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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 $^{a}$
\r
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.
\r
38 \begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, 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)~\citep{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~\citep{yick2008wireless}. Typically, a sensor node contains
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57 three main components~\citep{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~\citep{rault2014energy}.\\\\
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74 This paper makes the following contributions.
\r
76 \item We have devised a framework to schedule nodes to be activated alternatively such
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77 that the network lifetime is prolonged while ensuring that a certain level of
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78 coverage is preserved. A key idea in our framework is to exploit spatial and
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79 temporal subdivision. On the one hand, the area of interest is divided into
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80 several smaller subregions and, on the other hand, the time line is divided into
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81 periods of equal length. In each subregion the sensor nodes will cooperatively
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82 choose a leader which will schedule nodes' activities, and this grouping of
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83 sensors is similar to typical cluster architecture.
\r
84 \item We have proposed a new mathematical optimization model. Instead of trying to
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85 cover a set of specified points/targets as in most of the methods proposed in
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86 the literature, we formulate an integer program based on perimeter coverage of
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87 each sensor. The model involves integer variables to capture the deviations
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88 between the actual level of coverage and the required level. Hence, an
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89 optimal scheduling will be obtained by minimizing a weighted sum of these
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91 \item We have conducted extensive simulation experiments, using the discrete event
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92 simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
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93 our PeCO protocol to two approaches found in the literature:
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94 DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
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95 work published in~\citep{Idrees2} which is based on another optimization model
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96 for sensor scheduling.
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104 The rest of the paper is organized as follows. In the next section we review
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105 some related work in the field. Section~\ref{sec:The PeCO Protocol Description}
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106 is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
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107 coverage model formulation which is used to schedule the activation of sensor
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108 nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
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109 results and discusses the comparison with other approaches. Finally, concluding
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110 remarks are drawn and some suggestions are given for future works in
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111 Section~\ref{sec:Conclusion and Future Works}.
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113 \section{Related Literature}
\r
114 \label{sec:Literature Review}
\r
116 \noindent In this section, we summarize some related works regarding the
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117 coverage problem and distinguish our PeCO protocol from the works presented in
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120 The most discussed coverage problems in literature can be classified in three
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121 categories~\citep{li2013survey} according to their respective monitoring
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122 objective. Hence, area coverage \citep{Misra} means that every point inside a
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123 fixed area must be monitored, while target coverage~\citep{yang2014novel} refers
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124 to the objective of coverage for a finite number of discrete points called
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125 targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
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126 preventing intruders from entering into the region of interest. In
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127 \citep{Deng2012} authors transform the area coverage problem into the target
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128 coverage one taking into account the intersection points among disks of sensors
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129 nodes or between disk of sensor nodes and boundaries. In
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130 \citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
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131 sensors are sufficiently covered it will be the case for the whole area. They
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132 provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
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133 each sensor, where $d$ denotes the maximum number of sensors that are
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134 neighbors to a sensor and $n$ is the total number of sensors in the
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135 network. {\it In PeCO protocol, instead of determining the level of coverage of
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136 a set of discrete points, our optimization model is based on checking the
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137 perimeter-coverage of each sensor to activate a minimal number of sensors.}
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139 The major approach to extend network lifetime while preserving coverage is to
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140 divide/organize the sensors into a suitable number of set covers (disjoint or
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141 non-disjoint)\citep{wang2011coverage}, where each set completely covers a region of interest, and to
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142 activate these set covers successively. The network activity can be planned in
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143 advance and scheduled for the entire network lifetime or organized in periods,
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144 and the set of active sensor nodes is decided at the beginning of each period
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145 \citep{ling2009energy}. Active node selection is determined based on the problem
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146 requirements (e.g. area monitoring, connectivity, or power efficiency). For
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147 instance, \citet{jaggi2006} address the problem of maximizing
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148 the lifetime by dividing sensors into the maximum number of disjoint subsets
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149 such that each subset can ensure both coverage and connectivity. A greedy
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150 algorithm is applied once to solve this problem and the computed sets are
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151 activated in succession to achieve the desired network lifetime.
