted dynamically. On the one hand a small sensing period would allow to be more reliable but would have higher communication costs. On the other hand the choice of a long duration may cause problems in case of nodes failure during the sensing period.}}\\ -\noindent {\ding{90} Page 9, Section 4, is the Perimeter-based coverage problem NP-hard? This question is important for justifying the use of a Mixed Integer Linear Programming model. } \\ +\noindent {\bf 2.}Page 9, Section 4, is the Perimeter-based coverage problem NP-hard? This question is important for justifying the use of a Mixed Integer Linear Programming model. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The perimeter scheduling coverage problem is NP-hard in general, it has been proved + in the paper entitled "Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors with a Single Continuous Cover Range" from Ka-Shun Hung and King-Shan Lui (EURASIP Journal on Wireless Communications and Networking 2010, 2010:926075 doi:10.1155/2010/926075). In this paper, authors study the coverage of the perimeter of a large object requiring to be monitored. In our study, the large object to be monitored is the sensor itself (or more precisely its sensing area). }}\\ -\noindent {\ding{90} Page 9, the major problem with the present paper is, in my opinion, the objective function of the Mixed Integer Linear Program (2). It is not described in the paper, and looks like an attempt to address a multiobjective problem (like minimizing overcoverage and undercoverage). However, using a weighted sum is well known not to be an efficient way to address biobjective problems. The introduction of various performance metrics in Section 5.1 also suggests that the authors have not decided exactly which objective function to use, and compare their protocols against competitors without mentioning the exact purpose of each of them. If the performance metrics list given in Section 5.1 is exhaustive, then the authors should mention at the beginning of the paper what are the aims of the protocol, and explain how the protocol is built to optimize these objectives. } \\ +\noindent {\bf 3.} Page 9, the major problem with the present paper is, in my opinion, the objective function of the Mixed Integer Linear Program (2). It is not described in the paper, and looks like an attempt to address a multiobjective problem (like minimizing overcoverage and undercoverage). However, using a weighted sum is well known not to be an efficient way to address biobjective problems. The introduction of various performance metrics in Section 5.1 also suggests that the authors have not decided exactly which objective function to use, and compare their protocols against competitors without mentioning the exact purpose of each of them. If the performance metrics list given in Section 5.1 is exhaustive, then the authors should mention at the beginning of the paper what are the aims of the protocol, and explain how the protocol is built to optimize these objectives. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} As far as we know, representing the objective function as a weighted sum of criteria to be minimized in case of multicriteria optimization is a classical method. }}\\ -\noindent {\ding{90} Page 11 Section 5.2, the sensor nodes are said to be based on Atmels AVR ATmega103L microcontroller. If I am not mistaken, these devices have 128 KBytes of memory, and I didn't find any clue that they can run an operating system like Linux. This point is of primary importance for the proposed protocol, since GLPK (a C API) is supposed to be executed by the cluster leader. In addition to that, GLPK requires a non negligible amount of memory to run properly, and the Atmels AVR ATmega103L microcontroller might be insufficient for that purpose. The authors are urged to provide references of previous works showing that these technical constraints are not preventing their protocol to be implemented on the aforementioned microcontroller. Then, on page 13, in Section "5.2.3 Energy Consumption", the estimation of $E_p^com$ for the considered microcontroller seems quite challenging and should be carefully documented. Indeed, this is a key point in providing a fair comparison of PeCO with its competitors. } \\ +\noindent {\bf 4.}Page 11 Section 5.2, the sensor nodes are said to be based on Atmels AVR ATmega103L microcontroller. If I am not mistaken, these devices have 128 KBytes of memory, and I didn't find any clue that they can run an operating system like Linux. This point is of primary importance for the proposed protocol, since GLPK (a C API) is supposed to be executed by the cluster leader. In addition to that, GLPK requires a non negligible amount of memory to run properly, and the Atmels AVR ATmega103L microcontroller might be insufficient for that purpose. The authors are urged to provide references of previous works showing that these technical constraints are not preventing their protocol to be implemented on the aforementioned microcontroller. Then, on page 13, in Section "5.2.3 Energy Consumption", the estimation of $E_p^{com}$ for the considered microcontroller seems quite challenging and should be carefully documented. Indeed, this is a key point in providing a fair comparison of PeCO with its competitors. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} }}\\ -\noindent\textcolor{black}{\textbf{\Large MINOR COMMENTS:}} \\ +\noindent\textcolor{black}{\textbf{MINOR COMMENTS:}} \\ \noindent {\ding{90} Page 12, lines 7-15, the authors mention that DiLCO protocol is close to PeCO. This should be mentioned earlier in the paper, ideally in Section 2 (Related Literature), along with the detailed description of DESK and GAF, the competitors of the proposed protocol, PeCO. } \\ @@ -189,86 +191,85 @@ The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in \noindent {\ding{90} Page 2, line 20, "An optimal scheduling" should be replaced with "An optimal schedule" } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 4, we first read (line 23) "we assume that each sensor node can directly transmit its measurements to a mobile sink", then on line 30, "We also assume that the communication range Rc satisfies $Rc >=2Rs$. In fact, Zhang and Hou (2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes.". These two assumptions seems redundant. } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Yes, you are right and we removed sentences about the sink. Indeed we consider multi-hops communication.}}.\\ \noindent {\ding{90} Page 4, line 37, a definition for k-covered is missing (the sentence is an equivalence property).} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right. A network area is said to be $k$-covered if every point in the area covered by at least k sensors. We added this definition in the paper}}.\\ \noindent {\ding{90} Page 5, lines 34 and 37, replace [0, $2\pi$] with [0, $2\pi$) } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 5, line 36 and 43, replace "figure 2" with "Figure 2" } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 5, line 50, replace "section 4" with "Section 4" } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 5, line 51, replace "figure 3" with "Figure 3"} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 7, line 20 "regular homogeneous subregions" is too vague. } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} As mentioned in the previous remark, the spatial subdivision was not clearly explained in the paper. We added a discussion about this question in the article. Thank you for highlighting it. A FAIRE }}.\\ \noindent {\ding{90} Page 7, line 24, replace "figure 4" with "Figure 4"} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 7, line 47, replace "Five status" with "Five statuses" } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 9, the constraints of the Mixed Integer Linear Program (2) are not numbered. There are two inequalities for overcoverage and undercoverage that are used to define Mij and Vij. Why not using replacing these inequalities by equalities? } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ - +\textcolor{blue}{\textbf{\textsc{Answer:} In fact, replacing these inequalities by equalities does not impact the final result because of the structure of the integer programming. For minimizing the objective function, $M_{i}^{j}$ and $V_{i}^{j}$ should be set to the smallest possible value such that the inequalities are satisfied. It is explained in the answer 4 for the reviewer 1. So, at optimality, constraints are satisfied with equality. So, we thank for your remark and we changed it in the formulation, even if there is no incidence about the final result.}}\\ \noindent {\ding{90} Page 10, line 50, "or if the network is no more connected". In order to assess this, the communication range should be known, but it is not given in Table 2. } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed}}.\\ \noindent {\ding{90} Page 10, line 53, the "Coverage ratio" definition is provided for a given period p? Then in the formula on top of page 11, N is set to 51 times 26, why? Is it somehow related to the sensing area having size 50 times 25? } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Yes, the "Coverage ratio" definition is provided for a given period p. N is set to 51 times 26 = 1326 grid points because we discretized the sensing field as a regular grid. Yes, it is related to the sensing area having size 50 times 25. }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Yes, the "Coverage ratio" definition is provided for a given period p. N is set to 51 times 26 = 1326 grid points because we discretized the sensing field as a regular grid, a point on the contour and a point every meter. Yes, it is related to the sensing area having size 50 meters times 25 meters. }}\\ \noindent {\ding{90} Page 11, line 17 in the formula of ASR, |S| should be replaced with J (where J is defined page 4 line 16). } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\ \noindent {\ding{90} Page 13, line 41 and 43, replace "figure 8" with "Figure 8" } \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\