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\r
13 \title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}}
\r
15 \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 $^{a}$
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16 $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
\r
23 The most important problem in a Wireless Sensor Network (WSN) is to optimize the
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24 use of its limited energy provision, so that it can fulfill its monitoring task
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25 as long as possible. Among known available approaches that can be used to
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26 improve power management, lifetime coverage optimization provides activity
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27 scheduling which ensures sensing coverage while minimizing the energy cost. In
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28 this paper, we propose such an approach called Perimeter-based Coverage Optimization
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29 protocol (PeCO). It is a hybrid of centralized and distributed methods: the
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30 region of interest is first subdivided into subregions and our protocol is then
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31 distributed among sensor nodes in each subregion.
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32 The novelty of our approach lies essentially in the formulation of a new
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33 mathematical optimization model based on the perimeter coverage level to schedule
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34 sensors' activities. Extensive simulation experiments have been performed using
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35 OMNeT++, the discrete event simulator, to demonstrate that PeCO can
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36 offer longer lifetime coverage for WSNs in comparison with some other protocols.
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38 \begin{keywords}Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling.
\r
44 \section{Introduction}
\r
45 \label{sec:introduction}
\r
47 \noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
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48 wireless communication hardware has given rise to the opportunity to use large
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49 networks of tiny sensors, called Wireless Sensor Networks
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50 (WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
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51 tasks. A WSN consists of small low-powered sensors working together by
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52 communicating with one another through multi-hop radio communications. Each node
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53 can send the data it collects in its environment, thanks to its sensor, to the
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54 user by means of sink nodes. The features of a WSN made it suitable for a wide
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55 range of application in areas such as business, environment, health, industry,
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56 military, and so on~\cite{yick2008wireless}. Typically, a sensor node contains
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57 three main components~\cite{anastasi2009energy}: a sensing unit able to measure
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58 physical, chemical, or biological phenomena observed in the environment; a
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59 processing unit which will process and store the collected measurements; a radio
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60 communication unit for data transmission and receiving.
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62 The energy needed by an active sensor node to perform sensing, processing, and
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63 communication is supplied by a power supply which is a battery. This battery has
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64 a limited energy provision and it may be unsuitable or impossible to replace or
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65 recharge it in most applications. Therefore it is necessary to deploy WSN with
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66 high density in order to increase reliability and to exploit node redundancy
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67 thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
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68 of sensing areas can be exploited to schedule alternatively some sensors in a
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69 low power sleep mode and thus save energy. Overall, the main question that must
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70 be answered is: how to extend the lifetime coverage of a WSN as long as possible
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71 while ensuring a high level of coverage? These past few years many
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72 energy-efficient mechanisms have been suggested to retain energy and extend the
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73 lifetime of the WSNs~\cite{rault2014energy}.
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75 This paper makes the following contributions.
\r
77 \item We have devised a framework to schedule nodes to be activated alternatively such
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78 that the network lifetime is prolonged while ensuring that a certain level of
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79 coverage is preserved. A key idea in our framework is to exploit spatial and
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80 temporal subdivision. On the one hand, the area of interest is divided into
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81 several smaller subregions and, on the other hand, the time line is divided into
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82 periods of equal length. In each subregion the sensor nodes will cooperatively
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83 choose a leader which will schedule nodes' activities, and this grouping of
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84 sensors is similar to typical cluster architecture.
\r
85 \item We have proposed a new mathematical optimization model. Instead of trying to
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86 cover a set of specified points/targets as in most of the methods proposed in
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87 the literature, we formulate an integer program based on perimeter coverage of
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88 each sensor. The model involves integer variables to capture the deviations
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89 between the actual level of coverage and the required level. Hence, an
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90 optimal scheduling will be obtained by minimizing a weighted sum of these
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92 \item We have conducted extensive simulation experiments, using the discrete event
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93 simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
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94 our PeCO protocol to two approaches found in the literature:
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95 DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous
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96 work published in~\cite{Idrees2} which is based on another optimization model
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97 for sensor scheduling.
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105 The rest of the paper is organized as follows. In the next section we review
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106 some related work in the field. Section~\ref{sec:The PeCO Protocol Description}
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107 is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
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108 coverage model formulation which is used to schedule the activation of sensor
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109 nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
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110 results and discusses the comparison with other approaches. Finally, concluding
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111 remarks are drawn and some suggestions are given for future works in
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112 Section~\ref{sec:Conclusion and Future Works}.
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114 % that show that our protocol outperforms others protocols.