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152 \citet{chin2007}, \citet{yan2008design}, \citet{pc10}, propose algorithms
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153 working in a periodic fashion where a cover set is computed at the beginning of
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154 each period. {\it Motivated by these works, PeCO protocol works in periods,
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155 where each period contains a preliminary phase for information exchange and
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156 decisions, followed by a sensing phase where one cover set is in charge of the
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159 Various centralized and distributed approaches, or even a mixing of these two
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160 concepts, have been proposed to extend the network lifetime \citep{zhou2009variable}. In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
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161 own activity scheduling after an information exchange with its neighbors. The
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162 main interest of such an approach is to avoid long range communications and thus
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163 to reduce the energy dedicated to the communications. Unfortunately, since each
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164 node has only information on its immediate neighbors (usually the one-hop ones)
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165 it may make a bad decision leading to a global suboptimal solution. Conversely,
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167 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always
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168 provide nearly or close to optimal solution since the algorithm has a global
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169 view of the whole network. The disadvantage of a centralized method is obviously
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170 its high cost in communications needed to transmit to a single node, the base
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171 station which will globally schedule nodes' activities, data from all the other
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172 sensor nodes in the area. The price in communications can be huge since
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173 long range communications will be needed. In fact the larger the WNS is, the
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174 higher the communication and thus the energy cost are. {\it In order to be
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175 suitable for large-scale networks, in the PeCO protocol, the area of interest
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176 is divided into several smaller subregions, and in each one, a node called the
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177 leader is in charge of selecting the active sensors for the current
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178 period. Thus our protocol is scalable and is a globally distributed method,
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179 whereas it is centralized in each subregion.}
\r
181 Various coverage scheduling algorithms have been developed these past few years.
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182 Many of them, dealing with the maximization of the number of cover sets, are
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183 heuristics. These heuristics involve the construction of a cover set by
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184 including in priority the sensor nodes which cover critical targets, that is to
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185 say targets that are covered by the smallest number of sensors
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186 \citep{berman04,zorbas2010solving}. Other approaches are based on mathematical
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187 programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014}
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188 and dedicated techniques (solving with a branch-and-bound algorithm available in
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189 optimization solver). The problem is formulated as an optimization problem
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190 (maximization of the lifetime or number of cover sets) under target coverage and
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191 energy constraints. Column generation techniques, well-known and widely
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192 practiced techniques for solving linear programs with too many variables, have
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194 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it In the PeCO
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195 protocol, each leader, in charge of a subregion, solves an integer program
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196 which has a twofold objective: minimize the overcoverage and the undercoverage
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197 of the perimeter of each sensor.}
\r
201 \section{ The P{\scshape e}CO Protocol Description}
\r
202 \label{sec:The PeCO Protocol Description}
\r
204 \noindent In this section, we describe in details our Perimeter-based Coverage
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205 Optimization protocol. First we present the assumptions we made and the models
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206 we considered (in particular the perimeter coverage one), second we describe the
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207 background idea of our protocol, and third we give the outline of the algorithm
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208 executed by each node.
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211 \subsection{Assumptions and Models}
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214 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
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215 distributed in a bounded sensor field is considered. The wireless sensors are
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216 deployed in high density to ensure initially a high coverage ratio of the area
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217 of interest. We assume that all the sensor nodes are homogeneous in terms of
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218 communication, sensing, and processing capabilities and heterogeneous from
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219 the energy provision point of view. The location information is available to a
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220 sensor node either through hardware such as embedded GPS or location discovery
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221 algorithms. We assume that each sensor node can directly transmit its
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222 measurements to a mobile sink node. For example, a sink can be an unmanned
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223 aerial vehicle (UAV) flying regularly over the sensor field to collect
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224 measurements from sensor nodes. A mobile sink node collects the measurements and
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225 transmits them to the base station. We consider a Boolean disk coverage model,
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226 which is the most widely used sensor coverage model in the literature, and all
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227 sensor nodes have a constant sensing range $R_s$. Thus, all the space points
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228 within a disk centered at a sensor with a radius equal to the sensing range are
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229 said to be covered by this sensor. We also assume that the communication range
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230 $R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, \citet{Zhang05}
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231 proved that if the transmission range fulfills the previous hypothesis, the
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232 complete coverage of a convex area implies connectivity among active nodes.
