1 \documentclass[a4paper,twoside]{article}
13 \usepackage{SCITEPRESS}
14 \usepackage[small]{caption}
16 \usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
17 \usepackage{mathtools}
25 %\title{Authors' Instructions \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
27 \title{Distributed Lifetime Coverage Optimization Protocol \\in Wireless Sensor Networks}
29 \author{\authorname{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
30 \affiliation{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, Belfort, France}
31 %\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry}
32 \email{ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
33 %\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu}
36 \keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,
37 Optimization, Scheduling.}
39 \abstract{One of the fundamental challenges in Wireless Sensor Networks (WSNs) is the
40 coverage preservation and the extension of the network lifetime continuously and
41 effectively when monitoring a certain area (or region) of interest. In this
42 paper, a Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
43 the coverage and to improve the lifetime in wireless sensor networks is
44 proposed. The area of interest is first divided into subregions using a
45 divide-and-conquer method and then the DiLCO protocol is distributed on the
46 sensor nodes in each subregion. The DiLCO combines two efficient techniques:
47 leader election for each subregion, followed by an optimization-based planning
48 of activity scheduling decisions for each subregion. The proposed DiLCO works
49 into periods during which a small number of nodes, remaining active for sensing,
50 is selected to ensure coverage so as to maximize the lifetime of wireless sensor
51 network. Each period consists of four phases: (i)~Information Exchange,
52 (ii)~Leader Election, (iii)~Decision, and (iv)~Sensing. The decision process is
53 carried out by a leader node, which solves an integer program. Compared with
54 some existing protocols, simulation results show that the proposed protocol can
55 prolong the network lifetime and improve the coverage performance effectively.}
57 \onecolumn \maketitle \normalsize \vfill
59 \section{\uppercase{Introduction}}
60 \label{sec:introduction}
62 Energy efficiency is very important issue in WSNs since sensors are powered by batteries. Therefore, reducing energy consumption and extending network lifetime are the main challenges in the design of WSNs. One of the major scientific research challenges in WSNs, which has been addressed by a large amount of literature during the last few years, is the design of energy efficient approaches for coverage and connectivity~\cite{conti2014mobile}.
63 Coverage reflects how well a sensor field is monitored. The most discussed coverage problems in literature can be classified
64 into three types \cite{li2013survey}: area coverage (where every
65 point inside an area is to be monitored), target coverage (where the main objective is to cover only a finite number of discrete
66 points called targets), and barrier coverage (the problem of preventing an intruder from entering a region of interest is referred to as the barrier coverage).
67 It is required to monitor the area of interest efficiently~\cite{Nayak04}, but in the same time the power consumption should be minimized. Sensor nodes runs on batteries with limited capacities~\cite{Sudip03} and it is impossible, difficult or expensive to recharge and/or replace batteries in remote, hostile, or unpractical environments. Therefore, it is desired that the WSNs are deployed with high densities so as to exploit the overlapping sensing regions of some sensor nodes to save energy by turning off some of them during the sensing phase to prolong the network lifetime.
69 In this paper we concentrate on the area coverage problem with the objective of
70 maximizing the network lifetime by using DiLCO protocol to maintain the coverage and to improve the lifetime in WSNs. The area of interest is divided into subregions using divide-and-conquer method and an activity scheduling for sensor nodes is planned by the elected leader in each subregion. In fact, the nodes in a subregion can be seen as a cluster where each node sends sensing data to the cluster head or the sink node. Furthermore, the activities in a subregion/cluster can continue even if another cluster stops due to too many node failures. Our DiLCO protocol considers periods, where a period starts with a discovery phase to exchange information between sensors of the subregion, in order to choose in a suitable manner a sensor node (the leader) to carry out the coverage strategy. Our DiLCO protocol involves solving an integer program, which provides the activation of the sensors for the sensing phase of the current period.