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115 \section{Related Literature}
\r
116 \label{sec:Literature Review}
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118 \noindent In this section, we summarize some related works regarding the
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119 coverage problem and distinguish our PeCO protocol from the works presented in
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122 The most discussed coverage problems in literature can be classified in three
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123 categories~\cite{li2013survey} according to their respective monitoring
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124 objective. Hence, area coverage \cite{Misra} means that every point inside a
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125 fixed area must be monitored, while target coverage~\cite{yang2014novel} refers
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126 to the objective of coverage for a finite number of discrete points called
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127 targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on
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128 preventing intruders from entering into the region of interest. In
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129 \cite{Deng2012} authors transform the area coverage problem into the target
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130 coverage one taking into account the intersection points among disks of sensors
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131 nodes or between disk of sensor nodes and boundaries. In
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132 \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
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133 sensors are sufficiently covered it will be the case for the whole area. They
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134 provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
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135 each sensor, where $d$ denotes the maximum number of sensors that are
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136 neighbors to a sensor and $n$ is the total number of sensors in the
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137 network. {\it In PeCO protocol, instead of determining the level of coverage of
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138 a set of discrete points, our optimization model is based on checking the
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139 perimeter-coverage of each sensor to activate a minimal number of sensors.}
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141 The major approach to extend network lifetime while preserving coverage is to
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142 divide/organize the sensors into a suitable number of set covers (disjoint or
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143 non-disjoint)\cite{wang2011coverage}, where each set completely covers a region of interest, and to
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144 activate these set covers successively. The network activity can be planned in
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145 advance and scheduled for the entire network lifetime or organized in periods,
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146 and the set of active sensor nodes is decided at the beginning of each period
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147 \cite{ling2009energy}. Active node selection is determined based on the problem
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148 requirements (e.g. area monitoring, connectivity, or power efficiency). For
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149 instance, Jaggi {\em et al.}~\cite{jaggi2006} address the problem of maximizing
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150 the lifetime by dividing sensors into the maximum number of disjoint subsets
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151 such that each subset can ensure both coverage and connectivity. A greedy
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152 algorithm is applied once to solve this problem and the computed sets are
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153 activated in succession to achieve the desired network lifetime. Vu
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154 \cite{chin2007}, \cite{yan2008design}, Padmatvathy {\em et al.}~\cite{pc10}, propose algorithms
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155 working in a periodic fashion where a cover set is computed at the beginning of
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156 each period. {\it Motivated by these works, PeCO protocol works in periods,
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157 where each period contains a preliminary phase for information exchange and
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158 decisions, followed by a sensing phase where one cover set is in charge of the
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161 Various centralized and distributed approaches, or even a mixing of these two
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162 concepts, have been proposed to extend the network lifetime \cite{zhou2009variable}. In distributed algorithms~\cite{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
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163 own activity scheduling after an information exchange with its neighbors. The
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164 main interest of such an approach is to avoid long range communications and thus
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165 to reduce the energy dedicated to the communications. Unfortunately, since each
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166 node has only information on its immediate neighbors (usually the one-hop ones)
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167 it may make a bad decision leading to a global suboptimal solution. Conversely,
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169 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
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170 provide nearly or close to optimal solution since the algorithm has a global
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171 view of the whole network. The disadvantage of a centralized method is obviously
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172 its high cost in communications needed to transmit to a single node, the base
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173 station which will globally schedule nodes' activities, data from all the other
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174 sensor nodes in the area. The price in communications can be huge since
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175 long range communications will be needed. In fact the larger the WNS is, the
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176 higher the communication and thus the energy cost are. {\it In order to be
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177 suitable for large-scale networks, in the PeCO protocol, the area of interest
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178 is divided into several smaller subregions, and in each one, a node called the
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179 leader is in charge of selecting the active sensors for the current
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180 period. Thus our protocol is scalable and is a globally distributed method,
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181 whereas it is centralized in each subregion.}
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183 Various coverage scheduling algorithms have been developed these past few years.
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184 Many of them, dealing with the maximization of the number of cover sets, are
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185 heuristics. These heuristics involve the construction of a cover set by
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186 including in priority the sensor nodes which cover critical targets, that is to
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187 say targets that are covered by the smallest number of sensors
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188 \cite{berman04,zorbas2010solving}. Other approaches are based on mathematical
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189 programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
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190 and dedicated techniques (solving with a branch-and-bound algorithm available in
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191 optimization solver). The problem is formulated as an optimization problem
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192 (maximization of the lifetime or number of cover sets) under target coverage and
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193 energy constraints. Column generation techniques, well-known and widely
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194 practiced techniques for solving linear programs with too many variables, have
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196 used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the PeCO
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197 protocol, each leader, in charge of a subregion, solves an integer program
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198 which has a twofold objective: minimize the overcoverage and the undercoverage
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199 of the perimeter of each sensor.}
\r
201 %\noindent Recently, the coverage problem has been received a high attention, which concentrates on how the physical space could be well monitored after the deployment. Coverage is one of the Quality of Service (QoS) parameters in WSNs, which is highly concerned with power depletion~\cite{zhu2012survey}. Most of the works about the coverage protocols have been suggested in the literature focused on three types of the coverage in WSNs~\cite{mulligan2010coverage}: the first, area coverage means that each point in the area of interest within the sensing range of at least one sensor node; the second, target coverage in which a fixed set of targets need to be monitored; the third, barrier coverage refers to detect the intruders crossing a boundary of WSN. The work in this paper emphasized on the area coverage, so, some area coverage protocols have been reviewed in this section, and the shortcomings of reviewed approaches are being summarized.
\r
203 %The problem of k-coverage in WSNs was addressed~\cite{ammari2012centralized}. It mathematically formulated and the spacial sensor density for full k-coverage determined, where the relation between the communication range and the sensing range constructed by this work to retain the k-coverage and connectivity in WSN. After that, a four configuration protocols have proposed for treating the k-coverage in WSNs.
\r
205 %In~\cite{rebai2014branch}, the problem of full grid coverage is formulated using two integer linear programming models: the first, a model that takes into account only the overall coverage constraint; the second, both the connectivity and the full grid coverage constraints have taken into consideration. This work did not take into account the energy constraint.