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234 The PeCO protocol uses the same perimeter-coverage model as \citet{huang2005coverage}. It can be expressed as follows: a sensor is
\r
235 said to be perimeter covered if all the points on its perimeter are covered by
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236 at least one sensor other than itself. They proved that a network area is
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237 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
\r
239 Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this
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240 figure, we can see that sensor~$0$ has nine neighbors and we have reported on
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241 its perimeter (the perimeter of the disk covered by the sensor) for each
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242 neighbor the two points resulting from the intersection of the two sensing
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243 areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
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244 for left and right from a neighboing point of view. The resulting couples of
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245 intersection points subdivide the perimeter of sensor~$0$ into portions called
\r
248 \begin{figure}[ht!]
\r
250 \begin{tabular}{@{}cr@{}}
\r
251 \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
\r
252 \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)}
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254 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
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255 $u$'s perimeter covered by $v$.}
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259 Figure~\ref{figure1}(b) describes the geometric information used to find the
\r
260 locations of the left and right points of an arc on the perimeter of a sensor
\r
261 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
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262 west side of sensor~$u$, with the following respective coordinates in the
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263 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
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264 compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
\r
265 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
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266 obtained through the formula:
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268 \alpha = \arccos \left(\frac{Dist(u,v)}{2R_s}
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271 The arc on the perimeter of~$u$ defined by the angular interval $[\pi
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272 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
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274 Every couple of intersection points is placed on the angular interval $[0,2\pi]$
\r
275 in a counterclockwise manner, leading to a partitioning of the interval.
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276 Figure~\ref{figure1}(a) illustrates the arcs for the nine neighbors of
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277 sensor $0$ and figure~\ref{figure2} gives the position of the corresponding arcs
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278 in the interval $[0,2\pi]$. More precisely, we can see that the points are
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279 ordered according to the measures of the angles defined by their respective
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280 positions. The intersection points are then visited one after another, starting
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281 from the first intersection point after point~zero, and the maximum level of
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282 coverage is determined for each interval defined by two successive points. The
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283 maximum level of coverage is equal to the number of overlapping arcs. For
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285 between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
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286 (the value is highlighted in yellow at the bottom of figure~\ref{figure2}), which
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287 means that at most 2~neighbors can cover the perimeter in addition to node $0$.
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288 Table~\ref{my-label} summarizes for each coverage interval the maximum level of
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289 coverage and the sensor nodes covering the perimeter. The example discussed
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290 above is thus given by the sixth line of the table.
\r
293 \begin{figure*}[t!]
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295 \includegraphics[width=127.5mm]{figure2.eps}
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296 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
\r
304 \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}
\r
305 {\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\r
307 \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
308 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
\r
309 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
\r
310 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
\r
311 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
\r
312 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
\r
313 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
\r
314 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
\r
315 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
\r
316 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
\r
317 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
\r
318 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
\r
319 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
\r
320 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
\r
321 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
\r
322 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
\r
323 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
\r
324 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
\r
325 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
\r
334 In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an
\r
335 integer program based on coverage intervals. The formulation of the coverage
\r
336 optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
\r
337 node has a part of its sensing range outside the WSN sensing field, as in
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338 figure~\ref{figure3}, the maximum coverage level for this arc is set to $\infty$
\r
339 and the corresponding interval will not be taken into account by the
\r
340 optimization algorithm.
