Target location based sink positioning in wirelesssensor networks

Dimitrios Zorbas∗, Christos Douligeris∗ and Viktoria Fodor†∗Department of Informatics, University of Piraeus

Piraeus, Greecejim@students.cs.unipi.gr, cdoulig@unipi.gr

†Access Linnaeus CenterKTH, Royal Institute of Technology

Stockholm, Swedenvfodor@kth.se

Abstract—One of the main challenges in wireless sensor net-works is to prolong the network lifetime by efficiently handlingthe limited battery life of the nodes. This problem becomesharder in applications where the nodes are randomly droppedin the field. In this paper we deal with the problem of the sinkplacement and of the network longevity, assuming a number ofpoints in the field with known positions which must be coveredby the sensors. Unlike other approaches, we consider the morerealistic scenario where the coordinates of the sensors are notassumed to be known in advance and, thus, they cannot be usedfor the computation of the positions of the sinks. We presenttwo solutions for the above problem; one based on the distancebetween the points and the second on the probability that asensor may cover many points. We evaluate our approachesand compare them to algorithms that use the knowledge of thepositions of the sensors in order to compute likely sink locations.It is shown that both proposed approaches present similar orbetter performance concerning network lifetime, while at thesame time they significantly decrease the algorithm complexity.

I. INTRODUCTION

Wireless sensors networks (WSNs) consist of hundreds oftiny nodes with low computational capabilities and limitedbattery lifetime. The nodes are used to monitor a numberof events that periodically occur in the field. The energyconsumption of the nodes is mainly attributed to the sensingand communication operation. The goal of researchers is toprolong the network lifetime. In multi-hop environments asingle sink communicates with a small number of nodes thatbecome bottlenecks for the rest of the network. When thesebottleneck nodes exhaust their battery the network loses itsconnectivity. On the other side, nodes that can monitor andforward data at the same time consume significant energy aswell. In other words, sensor networks usually suffer from theexhaustion faced by the neighbouring nodes of a single sinkand by nodes close to targets. These issues can be addressedby placing multiple sinks in the field. A critical question thenis where to place the sinks, since a correct placement maysignificantly improve the network lifetime.

Previously analysed approaches to the sink placement prob-lem are based on the assumption that the positions of the

sensor nodes are known in advance. Unlike the previous ap-proaches, our placement methods do not take into account theposition of the sensors, but they are based on the coordinatesof the targets that are assumed to be known in advance. Themain advantages of not considering the position of the sensorsinto the computation of the sinks location are: (a) there is noprotocol cost for locating and moving the sinks, (b) there is norestriction on what kind of algorithm (distributed or not) willbe used for the data collection, (c) the computation processmay take place before the placement of the sensors in the field,allowing the network to operate without any inactive period,and (d) the computational complexity is low compared to thecase where the sensor locations are taken into account.

In this paper we propose two methods in order to efficientlyplace a given number (i.e. k) of sinks in the field. Thefirst method decreases the mean distance between the targetsand the sinks by separating the targets into k groups usingthe k-means algorithm and placing one sink per group. Thesecond method takes into account the possibility that a sensormay cover two or more targets at the same time. Such asensor monitors and forwards a large amount of data, anoperation that exhausts its battery very quickly. Thus, thesecond method places sinks close to nearby targets, decreasingthe energy consumption that comes from the data transmission.We evaluate our methods through a series of simulations andwe compare them to approaches that take into account theposition of the nodes [1], [2]. The rest of the paper is organisedas follows. In Section II, we provide a detailed descriptionof the system. Our sink placement solutions are presentedin Section III, while in Section IV we evaluate our methodsand we compare them to other approaches. In Section V, wepresent the related work in the field of the sink placement.Finally, Section VI concludes the paper.

II. SYSTEM DESCRIPTION

The system is modelled as shown in Figure 1. Given a setof targets T0 with known coordinates and a sensor networkwhere each target is covered by at least one sensor, a givennumber of sinks is placed using a sink placement algorithm.