\r
207 %Li et al.~\cite{li2011transforming} presented a framework to convert any complete coverage problem to a partial coverage one with any coverage ratio by means of executing a complete coverage algorithm to find a full coverage sets with virtual radii and transforming the coverage sets to a partial coverage sets by adjusting sensing radii. The properties of the original algorithms can be maintained by this framework and the transformation process has a low execution time.
\r
209 %The authors in~\cite{liu2014generalized} explained that in some applications of WSNs such as structural health monitoring (SHM) and volcano monitoring, the traditional coverage model which is a geographic area defined for individual sensors is not always valid. For this reason, they define a generalized coverage model, which is not need to have the coverage area of individual nodes, but only based on a function to determine whether a set of
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210 %sensor nodes is capable of satisfy the requested monitoring task for a certain area. They have proposed two approaches to divide the deployed nodes into suitable cover sets, which can be used to prolong the network lifetime.
\r
212 %The work in~\cite{wang2010preserving} addressed the target area coverage problem by proposing a geometric-based activity scheduling scheme, named GAS, to fully cover the target area in WSNs. The authors deals with small area (target area coverage), which can be monitored by a single sensor instead of area coverage, which focuses on a large area that should be monitored by many sensors cooperatively. They explained that GAS is capable to monitor the target area by using a few sensors as possible and it can produce as many cover sets as possible.
\r
214 %Cho et al.~\cite{cho2007distributed} proposed a distributed node scheduling protocol, which can retain sensing coverage needed by applications
\r
215 %and increase network lifetime via putting in sleep mode some redundant nodes. In this work, the effective sensing area (ESA) concept of a sensor node is used, which refers to the sensing area that is not overlapping with another sensor's sensing area. A sensor node and by compute it's ESA can be determine whether it will be active or sleep. The suggested work permits to sensor nodes to be in sleep mode opportunistically whilst fulfill the needed sensing coverage.
\r
217 %In~\cite{quang2008algorithm}, the authors defined a maximum sensing coverage region problem (MSCR) in WSNs and then proposed an algorithm to solve it. The
\r
218 %maximum observed area fully covered by a minimum active sensors. In this work, the major property is to getting rid from the redundant sensors in high-density WSNs and putting them in sleep mode, and choosing a smaller number of active sensors so as to be sure that the full area is k-covered, and all events appeared in that area can be precisely and timely detected. This algorithm minimized the total energy consumption and increased the lifetime.
\r
220 %A novel method to divide the sensors in the WSN, called node coverage grouping (NCG) suggested~\cite{lin2010partitioning}. The sensors in the connectivity group are within sensing range of each other, and the data collected by them in the same group are supposed to be similar. They are proved that dividing n sensors via NCG into connectivity groups is a NP-hard problem. So, a heuristic algorithm of NCG with time complexity of $O(n^3)$ is proposed.
\r
221 %For some applications, such as monitoring an ecosystem with extremely diversified environment, It might be premature assumption that sensors near to each other sense similar data.
\r
223 %In~\cite{zaidi2009minimum}, the problem of minimum cost coverage in which full coverage is performed by using the minimum number of sensors for an arbitrary geometric shape region is addressed. a geometric solution to the minimum cost coverage problem under a deterministic deployment is proposed. The probabilistic coverage solution which provides a relationship between the probability of coverage and the number of randomly deployed sensors in an arbitrarily-shaped region is suggested. The authors are clarified that with a random deployment about seven times more nodes are required to supply full coverage.
\r
225 %A graph theoretical framework for connectivity-based coverage with configurable coverage granularity was proposed~\cite{dong2012distributed}. A new coverage criterion and scheduling approach is proposed based on cycle partition. This method is capable of build a sparse coverage set in distributed way by means of only connectivity information. This work considers only the communication range of the sensor is smaller two times the sensing range of sensor.
\r
227 %Liu et al.~\cite{liu2010energy} formulated maximum disjoint sets problem for retaining coverage and connectivity in WSN. Two algorithms are proposed for solving this problem, heuristic algorithm and network flow algorithm. This work did not take into account the sensor node failure, which is an unpredictable event because the two solutions are full centralized algorithms.
\r
229 %The work that presented in~\cite{aslanyan2013optimal} solved the coverage and connectivity problem in sensor networks in
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230 %an integrated way. The network lifetime is divided in a fixed number of rounds. A coverage bitmap of sensors of the domain has been generated in each round and based on this bitmap, it has been decided which sensors
\r
231 %stay active or turn it to sleep. They checked the connection of the graph via laplacian of adjancy graph of active sensors in each round. the generation of coverage bitmap by using Minkowski technique, the network is able to providing the desired ratio of coverage. They have been defined the connected coverage problem as an optimization problem and a centralized genetic algorithm is used to find the solution.
\r
233 %Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{cardei2006energy,wang2011coverage}.
\r
235 %\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.
\r
237 %\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (PeCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a PeCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
\r
239 \section{ The P{\scshape e}CO Protocol Description}
\r
240 \label{sec:The PeCO Protocol Description}
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242 \noindent In this section, we describe in details our Perimeter-based Coverage
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243 Optimization protocol. First we present the assumptions we made and the models
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244 we considered (in particular the perimeter coverage one), second we describe the
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245 background idea of our protocol, and third we give the outline of the algorithm
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246 executed by each node.
\r
248 % It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion; the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period. Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently.