72 The remainder of the paper is organized as follows. The next section reviews the related work in the field. Section~\ref{sec:The DiLCO Protocol Description} is devoted to the DiLCO protocol Description. Section~\ref{cp} gives the coverage model
73 formulation which is used to schedule the activation of sensors.
74 Section~\ref{sec:Simulation Results and Analysis} shows the simulation results. Finally, we give concluding remarks and some suggestions for
75 future works in Section~\ref{sec:Conclusion and Future Works}.
77 \section{\uppercase{Literature Review}}
78 \label{sec:Literature Review}
79 \noindent In this section, we summarize some related works regarding coverage lifetime maximization and scheduling, and distinguish our DiLCO protocol from the works presented in the literature.
81 The work presented in~\cite{luo2014parameterized,tian2014distributed} tries to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
82 %Je ne comprends pas la phrase ci-dessus
83 The work proposed in~\cite{kim2013maximum} considers the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
84 %inutile de parler de ce papier car il concerne barrier coverage
85 In \cite{ChinhVu}, the authors propose a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network.
86 Our Work in~\cite{idrees2014coverage} proposes a coverage optimization protocol to improve the lifetime in heterogeneous energy wireless sensor networks. In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We are considered only distributing the coverage protocol over two subregions.
88 The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
90 The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
94 Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to extend the network lifetime with connectivity and coverage constraints. They are included two heuristic methods within the CG framework so as to accelerate the solution process.
95 In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution taking into consideration frequent nodes failure.
96 Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
97 approach (CWSC) to maintain k-coverage and connectivity. This approach try to select the minimum number of connected sensor nodes that can provide k-coverage ($k \geq 1$).
98 In~\cite{cheng2014achieving}, the authors are presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to provide a flexible and efficient coverage in sensor networks.
100 In~\cite{yang2013energy}, the authors are investigated full area coverage problem
101 under the probabilistic sensing model in the sensor networks. %They are designed $\varepsilon-$full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
102 In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
104 The main contributions of our DiLCO Protocol can be summarized as follows:
105 (1) The distributed optimization over the subregions in the area of interest,
106 (2) The distributed dynamic leader election at each round by each sensor node in the subregion,
107 (3) The primary point coverage model to represent each sensor node in the network,
108 (4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion,
109 (5) The improved energy consumption model.
113 \section{ The DiLCO Protocol Description}
114 \label{sec:The DiLCO Protocol Description}
116 \noindent In this section, we introduce a Distributed Lifetime Coverage Optimization protocol, which is called DiLCO. It is distributed on each subregion in the area of interest. It is based on two efficient techniques: network leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.
117 \iffalse The main features of our DiLCO protocol:
118 i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into rounds, iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi) it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative set of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our protocol.
120 \subsection{ Assumptions and Models}
121 \noindent We consider a randomly and uniformly deployed network consisting of
122 static wireless sensors. The wireless sensors are deployed in high
123 density to ensure initially a high coverage ratio of the interested area. We
124 assume that all nodes are homogeneous in terms of communication and
125 processing capabilities and heterogeneous in term of energy provision.
126 The location information is available to the sensor node either
127 through hardware such as embedded GPS or through location discovery
128 algorithms. We consider a boolean disk coverage model which is the most
129 widely used sensor coverage model in the literature. Each sensor has a
130 constant sensing range $R_s$. All space points within a disk centered
131 at the sensor with the radius of the sensing range is said to be
132 covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$.
133 In fact, Zhang and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the
134 previous hypothesis, a complete coverage of a convex area implies
135 connectivity among the working nodes in the active mode.
137 \indent Instead of working with the coverage area, we consider for each
138 sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the
139 sensing disk defined by a sensor is covered if all the primary points of
140 this sensor are covered.
143 By knowing the position (point center: ($p_x,p_y$)) of a wireless
144 sensor node and its $R_s$, we calculate the primary points directly
145 based on the proposed model. We use these primary points (that can be
146 increased or decreased if necessary) as references to ensure that the
147 monitored region of interest is covered by the selected set of
148 sensors, instead of using all the points in the area.