\r
345 \includegraphics[width=62.5mm]{figure3.eps}
\r
346 \caption{Sensing range outside the WSN's area of interest.}
\r
351 \subsection{The Main Idea}
\r
353 \noindent The WSN area of interest is, in a first step, divided into regular
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354 homogeneous subregions using a divide-and-conquer algorithm. In a second step
\r
355 our protocol will be executed in a distributed way in each subregion
\r
356 simultaneously to schedule nodes' activities for one sensing period.
\r
358 As shown in figure~\ref{figure4}, node activity scheduling is produced by our
\r
359 protocol in a periodic manner. Each period is divided into 4 stages: Information
\r
360 (INFO) Exchange, Leader Election, Decision (the result of an optimization
\r
361 problem), and Sensing. For each period there is exactly one set cover
\r
362 responsible for the sensing task. Protocols based on a periodic scheme, like
\r
363 PeCO, are more robust against an unexpected node failure. On the one hand, if
\r
364 a node failure is discovered before taking the decision, the corresponding sensor
\r
365 node will not be considered by the optimization algorithm. On the other
\r
366 hand, if the sensor failure happens after the decision, the sensing task of the
\r
367 network will be temporarily affected: only during the period of sensing until a
\r
368 new period starts, since a new set cover will take charge of the sensing task in
\r
369 the next period. The energy consumption and some other constraints can easily be
\r
370 taken into account since the sensors can update and then exchange their
\r
371 information (including their residual energy) at the beginning of each period.
\r
372 However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
\r
373 are energy consuming, even for nodes that will not join the set cover to monitor
\r
378 \includegraphics[width=80mm]{figure4.eps}
\r
379 \caption{PeCO protocol.}
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383 We define two types of packets to be used by PeCO protocol:
\r
386 \item INFO packet: sent by each sensor node to all the nodes inside a same
\r
387 subregion for information exchange.
\r
388 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion
\r
389 to transmit to them their respective status (stay Active or go Sleep) during
\r
394 Five status are possible for a sensor node in the network:
\r
397 \item LISTENING: waits for a decision (to be active or not);
\r
398 \item COMPUTATION: executes the optimization algorithm as leader to
\r
399 determine the activities scheduling;
\r
400 \item ACTIVE: node is sensing;
\r
401 \item SLEEP: node is turned off;
\r
402 \item COMMUNICATION: transmits or receives packets.
\r
406 \subsection{PeCO Protocol Algorithm}
\r
408 \noindent The pseudocode implementing the protocol on a node is given below.
\r
409 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
\r
410 protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
\r
415 % \KwIn{all the parameters related to information exchange}
\r
416 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
\r
418 %\emph{Initialize the sensor node and determine it's position and subregion} \;
\r
420 \noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
\r
421 \hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
\r
422 \hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
\r
423 \hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
\r
424 \hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
\r
425 \hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
\r
426 \hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
\r
427 \hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
\r
428 \hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
\r
429 \hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
\r
430 \hspace*{1.2cm} {\bf end}\\
\r
431 \hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
\r
432 \hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
\r
433 \hspace*{1.2cm} {\bf end}\\
\r
434 \hspace*{1.2cm} {\bf else}\\
\r
435 \hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
\r
436 \hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
\r
437 \hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
\r
438 \hspace*{1.2cm} {\bf end}\\
\r
439 \hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
\r
440 \hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
\r
441 \hspace*{1.2cm}\emph{Update $RE_k $;}\\
\r
442 \hspace*{0.6cm} {\bf end}\\
\r
443 \hspace*{0.6cm} {\bf else}\\
\r
444 \hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
\r
445 \hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
\r
446 \hspace*{1.2cm}\emph{Update $RE_k $;}\\
\r
447 \hspace*{0.6cm} {\bf end}\\
\r
450 \hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
\r
457 In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
\r
458 current number and the previous number of living nodes in the subnetwork of the
\r
459 subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
\r
460 must be greater than a threshold $E_{th}$ in order to participate in the current
\r
461 period. Each sensor node determines its position and its subregion using an
\r
462 embedded GPS or a location discovery algorithm. After that, all the sensors
\r
463 collect position coordinates, remaining energy, sensor node ID, and the number
\r
464 of their one-hop live neighbors during the information exchange. The sensors
\r
465 inside a same region cooperate to elect a leader. The selection criteria for the
\r
466 leader, in order of priority, are: larger numbers of neighbors, larger remaining
\r
467 energy, and then in case of equality, larger index. Once chosen, the leader
\r
468 collects information to formulate and solve the integer program which allows to
\r
469 construct the set of active sensors in the sensing stage.