\r
249 %Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
\r
251 \subsection{Assumptions and Models}
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254 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
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255 distributed in a bounded sensor field is considered. The wireless sensors are
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256 deployed in high density to ensure initially a high coverage ratio of the area
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257 of interest. We assume that all the sensor nodes are homogeneous in terms of
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258 communication, sensing, and processing capabilities and heterogeneous from
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259 the energy provision point of view. The location information is available to a
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260 sensor node either through hardware such as embedded GPS or location discovery
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261 algorithms. We assume that each sensor node can directly transmit its
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262 measurements to a mobile sink node. For example, a sink can be an unmanned
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263 aerial vehicle (UAV) flying regularly over the sensor field to collect
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264 measurements from sensor nodes. A mobile sink node collects the measurements and
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265 transmits them to the base station. We consider a Boolean disk coverage model,
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266 which is the most widely used sensor coverage model in the literature, and all
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267 sensor nodes have a constant sensing range $R_s$. Thus, all the space points
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268 within a disk centered at a sensor with a radius equal to the sensing range are
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269 said to be covered by this sensor. We also assume that the communication range
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270 $R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, Zhang and Zhou~\cite{Zhang05}
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271 proved that if the transmission range fulfills the previous hypothesis, the
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272 complete coverage of a convex area implies connectivity among active nodes.
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274 The PeCO protocol uses the same perimeter-coverage model as Huang and
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275 Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is
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276 said to be perimeter covered if all the points on its perimeter are covered by
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277 at least one sensor other than itself. They proved that a network area is
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278 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
\r
279 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model.
\r
280 Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this
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281 figure, we can see that sensor~$0$ has nine neighbors and we have reported on
\r
282 its perimeter (the perimeter of the disk covered by the sensor) for each
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283 neighbor the two points resulting from the intersection of the two sensing
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284 areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
\r
285 for left and right from a neighboing point of view. The resulting couples of
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286 intersection points subdivide the perimeter of sensor~$0$ into portions called
\r
289 \begin{figure}[ht!]
\r
291 \begin{tabular}{@{}cr@{}}
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292 \includegraphics[width=75mm]{figure1a.tiff} & \raisebox{3.25cm}{(a)} \\
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293 \includegraphics[width=75mm]{figure1b.tiff} & \raisebox{2.75cm}{(b)}
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295 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
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296 $u$'s perimeter covered by $v$.}
\r
297 \label{pcm2sensors}
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300 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
\r
301 locations of the left and right points of an arc on the perimeter of a sensor
\r
302 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
\r
303 west side of sensor~$u$, with the following respective coordinates in the
\r
304 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
\r
305 compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
\r
306 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
\r
307 obtained through the formula:
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309 \alpha = \arccos \left(\frac{Dist(u,v)}{2R_s}
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312 The arc on the perimeter of~$u$ defined by the angular interval $[\pi
\r
313 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
\r
315 Every couple of intersection points is placed on the angular interval $[0,2\pi]$
\r
316 in a counterclockwise manner, leading to a partitioning of the interval.
\r
317 Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
\r
318 sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs
\r
319 in the interval $[0,2\pi]$. More precisely, we can see that the points are
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320 ordered according to the measures of the angles defined by their respective
\r
321 positions. The intersection points are then visited one after another, starting
\r
322 from the first intersection point after point~zero, and the maximum level of
\r
323 coverage is determined for each interval defined by two successive points. The
\r
324 maximum level of coverage is equal to the number of overlapping arcs. For
\r
326 between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
\r
327 (the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which
\r
328 means that at most 2~neighbors can cover the perimeter in addition to node $0$.
\r
329 Table~\ref{my-label} summarizes for each coverage interval the maximum level of
\r
330 coverage and the sensor nodes covering the perimeter. The example discussed
\r
331 above is thus given by the sixth line of the table.
\r
333 %The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
\r
334 % to determine the level of the perimeter coverage for each left and right point of a segment.
\r
336 \begin{figure*}[t!]
\r
338 \includegraphics[width=127.5mm]{figure2.tiff}
\r
339 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
\r
343 %For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
\r
348 \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}
\r
349 {\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\r
351 \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
\r
352 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
\r
353 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
\r
354 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
\r
355 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
\r
356 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
\r
357 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
\r
358 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
\r
359 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
\r
360 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
\r
361 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
\r
362 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
\r
363 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
\r
364 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
\r
365 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
\r
366 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
\r
367 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
\r
368 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
\r
369 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
\r
376 %The optimization algorithm that used by PeCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
\r
378 In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an
\r
379 integer program based on coverage intervals. The formulation of the coverage
\r
380 optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
\r
381 node has a part of its sensing range outside the WSN sensing field, as in
\r
382 Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
\r
383 and the corresponding interval will not be taken into account by the
\r
384 optimization algorithm.
\r
388 \includegraphics[width=62.5mm]{figure3.tiff}
\r
389 \caption{Sensing range outside the WSN's area of interest.}
\r
392 %Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node $0$, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node $0$ has two segments outside the border of the network sensing field, so the left and right points of the two segments called $-1L$, $-1R$, $-2L$, and $-2R$.
\r
393 %\begin{figure}[ht!]
\r
395 %\includegraphics[width=75mm]{ex5pcm.jpg}
\r
396 %\caption{Coverage intervals and contributing sensors for sensor node 0 having a part of its sensing range outside the border.}
\r
400 \subsection{The Main Idea}
\r
402 \noindent The WSN area of interest is, in a first step, divided into regular
\r
403 homogeneous subregions using a divide-and-conquer algorithm. In a second step
\r
404 our protocol will be executed in a distributed way in each subregion
\r
405 simultaneously to schedule nodes' activities for one sensing period.