150 \indent We can calculate the positions of the selected primary
151 points in the circle disk of the sensing range of a wireless sensor
152 node (see figure~\ref{fig1}) as follows:\\
153 $(p_x,p_y)$ = point center of wireless sensor node\\
155 $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
156 $X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
157 $X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
158 $X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
159 $X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
160 $X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
161 $X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
162 $X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
163 $X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
164 $X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
165 $X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
166 $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
172 %\includegraphics[scale=0.20]{fig21.pdf}\\~ ~ ~ ~ ~(a)
173 %\includegraphics[scale=0.20]{fig22.pdf}\\~ ~ ~ ~ ~(b)
174 \includegraphics[scale=0.25]{principles13.pdf}%\\~ ~ ~ ~ ~(c)
175 %\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
176 %\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
177 %\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
179 \caption{Wireless Sensor Node represented by 13 primary points}
180 %\caption{Wireless Sensor Node represented by (a)5, (b)9 and (c)13 primary points respectively}
186 \subsection{The Main Idea}
187 \noindent The area of interest can be divided using the
188 divide-and-conquer strategy into smaller areas called subregions and
189 then our coverage protocol will be implemented in each subregion
190 simultaneously. Our DiLCO protocol works in periods fashion as shown in figure~\ref{fig2}.
193 \includegraphics[width=75mm]{FirstModel.pdf} % 70mm
194 \caption{DiLCO protocol}
198 %Modifier la figure pour faire apparaitre des periodes et dans le schema en bleu, indiquer sensing round au lieu de sensing tout seul.
200 Each period is divided into 4 phases : Information (INFO) Exchange,
201 Leader Election, Decision, and Sensing. For each period there is
202 exactly one set cover responsible for the sensing task. This protocol is
203 more reliable against an unexpected node failure because it works
204 in periods. On the one hand, if a node failure is detected before
205 making the decision, the node will not participate to this phase, and,
206 on the other hand, if the node failure occurs after the decision, the
207 sensing task of the network will be temporarily affected: only during
208 the period of sensing until a new period starts, since a new set cover
209 will take charge of the sensing task in the next period. The energy
210 consumption and some other constraints can easily be taken into
211 account since the sensors can update and then exchange their
212 information (including their residual energy) at the beginning of each
213 period. However, the pre-sensing phases (INFO Exchange, Leader
214 Election, Decision) are energy consuming for some nodes, even when
215 they do not join the network to monitor the area.
216 We define two types of packets to be used by our DiLCO protocol.
217 %\begin{enumerate}[(a)]
219 \item INFO packet: sent by each sensor node to all the nodes inside a same subregion for information exchange.
220 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion to inform them to be Active or Sleep during the sensing phase.
224 There are five status for each sensor node in the network :
225 %\begin{enumerate}[(a)]
227 \item LISTENING: Sensor is waiting for a decision (to be active or not)
228 \item COMPUTATION: Sensor applies the optimization process as leader
229 \item ACTIVE: Sensor is active
230 \item SLEEP: Sensor is turned off
231 \item COMMUNICATION: Sensor is transmitting or receiving packet
234 %Below, we describe each phase in more details.
235 Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_j$ for a sensor node indexed by $j$).
236 Initially, the sensor node checks its remaining energy in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy $RE_j$, sensor node id, and the number of its one-hop live neighbors during the information exchange.
237 Then all the sensor nodes in the same subregion will select the leader based on the received informations. The selection criteria for the leader in order of priority are: larger number of neighbours, larger remaining energy, and then in case of equality, larger index. After that, if the sensor node is leader, it will execute the integer program algorithm (see section~\ref{cp}) which provides a set of sensors planned to be active in the sensing round. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to indicate it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing round.