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2011 18th International Conference on Telecommunications

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Since knowledge of the sensors positions are not required bythe node placement process, the node deployment may takeplace after the placement of the sinks. Next, the coverage andthe routing process can be started by selecting source nodes(i.e. nodes that will be used for sensing) as well as nodes thatwill be used for relaying.

Given a number of targets with known locations and assuming a number of

sensors with unknown locations

Place a given number of sinks based on the targets' locations

Select sensors for coverage and relaying

Fig. 1. System modelling for the sink placement problem based on thetargets’ position

To estimate the performance loss due to the target based sinkplacement, let us consider the sink placement with and withoutconsidering the location of the source nodes for the case wherethe sink is placed in the centroid of the source nodes and ofthe targets respectively. The new sinks position will be at mostRs distance away from the location that computed using thesensors’ coordinates, where Rs is the sensing range of thenodes.

Theorem 1: Given k source nodes with locationss1, s2, · · · , sk, k targets with locations t1, t2, · · · , tk, where|s1 − t1| ≤ Rs, |s2 − t2| ≤ Rs, ..., |sk − tk| ≤ Rs andthe centroids Sc = s1+s2+···+sk

k and Tc = t1+t2+···+tkk , the

distance between the two centroids is at most Rs.Proof: Since |s1−t1| ≤ Rs, |s2−t2| ≤ Rs, ...,|sk−tk| ≤

Rs, adding these k elements it holds true that

|s1 − t1|+ |s2 − t2|+ · · ·+ |sk − tk| ≤ kRs.

However,

|s1 − t1|+ |s2 − t2|+ · · ·+ |sk − tk| ≥|s1 − t1 + s2 − t2 + · · ·+ sk − tk|.

Hence,

|s1 − t1 + s2 − t2 + · · ·+ sk − tk| ≤ kRs ⇔| s1−t1+s2−t2+···+sk−tk

k | ≤ Rs ⇔| s1+s2+···+sk

k − t1+t2+···+tkk | ≤ Rs

|Sc − Tc| ≤ Rs.

Thus, the distance between the two centroids is at most Rs.

A worst case scenario is shown in the example of Figure2. The two targets are covered by one source node. The leftfigure presents the case where the location of the sink based onthe position of the source nodes, while in the right figure the

new sink location is computed using the targets’ coordinates.Assuming that the first one is the optimum solution, thesecond solution places the sinks in Rs distance away fromthe optimum.

Fig. 2. A worst case scenario of a sink placement based on the location ofthe targets

After the sink placement, a node scheduling algorithm isneeded to select the source nodes and the nodes that willprovide routing in the network. This algorithm works inrounds, where in each round a set of sensors (i.e. source nodes)is selected to cover the available targets while relay nodes areselected to forward the monitoring data from the source nodesto the sinks. Both source nodes and nodes that do not cover anytarget can be selected for relaying. Only the selected sourceand relay nodes are active in each round, while the rest ofthe nodes remain in sleep-mode. Each round lasts until oneactive node depletes its battery. Then, the algorithm changesthe active nodes using sensors who have more remainingenergy. This process is repeated until there are no possiblesource or relay nodes in the network that provide coverage andconnectivity respectively. In order to connect a source nodeto a sink, a shortest path scheme is assumed (e.g. a Dijkstraalgorithm), where the cost indicates the remaining energy ofthe nodes and the distance between them. The network lifetimeis the sum of the time periods that each round lasts. Severalalgorithms that provide coverage and connectivity have beenpresented in the literature [3], [4], [5]. In this paper we usethe algorithm of [5].

Concerning the node energy consumption model, we assumethat each sensor has a maximum communication range Rc

and an initial battery life equal to l0. A node may spendthis energy for sensing, receiving or transmitting data. Theenergy it spends for sensing and receiving a bit is constantand equal to α3 and α12 respectively. The correspondingenergy used for transmitting a bit to distance δ ≤ Rc is equalto α11 + α2δ

α, where α11 is the energy consumed by thetransmitter electronics, α2 accounts for the energy dissipatedin the transmit operational amplifier and α is the loss exponentof the signal [6].