\r
472 \section{Perimeter-based Coverage Problem Formulation}
\r
475 \noindent In this section, the coverage model is mathematically formulated. We
\r
476 start with a description of the notations that will be used throughout the
\r
478 First, we have the following sets:
\r
480 \item $S$ represents the set of WSN sensor nodes;
\r
481 \item $A \subseteq S $ is the subset of alive sensors;
\r
482 \item $I_j$ designates the set of coverage intervals (CI) obtained for
\r
485 $I_j$ refers to the set of coverage intervals which have been defined according
\r
486 to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
\r
487 let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
\r
488 in coverage interval~$i$ of sensor~$j$, that is:
\r
490 a^j_{ik} = \left \{
\r
492 1 & \mbox{if sensor $k$ is involved in the } \\
\r
493 & \mbox{coverage interval $i$ of sensor $j$}, \\
\r
494 0 & \mbox{otherwise.}\\
\r
495 \end{array} \right.
\r
497 Note that $a^k_{ik}=1$ by definition of the interval.
\r
499 Second, we define several binary and integer variables. Hence, each binary
\r
500 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
\r
501 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
\r
502 variable which measures the undercoverage for the coverage interval $i$
\r
503 corresponding to sensor~$j$. In the same way, the overcoverage for the same
\r
504 coverage interval is given by the variable $V^j_i$.
\r
506 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
\r
507 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
\r
508 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
\r
509 previous notations, the number of active sensors in the coverage interval $i$ of
\r
510 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
\r
511 lifetime, the objective is to activate a minimal number of sensors in each
\r
512 period to ensure the desired coverage level. As the number of alive sensors
\r
513 decreases, it becomes impossible to reach the desired level of coverage for all
\r
514 coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure
\r
515 of the deviation between the desired number of active sensors in a coverage
\r
516 interval and the effective number. And we try to minimize these deviations,
\r
517 first to force the activation of a minimal number of sensors to ensure the
\r
518 desired coverage level, and if the desired level cannot be completely satisfied,
\r
519 to reach a coverage level as close as possible to the desired one.
\r
524 Our coverage optimization problem can then be mathematically expressed as follows:
\r
529 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
\r
530 \textrm{subject to :}&\\
\r
531 \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
532 \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
533 X_{k} \in \{0,1\}, \forall k \in A
\r
538 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
\r
539 relative importance of satisfying the associated level of coverage. For example,
\r
540 weights associated with coverage intervals of a specified part of a region may
\r
541 be given by a relatively larger magnitude than weights associated with another
\r
542 region. This kind of integer program is inspired from the model developed for
\r
543 brachytherapy treatment planning for optimizing dose distribution
\r
544 \citep{0031-9155-44-1-012}. The integer program must be solved by the leader in
\r
545 each subregion at the beginning of each sensing phase, whenever the environment
\r
546 has changed (new leader, death of some sensors). Note that the number of
\r
547 constraints in the model is constant (constraints of coverage expressed for all
\r
548 sensors), whereas the number of variables $X_k$ decreases over periods, since we
\r
549 consider only alive sensors (sensors with enough energy to be alive during one
\r
550 sensing phase) in the model.