242 \subsubsection{Information Exchange Phase}
244 Each sensor node $j$ sends its position, remaining energy $RE_j$, and
245 the number of neighbours $NBR_j$ to all wireless sensor nodes in
246 its subregion by using an INFO packet and then listens to the packets
247 sent from other nodes. After that, each node will have information
248 about all the sensor nodes in the subregion. In our model, the
249 remaining energy corresponds to the time that a sensor can live in the
252 \subsubsection{Leader Election Phase}
253 This step includes choosing the Wireless Sensor Node Leader (WSNL),
254 which will be responsible for executing the coverage algorithm. Each
255 subregion in the area of interest will select its own WSNL
256 independently for each round. All the sensor nodes cooperate to
257 select WSNL. The nodes in the same subregion will select the leader
258 based on the received information from all other nodes in the same
259 subregion. The selection criteria in order of priority are: larger
260 number of neighbours, larger remaining energy, and then in case of
261 equality, larger index.
263 \subsubsection{Decision phase}
264 The WSNL will solve an integer program (see section~\ref{cp}) to
265 select which sensors will be activated in the following sensing phase
266 to cover the subregion. WSNL will send Active-Sleep packet to each
267 sensor in the subregion based on the algorithm's results.
270 \subsubsection{Sensing phase}
271 Active sensors in the round will execute their sensing task to
272 preserve maximal coverage in the region of interest. We will assume
273 that the cost of keeping a node awake (or asleep) for sensing task is
274 the same for all wireless sensor nodes in the network. Each sensor
275 will receive an Active-Sleep packet from WSNL informing it to stay
276 awake or to go to sleep for a time equal to the period of sensing until
277 starting a new round. Algorithm 1, which
278 will be executed by each node at the beginning of a round, explains how the
279 Active-Sleep packet is obtained.
285 \subsection{DiLCO protocol Algorithm}
286 we first show the pseudo-code of DiLCO protocol, which is executed by each sensor in the subregion and then describe it in more detail.
289 \begin{algorithm}[h!]
290 % \KwIn{all the parameters related to information exchange}
291 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
293 %\emph{Initialize the sensor node and determine it's position and subregion} \;
295 \If{ $RE_j \geq E_{R}$ }{
296 \emph{$s_j.status$ = COMMUNICATION}\;
297 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
298 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
299 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
300 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
302 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
303 \emph{LeaderID = Leader election}\;
304 \If{$ s_j.ID = LeaderID $}{
305 \emph{$s_j.status$ = COMPUTATION}\;
306 \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{J}\right)\right\}$ =
307 Execute Integer Program Algorithm($J$)}\;
308 \emph{$s_j.status$ = COMMUNICATION}\;
309 \emph{Send $ActiveSleep()$ to each node $k$ in subregion} \;
310 \emph{Update $RE_j $}\;
313 \emph{$s_j.status$ = LISTENING}\;
314 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
315 % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
316 \emph{Update $RE_j $}\;
320 \Else { Exclude $s_j$ from entering in the current sensing phase}
323 \caption{DiLCO($s_j$)}
329 The DiLCO protocol work in rounds and executed at each sensor node in the network , each sensor node can still sense data while being in
330 LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
331 sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow:
332 Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
333 The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will select the set of sensor nodes to take the mission of coverage during the sensing phase. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's status during the period of sensing, either Active or sleep until the starting of next round. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, all the sensor nodes in the same subregion will start new round by executing the DiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
337 \section{Coverage problem formulation}
340 \indent Our model is based on the model proposed by
341 \cite{pedraza2006} where the objective is to find a maximum number of
342 disjoint cover sets. To accomplish this goal, authors proposed an
343 integer program, which forces undercoverage and overcoverage of targets
344 to become minimal at the same time. They use binary variables
345 $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
346 model, we consider binary variables $X_{j}$, which determine the
347 activation of sensor $j$ in the sensing round. We also
348 consider primary points as targets. The set of primary points is
349 denoted by $P$ and the set of sensors by $J$.