III. SINK PLACEMENT SOLUTIONS

A. The “k-means” solution

By grouping the targets into clusters and assigning a sinkas the head of each cluster, the communication load of thesource nodes and the sinks can be reduced. k-means groups thetargets into k clusters based on the Euclidean distance betweenthe targets according to the clustering algorithm k-means [7],

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where k is less or equal to the number of available targets andat the same time it is equal to the number of available sinks.The algorithm places a sink for each cluster, balancing thecommunication burden among the source and the relay nodes.

Figure 3 presents an example with 19 targets (non-filledsquares) that are grouped in 4 clusters and for each clusterone sink has been assigned (filled squares). The lines denotethe sink that each target belongs to.

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Fig. 3. Sink positioning using k-means

k-means does not take into account the possibility that anode may cover more than one target at the same time. Whena source node covers two ore more targets, it produces multipletimes the data that it would produce if it was covering a singletarget [8]. In case where such a sensor is in a long distanceaway from a sink, it either uses a long range link to reach thesink or it uses many relay nodes, exhausting its own energy orthe energy of the neighbouring relay nodes. Both cases leadto decreased network lifetime.

B. The “NeTa” solution

The second sink placement method, called NeTa (i.e. Neigh-bouring Targets), tries to eliminate the burden caused by thesensors that cover many targets. A node may cover multipletargets if these targets are in a distance lower than two timesthe sensing range from each other. These targets are calledneighbouring targets. NeTa prefers to place sinks close to thesetargets decreasing the probability of exhausting the batteryof the relay nodes that are neighbours with the sensors thatcover many targets. An example of two neighbouring targetsis shown in Figure 5. The disks denote the area where a sensormonitors the particular target. The node that lies in the hatchedarea can cover both targets. The probability of having one

sensor covering two neighbouring targets given a uniform nodedistribution is:

P1 =arccos(

d

2Rs)R2

s − sin(2 arccos(d

2Rs))R2

s

A, (1)

where the numerator corresponds to the hashed area, d is thedistance between the two targets and A is the terrain area. Thisprobability is higher when the distance between two targets islower and it increases as more sensors are dropped in the field.For n sensors the probability of having at least one sensor inthe hashed area is:

Pn = 1− (1− P1)n. (2)

Figure 4 shows that even for large terrain sizes (i.e. 25Km2) and a low number of targets this probability is high (over0.75), while in dense scenarios (i.e. 10K–15K m2) it is almostsure that at least one sensor will cover neighbouring targets.

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Fig. 4. Probability of covering neighbouring targets by at least one sensor– 200 sensors, variable number of targets, variable terrain size

First, NeTa follows a number of steps in order to placethe sinks. It constructs a weighted graph where the verticescorrespond to the targets and the edges connect neighbouringtargets, as it is shown in Figure 6. The black lines denote twoneighbouring targets, while the position of the sinks computedby the k-means solution is drawn with grey. Weights areassigned to the edges based on (1) and, in each step, NeTaselects the edge with the highest weight to place the sink. Thissink is placed halfway in between the two vertices. It thensearches for a fully connected component that the selectededge is part of. If there is such a component, NeTa movesthe sink to the centroid of the polygon that the componentformulates. A selected edge is deleted from the graph alongwith its vertices. If the edge is a member of a fully connectedcomponent, the algorithm deletes the other edges of thecomponent as well as the corresponding vertices. We mustmention that if a sensor is placed inside a small area of theconnected component it will cover a number of targets equalto the number of the component vertices. In Figure 6, F-K-Qformulate a triangle, where the centroid of the triangle is thesink location.

The algorithm checks if the distance from the new sinkto the previous selected sinks is lower than two times the

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sensing range. Two times the sensing range is enough to avoidhaving two sinks in a very close distance. The sink is placedif the previous check is true for all the already selected sinks.Otherwise, the sink position is held in a temporary set for apossible future selection.