\r
407 As shown in Figure~\ref{fig2}, node activity scheduling is produced by our
\r
408 protocol in a periodic manner. Each period is divided into 4 stages: Information
\r
409 (INFO) Exchange, Leader Election, Decision (the result of an optimization
\r
410 problem), and Sensing. For each period there is exactly one set cover
\r
411 responsible for the sensing task. Protocols based on a periodic scheme, like
\r
412 PeCO, are more robust against an unexpected node failure. On the one hand, if
\r
413 a node failure is discovered before taking the decision, the corresponding sensor
\r
414 node will not be considered by the optimization algorithm. On the other
\r
415 hand, if the sensor failure happens after the decision, the sensing task of the
\r
416 network will be temporarily affected: only during the period of sensing until a
\r
417 new period starts, since a new set cover will take charge of the sensing task in
\r
418 the next period. The energy consumption and some other constraints can easily be
\r
419 taken into account since the sensors can update and then exchange their
\r
420 information (including their residual energy) at the beginning of each period.
\r
421 However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
\r
422 are energy consuming, even for nodes that will not join the set cover to monitor
\r
427 \includegraphics[width=80mm]{figure4.tiff}
\r
428 \caption{PeCO protocol.}
\r
432 We define two types of packets to be used by PeCO protocol:
\r
433 %\begin{enumerate}[(a)]
\r
435 \item INFO packet: sent by each sensor node to all the nodes inside a same
\r
436 subregion for information exchange.
\r
437 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion
\r
438 to transmit to them their respective status (stay Active or go Sleep) during
\r
443 Five status are possible for a sensor node in the network:
\r
444 %\begin{enumerate}[(a)]
\r
446 \item LISTENING: waits for a decision (to be active or not);
\r
447 \item COMPUTATION: executes the optimization algorithm as leader to
\r
448 determine the activities scheduling;
\r
449 \item ACTIVE: node is sensing;
\r
450 \item SLEEP: node is turned off;
\r
451 \item COMMUNICATION: transmits or receives packets.
\r
454 %Below, we describe each phase in more details.
\r
456 \subsection{PeCO Protocol Algorithm}
\r
458 \noindent The pseudocode implementing the protocol on a node is given below.
\r
459 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
\r
460 protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
\r
465 % \KwIn{all the parameters related to information exchange}
\r
466 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
\r
468 %\emph{Initialize the sensor node and determine it's position and subregion} \;
\r
470 \If{ $RE_k \geq E_{th}$ }{
\r
471 \emph{$s_k.status$ = COMMUNICATION}\;
\r
472 \emph{Send $INFO()$ packet to other nodes in subregion}\;
\r
473 \emph{Wait $INFO()$ packet from other nodes in subregion}\;
\r
474 \emph{Update K.CurrentSize}\;
\r
475 \emph{LeaderID = Leader election}\;
\r
476 \If{$ s_k.ID = LeaderID $}{
\r
477 \emph{$s_k.status$ = COMPUTATION}\;
\r
479 \If{$ s_k.ID $ is Not previously selected as a Leader }{
\r
480 \emph{ Execute the perimeter coverage model}\;
\r
481 % \emph{ Determine the segment points using perimeter coverage model}\;
\r
484 \If{$ (s_k.ID $ is the same Previous Leader) And (K.CurrentSize = K.PreviousSize)}{
\r
486 \emph{ Use the same previous cover set for current sensing stage}\;
\r
489 \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
\r
490 \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
\r
491 \emph{K.PreviousSize = K.CurrentSize}\;
\r
494 \emph{$s_k.status$ = COMMUNICATION}\;
\r
495 \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;
\r
496 \emph{Update $RE_k $}\;
\r
499 \emph{$s_k.status$ = LISTENING}\;
\r
500 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
\r
501 \emph{Update $RE_k $}\;
\r
504 \Else { Exclude $s_k$ from entering in the current sensing stage}
\r
506 %\caption{PeCO($s_k$)}
\r
511 In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
\r
512 current number and the previous number of living nodes in the subnetwork of the
\r
513 subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
\r
514 must be greater than a threshold $E_{th}$ in order to participate in the current
\r
515 period. Each sensor node determines its position and its subregion using an
\r
516 embedded GPS or a location discovery algorithm. After that, all the sensors
\r
517 collect position coordinates, remaining energy, sensor node ID, and the number
\r
518 of their one-hop live neighbors during the information exchange. The sensors
\r
519 inside a same region cooperate to elect a leader. The selection criteria for the
\r
520 leader, in order of priority, are: larger numbers of neighbors, larger remaining
\r
521 energy, and then in case of equality, larger index. Once chosen, the leader
\r
522 collects information to formulate and solve the integer program which allows to
\r
523 construct the set of active sensors in the sensing stage.
\r
525 %After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the PeCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
\r
527 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform 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 stage.