351 \noindent For a primary point $p$, let $\alpha_{jp}$ denote the
352 indicator function of whether the point $p$ is covered, that is:
354 \alpha_{jp} = \left \{
356 1 & \mbox{if the primary point $p$ is covered} \\
357 & \mbox{by sensor node $j$}, \\
358 0 & \mbox{otherwise.}\\
362 The number of active sensors that cover the primary point $p$ is equal
363 to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
367 1& \mbox{if sensor $j$ is active,} \\
368 0 & \mbox{otherwise.}\\
372 We define the Overcoverage variable $\Theta_{p}$ as:
374 \Theta_{p} = \left \{
376 0 & \mbox{if the primary point}\\
377 & \mbox{$p$ is not covered,}\\
378 \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
382 \noindent More precisely, $\Theta_{p}$ represents the number of active
383 sensor nodes minus one that cover the primary point $p$.\\
384 The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
389 1 &\mbox{if the primary point $p$ is not covered,} \\
390 0 & \mbox{otherwise.}\\
395 \noindent Our coverage optimization problem can then be formulated as follows
396 \begin{equation} \label{eq:ip2r}
399 \min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
400 \textrm{subject to :}&\\
401 \sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
403 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
405 \Theta_{p}\in \mathbb{N} , &\forall p \in P\\
406 U_{p} \in \{0,1\}, &\forall p \in P \\
407 X_{j} \in \{0,1\}, &\forall j \in J
415 \item $X_{j}$ : indicates whether or not the sensor $j$ is actively
416 sensing in the round (1 if yes and 0 if not);
417 \item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
418 one that are covering the primary point $p$;
419 \item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
420 $p$ is being covered (1 if not covered and 0 if covered).
423 The first group of constraints indicates that some primary point $p$
424 should be covered by at least one sensor and, if it is not always the
425 case, overcoverage and undercoverage variables help balancing the
426 restriction equations by taking positive values. There are two main
427 objectives. First, we limit the overcoverage of primary points in order to
428 activate a minimum number of sensors. Second we prevent the absence of monitoring on
429 some parts of the subregion by minimizing the undercoverage. The
430 weights $w_\theta$ and $w_U$ must be properly chosen so as to
431 guarantee that the maximum number of points are covered during each
437 \section{\uppercase{Simulation Results and Analysis}}
438 \label{sec:Simulation Results and Analysis}
439 \noindent \subsection{Simulation Framework}
440 In this subsection, we conducted a series of simulations to evaluate the
441 efficiency and the relevance of our DiLCO protocol, using the discrete event
442 simulator OMNeT++ \cite{varga}. The simulation parameters are summarized in
446 \caption{Relevant parameters for network initializing.}
449 % used for centering table
451 % centered columns (4 columns)
453 %inserts double horizontal lines
454 Parameter & Value \\ [0.5ex]
456 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
460 % inserts single horizontal line
461 Sensing Field & $(50 \times 25)~m^2 $ \\
462 % inserting body of the table
464 Nodes Number & 50, 100, 150, 200 and 250~nodes \\
466 Initial Energy & 500-700~joules \\
468 Sensing Period & 60 Minutes \\
469 $E_{th}$ & 36 Joules\\
473 % [1ex] adds vertical space
479 % is used to refer this table in the text
482 We performed simulations for five different densities varying from 50 to 250~nodes. Experimental results are the average obtained from 25 randomly generated networks (25 for each network density) in which nodes are deployed over a $(50 \times 25)~m^2 $ sensing field. More precisely, the deployment is controlled at a coarse scale in order to ensure that the deployed nodes can cover the sensing field with a high coverage ratio.\\
484 We first concentrate on the required number of subregions making effective our protocol. Thus our DiLCO protocol is declined into five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$ or $32$ subregions (leaders).
486 We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
487 The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
488 % We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node.
489 %The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU.
492 For our energy consumption model, we refer to the sensor node Medusa II which uses Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The typical architecture of a sensor is composed of four subsystems : the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for
493 transmitting/receiving messages, sensing subsystem that collects data, and the power supply which powers the complete sensor node ~\cite{raghunathan2002energy}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table4}.
