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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 5, JUNE 2014 2407

An Energy-Efficient Mobile-Sink Path Selection

Strategy for Wireless Sensor NetworksHamidreza Salarian, Kwan-Wu Chin, and Fazel Naghdy

AbstractSeveral studies have demonstrated the benefits of us-ing a mobile sink to reducethe energy consumption of nodes and toprevent the formation of energy holes in wireless sensor networks(WSNs). However, these benefits are dependent on the path takenby the mobile sink, particularly in delay-sensitive applications, asall sensed data must be collected within a given time constraint.An approach proposed to address this challenge is to form a hybridmoving pattern in which a mobile-sink node only visits rendezvouspoints (RPs), as opposed to all nodes. Sensor nodes that are notRPs forward their sensed data via multihopping to the nearestRP. The fundamental problem then becomes computing a tourthat visits all these RPs within a given delay bound. Identifyingthe optimal tour, however, is an NP-hard problem. To addressthis problem, a heuristic called weighted rendezvous planning(WRP) is proposed, whereby each sensor node is assigned a weightcorresponding to its hop distance from the tour and the number ofdata packets that it forwards to the closest RP. WRP is validatedvia extensive computer simulation, and our results demonstratethat WRP enables a mobile sink to retrieve all sensed data withina given deadline while conserving the energy expenditure of sensornodes. More specifically, WRP reduces energy consumption by22% and increases network lifetime by 44%, as compared withexisting algorithms.

Index TermsData collection, mobile sink, scheduling, wirelesssensor networks (WSNs).

I. INTRODUCTION

WIRELESS sensor networks (WSNs) are composed of a

large number of sensor nodes deployed in a field. They

have wide-ranging applications, some of which include military

[1][3], environment monitoring [4], [5], agriculture [6], [7],

home automation [8], smart transportation [9], [10], and health

[11]. Each sensor node has the capability to collect and process

data, and to forward any sensed data back to one or more sink

nodes via their wireless transceiver in a multihop manner. In

addition, it is equipped with a battery, which may be difficult

or impractical to replace, given the number of sensor nodes and

deployed environment. These constraints have led to intensiveresearch efforts on designing energy-efficient protocols [12].

In multihop communications, nodes that are near a sink tend

to become congested as they are responsible for forwarding

data from nodes that are farther away. Thus, the closer a sensor

node is to a sink, the faster its battery runs out, whereas those

Manuscript received March 11, 2012; revised March 9, 2013, June 20, 2013,September 15, 2013, and November 9, 2013; accepted November 14, 2013.Date of publication November 21, 2013; date of current version June 12, 2014.The review of this paper was coordinated by Dr. L. Li.

The authors are with the School of Electrical, Computer, and Telecommu-nications Engineering, University of Wollongong, Wollongong, NSW 2522,Australia (e-mail: [email protected]).

Digital Object Identifier 10.1109/TVT.2013.2291811

Fig. 1. Example showing a mobile sink performing data collection in a WSN.A source node determines and sends all data to a suitable site.

farther away may maintain more than 90% of their initial energy

[13]. This leads to nonuniform depletion of energy, which

results in network partition due to the formation of energy holes

[14], [15]. As a result, the sink becomes disconnected from

other nodes, thereby impairing the WSN. Hence, balancing the

energy consumption of sensor nodes to prevent energy holes is

a critical issue in WSNs.

To this end, previous works such as [15] and [16] employ

one or more mobile sinks. These mobile sinks survey and

collect sensed data directly from sensor nodes and thereby help

sensor nodes save energy that otherwise would be consumed

by multihop communications. Fig. 1 shows the feasible sites

of a mobile sink in an example WSN. Specifically, the squares

denote the feasible sites that the mobile sink will visit and

stop for data collection. The data forwarding path from sensor

nodes to the sink is dependent on the sinks current position.This requires sensor nodes to dynamically plan one or more

data forwarding paths to each feasible site whenever the sink

node changes its position over time. As demonstrated by [15],

a mobile sink that moves at the periphery of a sensor field max-

imizes the lifetime of sensor nodes. Intuitively, by changing the

position of the sink over time, the forwarding tree will involve

a different set of sensor nodes and, hence, will help to balance

energy consumption [17][21].

The traveling path of a mobile sink depends on the real-

time requirement of data produced by nodes. For example,

in hard real-time applications such as a fire-detection system

[22], environmental data need to be collected by a mobile sink

0018-9545 2013IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


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2408 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 5, JUNE 2014

Fig. 2. Hybrid movement pattern for a mobile sink node. Source nodes

generate and send sensed data to the nearest RP. Each RP buffers received dataand waits until the mobile sink arrives.

quickly. Moreover, a mobile-sink node may change its positionafter a certain period of time and select another data collection/

feasible site. The feasible sites and corresponding sojourn time

are dependent on the residual energy of sensor nodes [23]

[27]. In general, limitations such as the maximum number of

feasible sites [28], maximum distance between feasible sites,

and minimum sojourn time [24] govern the movement of a

mobile sink.