\r
552 \section{Performance Evaluation and Analysis}
\r
553 \label{sec:Simulation Results and Analysis}
\r
556 \subsection{Simulation Settings}
\r
559 The WSN area of interest is supposed to be divided into 16~regular subregions
\r
560 and we use the same energy consumption than in our previous work~\citep{Idrees2}.
\r
561 Table~\ref{table3} gives the chosen parameters settings.
\r
564 \tbl{Relevant parameters for network initialization \label{table3}}{
\r
568 \begin{tabular}{c|c}
\r
571 Parameter & Value \\ [0.5ex]
\r
574 % inserts single horizontal line
\r
575 Sensing field & $(50 \times 25)~m^2 $ \\
\r
577 WSN size & 100, 150, 200, 250, and 300~nodes \\
\r
579 Initial energy & in range 500-700~Joules \\
\r
581 Sensing period & duration of 60 minutes \\
\r
582 $E_{th}$ & 36~Joules\\
\r
585 $\alpha^j_i$ & 0.6 \\
\r
593 To obtain experimental results which are relevant, simulations with five
\r
594 different node densities going from 100 to 300~nodes were performed considering
\r
595 each time 25~randomly generated networks. The nodes are deployed on a field of
\r
596 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
\r
597 high coverage ratio. Each node has an initial energy level, in Joules, which is
\r
598 randomly drawn in the interval $[500-700]$. If its energy provision reaches a
\r
599 value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
\r
600 node to stay active during one period, it will no more participate in the
\r
601 coverage task. This value corresponds to the energy needed by the sensing phase,
\r
602 obtained by multiplying the energy consumed in active state (9.72 mW) with the
\r
603 time in seconds for one period (3600 seconds), and adding the energy for the
\r
604 pre-sensing phases. According to the interval of initial energy, a sensor may
\r
605 be active during at most 20 periods.
\r
607 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
\r
608 network coverage and a longer WSN lifetime. We have given a higher priority to
\r
609 the undercoverage (by setting the $\alpha^j_i$ with a larger value than
\r
610 $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
\r
611 sensor~$j$. On the other hand, we have assigned to
\r
612 $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
\r
613 in covering the interval.
\r
615 We introduce the following performance metrics to evaluate the efficiency of our
\r
620 \item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
\r
621 the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
\r
622 $Lifetime_{50}$ denote, respectively, the amount of time during which is
\r
623 guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
\r
624 fulfill the expected monitoring task until all its nodes have depleted their
\r
625 energy or if the network is no more connected. This last condition is crucial
\r
626 because without network connectivity a sensor may not be able to send to a
\r
627 base station an event it has sensed.
\r
628 \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
\r
629 observe the area of interest. In our case, we discretized the sensor field as
\r
630 a regular grid, which yields the following equation:
\r
635 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
\r
639 where $n$ is the number of covered grid points by active sensors of every
\r
640 subregions during the current sensing phase and $N$ is total number of grid
\r
641 points in the sensing field. In our simulations we have set a layout of
\r
642 $N~=~51~\times~26~=~1326$~grid points.
\r
643 \item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
\r
644 activate as few nodes as possible, in order to minimize the communication
\r
645 overhead and maximize the WSN lifetime. The active sensors ratio is defined as
\r
650 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
\r
653 where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
\r
654 current sensing period~$p$, $|S|$ is the number of sensors in the network, and
\r
655 $R$ is the number of subregions.
\r
656 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
\r
657 energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
\r
658 divided by the number of periods. The value of EC is computed according to
\r
663 \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
\r
664 + E^{a}_p+E^{s}_p \right)}{P},
\r
667 where $P$ corresponds to the number of periods. The total energy consumed by
\r
668 the sensors comes through taking into consideration four main energy
\r
669 factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
\r
670 energy consumption spent by all the nodes for wireless communications during
\r
671 period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to
\r
672 the energy consumed by the sensors in LISTENING status before receiving the
\r
673 decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$
\r
674 refers to the energy needed by all the leader nodes to solve the integer
\r
675 program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
\r
676 consumed by the WSN during the sensing phase (active and sleeping nodes).