496 \caption{The Energy Consumption Model}
499 % used for centering table
500 \begin{tabular}{|c|c|c|c|c|}
501 % centered columns (4 columns)
503 %inserts double horizontal lines
504 Sensor mode & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
506 % inserts single horizontal line
507 Listening & ON & ON & ON & 20.05 \\
508 % inserting body of the table
510 Active & ON & OFF & ON & 9.72 \\
512 Sleep & OFF & OFF & OFF & 0.02 \\
514 Computation & ON & ON & ON & 26.83 \\
516 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
521 % is used to refer this table in the text
524 For the sake of simplicity we ignore the energy needed to turn on the
525 radio, to start up the sensor node, the transition from one status to another, etc.
526 %We also do not consider the need of collecting sensing data. PAS COMPRIS
527 Thus, when a sensor becomes active (i.e., it already decides its status), it can turn its radio off to save battery. DiLCO protocol uses two types of packets for communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24 bits respectively.
528 The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets.
529 The energy needed to send or receive a 1-bit is equal to $0.2575 mW$.
531 The initial energy of each node is randomly set in the interval $[500-700]$. Each sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mW) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.\\
534 In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach:
536 %\begin{enumerate}[i)]
539 \item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area of a sensor field is covered. In our case, we treated the sensing fields as a grid, and used each grid point as a sample point
540 for calculating the coverage. The coverage ratio can be calculated by:
543 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
545 where $n$ is the number of covered grid points by the active sensors of all subregions during the current sensing phase and $N$ is total number of grid points in the sensing field of the network. In our simulation $N = 51 \times 26 = 1326$ grid points.
546 %The accuracy of this method depends on the distance between grids. In our
547 %simulations, the sensing field has been divided into 50 by 25 grid points, which means
548 %there are $51 \times 26~ = ~ 1326$ points in total.
549 % Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
553 \item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
554 in order to minimize the communication overhead and maximize the
555 network lifetime. The Active Sensors Ratio is defined as follows:
558 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r^t$}}{\mbox{$S$}} \times 100 .
560 Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round $t$ in the current sensing phase, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
564 \item {{\bf Network Lifetime}:} we define the network lifetime as the time until the coverage ratio drops below a predefined threshold. We denoted by $Lifetime95$ (respectively $Lifetime50$) as the amount of time during which the network can satisfy an area coverage greater than $95\%$ (repectively $50\%$). We assume that the network
565 is alive until all nodes have been drained of their energy or the
566 sensor network becomes disconnected . Network connectivity is important because an
567 active sensor node without connectivity towards a base station cannot
568 transmit information on an event in the area that it monitors.
571 \item {{\bf Energy Consumption}:}
573 Energy Consumption (EC) can be seen as the total energy consumed by the sensors during the $Lifetime95$ or $Lifetime50$ divided by the number of periods. The EC can be computed as follow: \\
576 \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m + E^{a}+E^{s} \right)}{M_L},
581 %\mbox{EC} = \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
584 where $M_L$ corresponds to the number of periods. The total energy consumed by the sensors
585 (EC) comes through taking into consideration four main energy factors. The first
586 one , denoted $E^{\scriptsize \mbox{com}}_m$, represent the energy consumption
587 spent by all the nodes for wireless communications during period $m$.
588 $E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to the energy
589 consumed by the sensors in LISTENING status before receiving the decision to go
590 active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the
591 energy needed by all the leader nodes to solve the integer program during a
592 period. Finally, $E^a_{m}$ and $E^s_{m}$ indicate the energy consummed by the whole network in the sensing round.
595 \item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power,
596 therefore it is important that the proposed algorithm has the shortest
597 possible execution time. The energy of a sensor node must be mainly
598 used for the sensing phase, not for the pre-sensing ones.
600 \item {{\bf Stopped simulation runs}:} A simulation
601 ends when the sensor network becomes
602 disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.