\r
529 \section{Perimeter-based Coverage Problem Formulation}
\r
532 \noindent In this section, the coverage model is mathematically formulated. We
\r
533 start with a description of the notations that will be used throughout the
\r
535 First, we have the following sets:
\r
537 \item $S$ represents the set of WSN sensor nodes;
\r
538 \item $A \subseteq S $ is the subset of alive sensors;
\r
539 \item $I_j$ designates the set of coverage intervals (CI) obtained for
\r
542 $I_j$ refers to the set of coverage intervals which have been defined according
\r
543 to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
\r
544 let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
\r
545 in coverage interval~$i$ of sensor~$j$, that is:
\r
547 a^j_{ik} = \left \{
\r
549 1 & \mbox{if sensor $k$ is involved in the } \\
\r
550 & \mbox{coverage interval $i$ of sensor $j$}, \\
\r
551 0 & \mbox{otherwise.}\\
\r
552 \end{array} \right.
\r
556 Note that $a^k_{ik}=1$ by definition of the interval.
\r
557 %, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.
\r
558 %We defined some parameters, which are related to our optimization model. In our model, we consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .
\r
559 Second, we define several binary and integer variables. Hence, each binary
\r
560 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
\r
561 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
\r
562 variable which measures the undercoverage for the coverage interval $i$
\r
563 corresponding to sensor~$j$. In the same way, the overcoverage for the same
\r
564 coverage interval is given by the variable $V^j_i$.
\r
566 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
\r
567 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
\r
568 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
\r
569 previous notations, the number of active sensors in the coverage interval $i$ of
\r
570 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
\r
571 lifetime, the objective is to activate a minimal number of sensors in each
\r
572 period to ensure the desired coverage level. As the number of alive sensors
\r
573 decreases, it becomes impossible to reach the desired level of coverage for all
\r
574 coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure
\r
575 of the deviation between the desired number of active sensors in a coverage
\r
576 interval and the effective number. And we try to minimize these deviations,
\r
577 first to force the activation of a minimal number of sensors to ensure the
\r
578 desired coverage level, and if the desired level cannot be completely satisfied,
\r
579 to reach a coverage level as close as possible to the desired one.
\r
581 %A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized.
\r
583 %\noindent In this paper, let us define some parameters, which are used in our protocol.
\r
584 %the set of segment points is denoted by $I$, the set of all sensors in the network by $J$, and the set of alive sensors within $J$ by $K$.
\r
587 %\noindent \begin{equation}
\r
589 %\begin{array}{l l}
\r
590 % 1& \mbox{if sensor $k$ is active,} \\
\r
591 % 0 & \mbox{otherwise.}\\
\r
592 %\end{array} \right.
\r
597 %\noindent $M^j_i (undercoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
\r
599 %\noindent $V^j_i (overcoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
\r
601 Our coverage optimization problem can then be mathematically expressed as follows:
\r
603 \begin{equation} %\label{eq:ip2r}
\r
606 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
\r
607 \textrm{subject to :}&\\
\r
608 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
\r
610 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
\r
612 % \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
\r
613 % U_{p} \in \{0,1\}, &\forall p \in P\\
\r
614 X_{k} \in \{0,1\}, \forall k \in A
\r
619 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
\r
620 relative importance of satisfying the associated level of coverage. For example,
\r
621 weights associated with coverage intervals of a specified part of a region may
\r
622 be given by a relatively larger magnitude than weights associated with another
\r
623 region. This kind of integer program is inspired from the model developed for
\r
624 brachytherapy treatment planning for optimizing dose distribution
\r
625 \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
\r
626 each subregion at the beginning of each sensing phase, whenever the environment
\r
627 has changed (new leader, death of some sensors). Note that the number of
\r
628 constraints in the model is constant (constraints of coverage expressed for all
\r
629 sensors), whereas the number of variables $X_k$ decreases over periods, since we
\r
630 consider only alive sensors (sensors with enough energy to be alive during one
\r
631 sensing phase) in the model.
\r
633 \section{Performance Evaluation and Analysis}
\r
634 \label{sec:Simulation Results and Analysis}
\r
635 %\noindent \subsection{Simulation Framework}
\r
637 \subsection{Simulation Settings}
\r
640 The WSN area of interest is supposed to be divided into 16~regular subregions
\r
641 and we use the same energy consumption than in our previous work~\cite{Idrees2}.
\r
642 Table~\ref{table3} gives the chosen parameters settings.
\r
645 \tbl{Relevant parameters for network initialization \label{table3}}{
\r
648 % used for centering table
\r
649 \begin{tabular}{c|c}
\r
650 % centered columns (4 columns)
\r
652 Parameter & Value \\ [0.5ex]
\r
655 % inserts single horizontal line
\r
656 Sensing field & $(50 \times 25)~m^2 $ \\
\r
658 WSN size & 100, 150, 200, 250, and 300~nodes \\
\r
660 Initial energy & in range 500-700~Joules \\
\r
662 Sensing period & duration of 60 minutes \\
\r
663 $E_{th}$ & 36~Joules\\
\r
666 $\alpha^j_i$ & 0.6 \\
\r
667 % [1ex] adds vertical space
\r
670 %inserts single line
\r
673 % is used to refer this table in the text
\r
675 To obtain experimental results which are relevant, simulations with five
\r
676 different node densities going from 100 to 300~nodes were performed considering
\r
677 each time 25~randomly generated networks. The nodes are deployed on a field of
\r
678 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
\r
679 high coverage ratio. Each node has an initial energy level, in Joules, which is
\r
680 randomly drawn in the interval $[500-700]$. If its energy provision reaches a
\r
681 value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
\r
682 node to stay active during one period, it will no more participate in the
\r
683 coverage task. This value corresponds to the energy needed by the sensing phase,
\r
684 obtained by multiplying the energy consumed in active state (9.72 mW) with the
\r
685 time in seconds for one period (3600 seconds), and adding the energy for the
\r
686 pre-sensing phases. According to the interval of initial energy, a sensor may
\r
687 be active during at most 20 periods.