\r
680 \subsection{Simulation Results}
\r
682 In order to assess and analyze the performance of our protocol we have
\r
683 implemented PeCO protocol in OMNeT++~\citep{varga} simulator. Besides PeCO, two
\r
684 other protocols, described in the next paragraph, will be evaluated for
\r
685 comparison purposes. The simulations were run on a DELL laptop with an Intel
\r
686 Core~i3~2370~M (1.8~GHz) processor (2 cores) whose MIPS (Million Instructions
\r
687 Per Second) rate is equal to 35330. To be consistent with the use of a sensor
\r
688 node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate
\r
689 equal to 6, the original execution time on the laptop is multiplied by 2944.2
\r
690 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for
\r
691 Mathematical Programming (AMPL)~\citep{AMPL} is employed to generate the integer
\r
692 program instance in a standard format, which is then read and solved by the
\r
693 optimization solver GLPK (GNU linear Programming Kit available in the public
\r
694 domain) \citep{glpk} through a Branch-and-Bound method.
\r
696 As said previously, the PeCO is compared to three other approaches. The first
\r
697 one, called DESK, is a fully distributed coverage algorithm proposed by
\r
698 \citep{ChinhVu}. The second one, called GAF~\citep{xu2001geography}, consists in
\r
699 dividing the monitoring area into fixed squares. Then, during the decision
\r
700 phase, in each square, one sensor is chosen to remain active during the sensing
\r
701 phase. The last one, the DiLCO protocol~\citep{Idrees2}, is an improved version
\r
702 of a research work we presented in~\citep{idrees2014coverage}. Let us notice that
\r
703 PeCO and DiLCO protocols are based on the same framework. In particular, the
\r
704 choice for the simulations of a partitioning in 16~subregions was made because
\r
705 it corresponds to the configuration producing the best results for DiLCO. The
\r
706 protocols are distinguished from one another by the formulation of the integer
\r
707 program providing the set of sensors which have to be activated in each sensing
\r
708 phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
\r
709 whereas the PeCO protocol objective is to reach a desired level of coverage for each
\r
710 sensor perimeter. In our experimentations, we chose a level of coverage equal to
\r
713 \subsubsection{\bf Coverage Ratio}
\r
715 Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes
\r
716 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
\r
717 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
\r
718 produced by PeCO for the first periods. This is due to the fact that at the
\r
719 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
\r
720 slightly decreases the coverage ratio), while the three other protocols activate
\r
721 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
\r
722 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
\r
723 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
\r
724 compared to DESK). The energy saved by PeCO in the early periods allows later a
\r
725 substantial increase of the coverage performance.
\r
730 \includegraphics[scale=0.5] {figure5.eps}
\r
731 \caption{Coverage ratio for 200 deployed nodes.}
\r
738 \subsubsection{\bf Active Sensors Ratio}
\r
740 Having the less active sensor nodes in each period is essential to minimize the
\r
741 energy consumption and thus to maximize the network lifetime. Figure~\ref{figure6}
\r
742 shows the average active nodes ratio for 200 deployed nodes. We observe that
\r
743 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
\r
744 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and
\r
745 20.16~\% active nodes during the same time interval. As the number of periods
\r
746 increases, PeCO protocol has a lower number of active nodes in comparison with
\r
747 the three other approaches, while keeping a greater coverage ratio as shown in
\r
748 figure \ref{figure5}.