610 %\subsection{Performance Analysis for differnet subregions}
611 \subsection{Performance Analysis}
613 In this subsection, we study the performance of our DiLCO protocol for different number of subregions (Leaders).
614 The DiLCO-1 protocol is a centralized approach on all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLC0-1 protocol in our simulation results because it requires high execution time to solve the integer program and thus it is too costly in term of energy.
616 Our method is compared with other two approaches. The first approach, called DESK and proposed by ~\cite{ChinhVu} is a full distributed coverage algorithm. The second approach, called GAF ~\cite{xu2001geography}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time.
619 \subsubsection{Coverage Ratio}
620 In this experiment, Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.
624 \includegraphics[scale=0.45] {R/CR.pdf}
625 \caption{The Coverage Ratio}
629 Figure~\ref{fig3} shows that DESK and GAF provide a
630 a little better coverage ratio compared to DiLCO in the first thirty periods. This is due to the fact that our DiLCO protocol versions put in sleep mode some sensors through optimization process (which slightly decreases the coverage ratio) while there are more active nodes with DESK or GAF. With DiLCO-2 (respectively DiLCO-4), the coverage ratio decreases rapidly to reach zero value in period ... (respectively in period ....) whereas other methods guarantee a coverage ratio greater than $50\%$ after this period. We believe that the results obtained with these two methods can be explained by a high consumption of energy
631 and we will check this assumption in the next paragraph. Concerning DiLCO-8, DiLCO-16 and DiLCO-32, these methods seem to be more efficient than DESK and GAF because they can provide the same level of coverage (except in the first periods, slightly lower) for a greater number of periods. Unlike other methods, their strategy enables to activate a restricted number of nodes, and thus extends the lifetime of the network.
632 %As shown in the figure ~\ref{fig3}, as the number of subregions increases, the coverage preservation for area of interest increases for a larger number of periods. Coverage ratio decreases when the number of periods increases due to dead nodes. Although some nodes are dead,
633 %thanks to DiLCO-8, DiLCO-16 and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16 and DiLCO-32 protocols are
634 %slightly more efficient than other protocols, because they subdivides
635 %the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%
639 \subsubsection{The Energy Consumption}
640 Based on previous results in figure~\ref{fig3}, we keep DiLCO-16 and DiLCO-32 and we compare their performances in terms of energy consumption with the two other approaches. We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities. Figure~\ref{fig95} illustrates the energy consumption for different network sizes.
641 % for $Lifetime95$ and $Lifetime50$.
642 We denote by $DiLCO-/50$ (respectively $DiLCO-/95$) as the amount of energy consumed during which the network can satisfy an area coverage greater than $50\%$ (repectively $95\%$) and we refer to the same definition for the two other approaches.
645 \includegraphics[scale=0.45]{R/EC.pdf}
646 \caption{The Energy Consumption}
650 The results show that DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes.
653 %In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
654 %As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.
657 \subsubsection{Execution Time}
658 We observe the impact of the network size and of the number of subregions on the computation time. We report the average execution times in seconds needed to solve the optimization problem for the different approaches and various numbers of sensors.
659 The original execution time is computed on a laptop DELL with intel Core i3 2370 M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6}\right)$ and reported on Figure~\ref{fig8}.
663 \includegraphics[scale=0.45]{R/T.pdf}
664 \caption{Execution Time (in seconds)}
669 Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison with other DiLCO versions, because the activity scheduling is tackled by a larger number of leaders and each leader solves an integer problem with a limited number of variables and constraints. Conversely, DiLCO-2 requires to solve an optimization problem with half of the network nodes and thus presents a high execution time. Nevertheless if we refer to figure~\ref{fig3}, we observe that DiLCO-32 is slightly less efficient than DilCO-16 to maintain as long as possible high coverage. Excessive subdivision of the area of interest prevents to ensure good coverage especially on the borders of the subregions.