\r
689 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
\r
690 network coverage and a longer WSN lifetime. We have given a higher priority to
\r
691 the undercoverage (by setting the $\alpha^j_i$ with a larger value than
\r
692 $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
\r
693 sensor~$j$. On the other hand, we have assigned to
\r
694 $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
\r
695 in covering the interval.
\r
697 We introduce the following performance metrics to evaluate the efficiency of our
\r
700 %\begin{enumerate}[i)]
\r
702 \item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
\r
703 the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
\r
704 $Lifetime_{50}$ denote, respectively, the amount of time during which is
\r
705 guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
\r
706 fulfill the expected monitoring task until all its nodes have depleted their
\r
707 energy or if the network is no more connected. This last condition is crucial
\r
708 because without network connectivity a sensor may not be able to send to a
\r
709 base station an event it has sensed.
\r
710 \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
\r
711 observe the area of interest. In our case, we discretized the sensor field as
\r
712 a regular grid, which yields the following equation:
\r
717 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
\r
721 where $n$ is the number of covered grid points by active sensors of every
\r
722 subregions during the current sensing phase and $N$ is total number of grid
\r
723 points in the sensing field. In our simulations we have set a layout of
\r
724 $N~=~51~\times~26~=~1326$~grid points.
\r
725 \item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
\r
726 activate as few nodes as possible, in order to minimize the communication
\r
727 overhead and maximize the WSN lifetime. The active sensors ratio is defined as
\r
732 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
\r
735 where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
\r
736 current sensing period~$p$, $|S|$ is the number of sensors in the network, and
\r
737 $R$ is the number of subregions.
\r
738 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
\r
739 energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
\r
740 divided by the number of periods. The value of EC is computed according to
\r
745 \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
\r
746 + E^{a}_p+E^{s}_p \right)}{P},
\r
749 where $P$ corresponds to the number of periods. The total energy consumed by
\r
750 the sensors comes through taking into consideration four main energy
\r
751 factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
\r
752 energy consumption spent by all the nodes for wireless communications during
\r
753 period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to
\r
754 the energy consumed by the sensors in LISTENING status before receiving the
\r
755 decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$
\r
756 refers to the energy needed by all the leader nodes to solve the integer
\r
757 program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
\r
758 consumed by the WSN during the sensing phase (active and sleeping nodes).
\r
762 \subsection{Simulation Results}
\r
764 In order to assess and analyze the performance of our protocol we have
\r
765 implemented PeCO protocol in OMNeT++~\cite{varga} simulator. Besides PeCO, two
\r
766 other protocols, described in the next paragraph, will be evaluated for
\r
767 comparison purposes. The simulations were run on a DELL laptop with an Intel
\r
768 Core~i3~2370~M (2.4~GHz) processor (2 cores) whose MIPS (Million Instructions
\r
769 Per Second) rate is equal to 35330. To be consistent with the use of a sensor
\r
770 node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate
\r
771 equal to 6, the original execution time on the laptop is multiplied by 2944.2
\r
772 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for
\r
773 Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer
\r
774 program instance in a standard format, which is then read and solved by the
\r
775 optimization solver GLPK (GNU linear Programming Kit available in the public
\r
776 domain) \cite{glpk} through a Branch-and-Bound method.
\r
778 As said previously, the PeCO is compared to three other approaches. The first
\r
779 one, called DESK, is a fully distributed coverage algorithm proposed by
\r
780 \cite{ChinhVu}. The second one, called GAF~\cite{xu2001geography}, consists in
\r
781 dividing the monitoring area into fixed squares. Then, during the decision
\r
782 phase, in each square, one sensor is chosen to remain active during the sensing
\r
783 phase. The last one, the DiLCO protocol~\cite{Idrees2}, is an improved version
\r
784 of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
\r
785 PeCO and DiLCO protocols are based on the same framework. In particular, the
\r
786 choice for the simulations of a partitioning in 16~subregions was made because
\r
787 it corresponds to the configuration producing the best results for DiLCO. The
\r
788 protocols are distinguished from one another by the formulation of the integer
\r
789 program providing the set of sensors which have to be activated in each sensing
\r
790 phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
\r
791 whereas the PeCO protocol objective is to reach a desired level of coverage for each
\r
792 sensor perimeter. In our experimentations, we chose a level of coverage equal to
\r
795 \subsubsection{\bf Coverage Ratio}
\r
797 Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes
\r
798 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
\r
799 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
\r
800 produced by PeCO for the first periods. This is due to the fact that at the
\r
801 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
\r
802 slightly decreases the coverage ratio), while the three other protocols activate
\r
803 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
\r
804 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
\r
805 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
\r
806 compared to DESK). The energy saved by PeCO in the early periods allows later a
\r
807 substantial increase of the coverage performance.
\r
812 \includegraphics[scale=0.5] {figure5.eps}
\r
813 \caption{Coverage ratio for 200 deployed nodes.}
\r
817 %When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to PeCO protocol. The coverage ratio of PeCO protocol is better than other approaches from the period 64.