\r
752 \includegraphics[scale=0.5]{figure6.eps}
\r
753 \caption{Active sensors ratio for 200 deployed nodes.}
\r
757 \subsubsection{\bf Energy Consumption}
\r
759 We studied the effect of the energy consumed by the WSN during the communication,
\r
760 computation, listening, active, and sleep status for different network densities
\r
761 and compared it for the four approaches. Figures~\ref{figure7}(a) and (b)
\r
762 illustrate the energy consumption for different network sizes and for
\r
763 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
\r
764 most competitive from the energy consumption point of view. As shown in both
\r
765 figures, PeCO consumes much less energy than the three other methods. One might
\r
766 think that the resolution of the integer program is too costly in energy, but
\r
767 the results show that it is very beneficial to lose a bit of time in the
\r
768 selection of sensors to activate. Indeed the optimization program allows to
\r
769 reduce significantly the number of active sensors and so the energy consumption
\r
770 while keeping a good coverage level.
\r
774 \begin{tabular}{@{}cr@{}}
\r
775 \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
\r
776 \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
\r
778 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
\r
784 \subsubsection{\bf Network Lifetime}
\r
786 We observe the superiority of PeCO and DiLCO protocols in comparison with the
\r
787 two other approaches in prolonging the network lifetime. In
\r
788 Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
\r
789 different network sizes. As highlighted by these figures, the lifetime
\r
790 increases with the size of the network, and it is clearly largest for DiLCO
\r
791 and PeCO protocols. For instance, for a network of 300~sensors and coverage
\r
792 ratio greater than 50\%, we can see on figure~\ref{figure8}(b) that the lifetime
\r
793 is about twice longer with PeCO compared to DESK protocol. The performance
\r
794 difference is more obvious in figure~\ref{figure8}(b) than in
\r
795 figure~\ref{figure8}(a) because the gain induced by our protocols increases with
\r
796 time, and the lifetime with a coverage of 50\% is far longer than with
\r
801 \begin{tabular}{@{}cr@{}}
\r
802 \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
\r
803 \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}
\r
805 \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
\r
806 and (b)~$Lifetime_{50}$.}
\r
812 Figure~\ref{figure9} compares the lifetime coverage of our protocols for
\r
813 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
\r
814 Protocol/90, and Protocol/95 the amount of time during which the network can
\r
815 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
\r
816 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
\r
817 that do not require a 100\% coverage of the area to be monitored. PeCO might be
\r
818 an interesting method since it achieves a good balance between a high level
\r
819 coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
\r
820 lower coverage ratios, moreover the improvements grow with the network
\r
821 size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
\r
822 not ineffective for the smallest network sizes.
\r
825 \centering \includegraphics[scale=0.5]{figure9.eps}
\r
826 \caption{Network lifetime for different coverage ratios.}
\r
833 \section{Conclusion and Future Works}
\r
834 \label{sec:Conclusion and Future Works}
\r
836 In this paper we have studied the problem of Perimeter-based Coverage Optimization in
\r
837 WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
\r
838 schedules nodes' activities (wake up and sleep stages) with the objective of
\r
839 maintaining a good coverage ratio while maximizing the network lifetime. This
\r
840 protocol is applied in a distributed way in regular subregions obtained after
\r
841 partitioning the area of interest in a preliminary step. It works in periods and
\r
842 is based on the resolution of an integer program to select the subset of sensors
\r
843 operating in active status for each period. Our work is original in so far as it
\r
844 proposes for the first time an integer program scheduling the activation of
\r
845 sensors based on their perimeter coverage level, instead of using a set of
\r
846 targets/points to be covered.
\r
849 We have carried out several simulations to evaluate the proposed protocol. The
\r
850 simulation results show that PeCO is more energy-efficient than other
\r
851 approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
\r
852 energy consumption.
\r
854 We plan to extend our framework so that the schedules are planned for multiple
\r
857 We also want to improve our integer program to take into account heterogeneous
\r
858 sensors from both energy and node characteristics point of views.
\r
860 Finally, it would be interesting to implement our protocol using a
\r
861 sensor-testbed to evaluate it in real world applications.
\r
863 \bibliographystyle{gENO}
\r
864 \bibliography{biblio}
\r