671 %The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more. We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
674 \subsubsection{The Network Lifetime}
675 In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. The term $/50$ (respectively $/95$) next to the name of the method refers to the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$))
679 \includegraphics[scale=0.45]{R/LT.pdf}
680 \caption{The Network Lifetime}
685 As highlighted by figure~\ref{figLT95}, the network lifetime obviously
686 increases when the size of the network increases. For the same level of coverage, DiLCO outperforms DESK and GAF for the lifetime of the network. If we focus on level of coverage greater than $95\%$, The subdivision in $16$ subregions seems to be the most appropriate.
689 % with our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
690 % that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best
691 % suited nodes, for each round, to cover the area of interest and by
692 % letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed
693 % independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
698 \section{\uppercase{Conclusion and Future Works}}
699 \label{sec:Conclusion and Future Works}
700 In this paper, we have addressed the problem of the coverage and the lifetime
701 optimization in wireless sensor networks. This is a key issue as
702 sensor nodes have limited resources in terms of memory, energy and
703 computational power. To cope with this problem, the field of sensing
704 is divided into smaller subregions using the concept of divide-and-conquer method, and then a DiLCO protocol for optimizing the coverage and lifetime performances in each subregion.
705 The proposed protocol combines two efficient techniques: network
706 leader election and sensor activity scheduling, where the challenges
707 include how to select the most efficient leader in each subregion and
708 the best representative set of active nodes to ensure a high level of coverage.
709 We have compared this method with two other approaches using many metrics as coverage ratio, execution time, lifetime.
710 Some experiments have been performed to study the choice of the number of
711 subregions which subdivide the sensing field, considering different network
712 sizes. They show that as the number of subregions increases, so does the network
713 lifetime. Moreover, it makes the DiLCO protocol more robust against random
714 network disconnection due to node failures. However, too much subdivisions
715 reduces the advantage of the optimization. In fact, there is a balance between
716 the benefit from the optimization and the execution time needed to solve
717 it. Therefore, the subdivision in $16$ subregions seems to be the most appropriate.
719 \noindent In this paper, we have addressed the problem of the coverage and the lifetime
720 optimization in wireless sensor networks. This is a key issue as
721 sensor nodes have limited resources in terms of memory, energy and
722 computational power. To cope with this problem, the field of sensing
723 is divided into smaller subregions using the concept of divide-and-conquer method, and then a DiLCO protocol for optimizing the coverage and lifetime performances in each subregion.
724 The proposed protocol combines two efficient techniques: network
725 leader election and sensor activity scheduling, where the challenges
726 include how to select the most efficient leader in each subregion and
727 the best representative active nodes that will optimize the network lifetime
728 while taking the responsibility of covering the corresponding
729 subregion. The network lifetime in each subregion is divided into
730 rounds, each round consists of four phases: (i) Information Exchange,
731 (ii) Leader Election, (iii) an optimization-based Decision in order to
732 select the nodes remaining active for the last phase, and (iv)
733 Sensing. The simulations show the relevance of the proposed DiLCO
734 protocol in terms of lifetime, coverage ratio, active sensors ratio, energy consumption, execution time, and the number of stopped simulation runs due to network disconnection. Indeed, when
735 dealing with large and dense wireless sensor networks, a distributed
736 approach like the one we are proposed allows to reduce the difficulty of a
737 single global optimization problem by partitioning it in many smaller
738 problems, one per subregion, that can be solved more easily.
740 In future work, we plan to study and propose a coverage optimization protocol, which
741 computes all active sensor schedules in one time, using
742 optimization methods. \iffalse The round will still consist of 4 phases, but the
743 decision phase will compute the schedules for several sensing phases
744 which, aggregated together, define a kind of meta-sensing phase.
745 The computation of all cover sets in one time is far more
746 difficult, but will reduce the communication overhead. \fi
748 \section*{\uppercase{Acknowledgements}}
749 \noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
756 \bibliographystyle{apalike}
758 \bibliography{Example}}