\r
819 %because the optimization algorithm used by PeCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of PeCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then PeCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by PeCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
\r
822 \subsubsection{\bf Active Sensors Ratio}
\r
824 Having the less active sensor nodes in each period is essential to minimize the
\r
825 energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444}
\r
826 shows the average active nodes ratio for 200 deployed nodes. We observe that
\r
827 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
\r
828 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and
\r
829 20.16~\% active nodes during the same time interval. As the number of periods
\r
830 increases, PeCO protocol has a lower number of active nodes in comparison with
\r
831 the three other approaches, while keeping a greater coverage ratio as shown in
\r
832 Figure \ref{fig333}.
\r
836 \includegraphics[scale=0.5]{figure6.eps}
\r
837 \caption{Active sensors ratio for 200 deployed nodes.}
\r
841 \subsubsection{\bf Energy Consumption}
\r
843 We studied the effect of the energy consumed by the WSN during the communication,
\r
844 computation, listening, active, and sleep status for different network densities
\r
845 and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
\r
846 illustrate the energy consumption for different network sizes and for
\r
847 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
\r
848 most competitive from the energy consumption point of view. As shown in both
\r
849 figures, PeCO consumes much less energy than the three other methods. One might
\r
850 think that the resolution of the integer program is too costly in energy, but
\r
851 the results show that it is very beneficial to lose a bit of time in the
\r
852 selection of sensors to activate. Indeed the optimization program allows to
\r
853 reduce significantly the number of active sensors and so the energy consumption
\r
854 while keeping a good coverage level.
\r
858 \begin{tabular}{@{}cr@{}}
\r
859 \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
\r
860 \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
\r
862 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
\r
866 %The optimization algorithm, which used by PeCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
\r
868 %The other approaches have a high energy consumption due to activating a larger number of sensors. 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.
\r
871 %\subsubsection{Execution Time}
\r
873 \subsubsection{\bf Network Lifetime}
\r
875 We observe the superiority of PeCO and DiLCO protocols in comparison with the
\r
876 two other approaches in prolonging the network lifetime. In
\r
877 Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
\r
878 different network sizes. As highlighted by these figures, the lifetime
\r
879 increases with the size of the network, and it is clearly largest for DiLCO
\r
880 and PeCO protocols. For instance, for a network of 300~sensors and coverage
\r
881 ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime
\r
882 is about twice longer with PeCO compared to DESK protocol. The performance
\r
883 difference is more obvious in Figure~\ref{fig3LT}(b) than in
\r
884 Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
\r
885 time, and the lifetime with a coverage of 50\% is far longer than with
\r
890 \begin{tabular}{@{}cr@{}}
\r
891 \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
\r
892 \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}
\r
894 \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
\r
895 and (b)~$Lifetime_{50}$.}
\r
899 %By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, PeCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
\r
901 Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for
\r
902 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
\r
903 Protocol/90, and Protocol/95 the amount of time during which the network can
\r
904 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
\r
905 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
\r
906 that do not require a 100\% coverage of the area to be monitored. PeCO might be
\r
907 an interesting method since it achieves a good balance between a high level
\r
908 coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
\r
909 lower coverage ratios, moreover the improvements grow with the network
\r
910 size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
\r
911 not ineffective for the smallest network sizes.
\r
914 \centering \includegraphics[scale=0.5]{figure9.eps}
\r
915 \caption{Network lifetime for different coverage ratios.}
\r
919 %Comparison shows that PeCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. PeCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
\r
922 \section{Conclusion and Future Works}
\r
923 \label{sec:Conclusion and Future Works}
\r
925 In this paper we have studied the problem of Perimeter-based Coverage Optimization in
\r
926 WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
\r
927 schedules nodes' activities (wake up and sleep stages) with the objective of
\r
928 maintaining a good coverage ratio while maximizing the network lifetime. This
\r
929 protocol is applied in a distributed way in regular subregions obtained after
\r
930 partitioning the area of interest in a preliminary step. It works in periods and
\r
931 is based on the resolution of an integer program to select the subset of sensors
\r
932 operating in active status for each period. Our work is original in so far as it
\r
933 proposes for the first time an integer program scheduling the activation of
\r
934 sensors based on their perimeter coverage level, instead of using a set of
\r
935 targets/points to be covered.
\r
937 %To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a PeCO protocol for optimizing the lifetime coverage in each subregion. PeCO protocol combines two efficient techniques: network
\r
938 %leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
\r
939 %in the subregion.
\r
940 %The network lifetime coverage in each subregion is divided into
\r
941 %periods, each period consists of four stages: (i) Information Exchange,
\r
942 %(ii) Leader Election, (iii) a Decision based new optimization model in order to
\r
943 %select the nodes remaining active for the last stage, and (iv) Sensing.
\r
944 We have carried out several simulations to evaluate the proposed protocol. The
\r
945 simulation results show that PeCO is more energy-efficient than other
\r
946 approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
\r
947 energy consumption.
\r
948 %Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have identified different research directions that arise out of the work presented here.
\r
949 We plan to extend our framework so that the schedules are planned for multiple
\r
951 %in order to compute all active sensor schedules in only one step for many periods;
\r
952 We also want to improve our integer program to take into account heterogeneous
\r
953 sensors from both energy and node characteristics point of views.
\r
954 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
\r
955 Finally, it would be interesting to implement our protocol using a
\r
956 sensor-testbed to evaluate it in real world applications.
\r
958 \bibliographystyle{gENO}
\r
959 \bibliography{biblio}
\r