In case where there are no other edges and the number ofsinks has not been completed, NeTa clusters the remainingtargets (mostly non-connected vertices) using k-means (e.g.R, M, N, T, C, G in the figure). The sinks that are in adistance of two times the sensing range away from all theprevious selected sinks are placed in the field. Otherwise, thesink positions are held in the temporary set.

If the number of sinks has not been completed yet, NeTaselects sink positions from the temporary set. In this case,the sink positions with the lower number of neighbouringsinks (computed by the previous checks) are selected. If twopositions have the same number of neighbours, NeTa selectsone of them randomly.

Fig. 5. Two neighbouring targets

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Fig. 6. Sink positioning using NeTa

IV. EVALUATION AND DISCUSSION OF THE RESULTS

In order to evaluate the proposed solutions and comparethem to other approaches, we used the centralised algorithmpresented in [5] assuming a 100% coverage ratio. This algo-rithm chooses the sensors that will be used for sensing andrelaying in each round. The heuristic algorithm presented in[4] was, also, tested showing a similar performance, but wepreferred [5] because of its lower complexity.

We compare our sink placement methods “k-means” and“NeTa” to three approaches. The first is the greedy algorithmpresented in [1]. This algorithm places the available sinksbased on the position of the sensors and it places the sinksclose to sensors that present the highest data flow. Since thenetwork data flow changes at each round, we move the sinksto new positions by executing [1] at the beginning of eachround. The second approach [2] computes the position ofthe sinks using the k-means clustering algorithm based onthe location of the source nodes. Next, it moves the sinksto their closest sensor in the network in order to decreasethe energy consumption caused by the transmission of thedata. Note that these two algorithms are suboptimal withoutany performance guarantee, since the sink positioning problembased on the location of the sensors is NP-complete. We havealso implemented an algorithm that randomly places the sinksin the field using a uniform distribution. These three algorithmsare called “bogdanov”, “local+” and “random” respectively.

We assess the algorithms in 50 scenarios, with random targetand sensor deployments and we compute the average networklifetime of these 50 scenarios. The 95% confidence intervalsare shown in the 2-dimensional figures. The communicationrange of the nodes is 50m and their sensing range is 10m.We assume that a source node generates data of 500bits everysecond in order to monitor a target. The size of a data packetis 125bytes and no data aggregation is used. Concerning theenergy consumption model, the following values are used [9]:α3 = 100nJ/bit, α11 = 50nJ/bit, α12 = 100nJ/bit, α2 =100pJ/bit/m2, l0 = 20J .

A. Simulation results

In the first set of our measurements, we assess the impact ofthe network density on the network lifetime for various targetpopulations having 5 sinks and 200 sensors. We modify thenetwork density by changing the terrain size. As it is shownin Figure 7, “k-means” and “NeTa” present good performancefor low terrain sizes very close to the “bogdanov” algorithm,but when the terrain becomes large NeTa outperforms k-meansand both sensor-based solutions. This occurs due to the factthat when the terrain becomes large, the distances betweenthe nodes and the targets become large as well, so it is morepreferable to have sinks close to the sensors that cover manytargets leaving some others with low energy consumption touse relay nodes in the network. Finally, the random solutionperforms 15-30% worse than the other solutions.

Figure 8 illustrates the performance of NeTa for 2 and5 sinks, varying the number of targets and the terrain size.The various shades on the surface denote the percentage

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Fig. 7. Performance results for 5 sinks, 200 sensors and variable number oftargets – 10K, 15K, 20K and 25K m2 terrain size

differences between NeTa and k-means. k-means performssimilar to NeTa in most dense network scenarios (10K m2),but as we are moving to more sparse scenarios (20K, 25K m2)NeTa performs up to 18% better than k-means (dark areas).The maximum superiority of NeTa is smaller when 5 sinksare deployed (up to 11%), since the mean distance betweenthe sinks and the targets become shorter and the nodes donot consume much energy. We can observe, though, that thedark area has been moved to more sparse deployments andto larger target populations, where the possibility of havingneighbouring targets is higher.

Figure 9 depicts the performance of NeTa and its differencefrom k-means for 10K and 25K m2 terrain sizes, varying thenumber of targets and the number of sinks. In scenarios wherethe terrain size is small (10K m2) k-means and NeTa performsimilarly, especially in the case with many sinks (over 5). Ifwe move to a larger terrain (25K m2), NeTa performs muchbetter than k-means in most of the scenarios and especiallyin the cases where the number of sinks is low (up to 5).k-means closes this gap for the rest of the scenarios wheremany sinks are deployed, since the target and the sink densityincreases and the mean distance between the targets decreases.This outweighs any performance advantage that NeTa gains bycovering neighbouring targets.

V. RELATED WORK

Previous works on the sink placement problem aim at thecomputation of the sensors with the maximum data rate, where

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Fig. 8. Performance of NeTa and % difference between NeTa and k-means– 2 and 5 sinks, 200 sensors, variable number of targets and terrain size

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Fig. 9. Performance of NeTa and % difference to k-means – 10K and 25Km2 terrain size, 200 sensors, variable number of targets and sinks

sinks are placed close to these sensors such as the data rate willbe optimum. Finding the optimum layout of sinks, however,turns out to be an NP-complete problem [1]. The authors of

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[1] formulate the sink placement problem as a maximum flowproblem and propose heuristics to improve the efficiency ofthe network.

In [10] the authors propose an Integer Linear Programming(ILP) solution with high complexity to place the sinks. How-ever, the sinks can be located only at certain sites on theperiphery of the network, called feasible sites. The monitoringprocess is divided in rounds and the sinks may move fromone feasible site to another at the beginning of each round.More efficient algorithms with a lower computation cost arepresented in [11]. The authors examine the case where anenergy aware routing scheme is applied for further energyconservation. The proposed solutions outperform the ILPalgorithm of [10]. In [12], the authors extend the work of[10] and [11] by allowing a sink to be placed anywhere in thefield. They propose an ILP solution for this purpose extendingthe network lifetime.

In [13] the network is divided in clusters, where each clusterhas a sink as its cluster-head. The sensors adjust the level oftransmission range in order to communicate with the sink. Asink must rapidly move inside the cluster area at the beginningof each monitoring round. The authors consider two strategiesin order to extend the network lifetime. They try to minimisethe average energy consumption as well as the maximumtransmission range. The sensor clustering is also used in [2],where the sensors are divided into groups using the k-meansalgorithm. After the deployment of a sink as the cluster-headof a group, the sink is moved to the sensor that is placedclosest to the sink location.

The problem of sink repositioning with mobile sinks isexamined in [14]. A scheme is proposed that moves the sinksto paths with high data rate. It tracks the changes in thenodes that act as the closest hop to the sinks and the trafficdensity that is going through these hops. The authors, also,deal with the problem of how to handle the sink’s motionwithout affecting the data traffic.

Finally, in [15], Kim et al. solve the sink positioningproblem by considering further parameters of the networksuch as the fault tolerance and the data delay, while theypropose heuristics based on a cost function that integrates allthe performance parameters.

Since the previous approaches are based on the location ofthe sensors, there is a performance loss due to the cost of theprotocol that moves the sinks and determines the possible basestation locations. From the other hand, since the most of thealgorithms work in a centralised manner, the nodes must beequipped with a GPS mechanism in order to be known theircoordinates. This requirement incurs an extra energy cost forthe algorithms that must know the locations of the nodes.

VI. CONCLUSION AND FUTURE WORK

In this paper we dealt with the sink positioning problemgiven a set of targets with known coordinates. A sensornetwork is deployed that is capable of covering these targetsand forwarding the monitoring data to one of the availablesinks. The location of the nodes is not considered in the

computation of the sink positions. We propose two methods,one based on the coordinates of the targets, taking into accountthe mean distance between the targets and another taking intoaccount the probability that a sensor may cover two or moretargets at the same time. We evaluated our approaches throughsimulation and showed that they present similar or even betterperformance compared to existing solutions despite their lowercomputation complexity. In the future, we will assess ourapproaches in non-uniform node deployments and examine thecase of the non-uniform traffic generation in the targets.

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