In WSNs with a mobile sink, one fundamental problem is

to determine how the mobile sink goes about collecting sensed

data. One approach is to visit each sensor node to receive sensed

data directly [29]. This is essentially the well-known traveling

salesman problem (TSP) [30], where the goal is to find theshortest tour that visits all sensor nodes. However, with an

increasing number of nodes, this problem becomes intractable

and impractical as the resulting tour length is likely to violate

the delay bound of applications. To this end, researchers have

proposed the use of rendezvous points (RPs) to bound the tour

length [31], [32]. This means a subset of sensor nodes are

designated as RPs, and non-RP nodes simply forward their data

to RPs. A tour is then computed for the set of RPs, as shown

in Fig. 2. As a result, the problem, which is called rendezvous

design, becomes selecting the most suitable RPs that minimize

energy consumption in multihop communications while meet-

ing a given packet delivery bound. A secondary problem here is

to select the set of RPs that result in uniform energy expenditure

among sensor nodes to maximize network lifetime.

In this paper, we call this problem the delay-aware energy-

efficient path (DEETP). We show that the DEETP is an NP-

hard problem and propose a heuristic method, which is called

weighted rendezvous planning (WRP), to determine the tour of

a mobile-sink node. In WRP, the sensor nodes with more con-

nections to other nodes and placed farther from the computed

tour in terms of hop count are given a higher priority. Thus, this

paper is summarized as follows.

We define the problem of finding a set of RPs to be visited

by a mobile sink. The objective is to minimize energy

consumption by reducing multihop transmissions fromsensor nodes to RPs. This also limits the number of RPs

such that the resulting tour does not exceed the required

deadline of data packets.

We propose WRP, which is a heuristic method that finds

a near-optimal traveling tour that minimizes the energy

consumption of sensor nodes. WRP assigns a weight to

sensor nodes based on the number of data packets that

they forward and hop distance from the tour, and selectsthe sensor nodes with the highest weight.

We mathematically prove that selecting the sensor node

that forwards the highest number of data packets and have

the longest hop distance from the tour reduces the network

energy consumption, as compared with other nodes. More-

over, we show that, in contrast to cluster-based (CB) [32],

rendezvous design for variable tracks (RD-VT) [33], and

rendezvous planning utility-based greedy (RP-UG) [31]

algorithms, WRP is guaranteed to find a tour if the latter

exists.

We demonstrate via computer simulation the properties

and effectiveness of WRP against the CB [32], RD-VT

[33], and RP-UG algorithms [31]. Our results show that

WRP achieves 14% more energy savings and 22% better

distribution of energy consumption between sensor nodes

than the said algorithms.

The remainder of this paper is structured as follows.

Section II reviews methods that employa hybrid model to collect

sensed data. Section III presents DEETP. In Section IV, we

illustrate WRP and present a detailed analysis of WRP and key

properties. Finally, in Section V, we compare the performance

of WRP with previous works before concluding in Section VI.

II. LITERATURER EVIEW

Existing methods on using a mobile sink in WSNs can be

grouped into two categories: 1) direct, where a mobile sink

visits each sensor node and collects data via a single hop;

and 2) rendezvous, where a mobile sink only visits nodes

designated as RPs. The main goal of protocols in category 1 is

to minimize data collection delays, whereas those in category 2

aim to find a subset of RPs that minimize energy consumption

while adhering to the delay bound provided by an application

[17]. In the following, we review the challenges faced by these

protocols.

A. Direct

Initial studies used a mobile sink that visits sensor nodes

randomly and transport collected data back to a fixed sink

node. An example is the use of animals as mobile-sink nodes

to assist in data collection from sensor nodes scattered on a

large farm [16]. To reduce the latency of visiting each sensor

node randomly, researchers have proposed TSP-based data col-

lection methods. In essence, the problem is reduced to finding

the shortest traveling path that visits each sensor node [29].

For example, TSP with neighborhood [34] involves finding

the shortest traveling tour for a mobile-sink node that passes

through the communication range of all sensor nodes. Another

TSP-based algorithm [35] called label-covering considers aWSN as a complete graph. For each edge, it calculates a cost


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SALARIANet al.: ENERGY-EFFICIENT MOBILE-SINK PATH SELECTION STRATEGY FOR WSNs 2409

and associates a label set. The cost of an edge is the Euclidean

distance between nodes, whereas the label set contains sensor

nodes whose transmission range intersects with the given edge.

The label-covering algorithm selects the minimum number of

edges where their associated label set covers all sensor nodes.

B. Rendezvous

The problem with collecting data directly from sensor nodes

is that it becomes impractical when there are a large number

of sensor nodes. Visiting each sensor node increases the mobile

sinks traveling path length and results in sensor nodes experi-

encing buffer overflow due to data collection delays. To address

this problem, researchers have proposed a rendezvous-based

model, in which a mobile sink only visits a subset of sensor

nodes called RPs. The sensor nodes outside the mobile sink

path send their data via multihop communications to these RPs.

Studies [31][33], [36][38] deploying this approach can be

classified according to the mobile sinks trajectory, i.e., whether

it moves along a fixed path or its path is unconstrained by any

external factors.

1) Fixed: In the studies conducted in [36][38], the path

of the mobile sink is fixed, and sensor nodes are randomly

deployed near the sinks traveling path. Sensor nodes that are

inside a mobile sinks communication range play the role of

RPs and collect data from other sensor nodes. An example

application is a traffic management system where mobile sinks

are public buses that roam a city to collect data from sensor

nodes placed on buildings [36]. In these approaches, the length

of the traveling path is not dependent on the buffer size of sensor

nodes or application deadline. Hence, the buffer of RPs may

overflow or packets may expire before they are collected by thesink.

Xing et al. [33] propose RD-FT, where the movement of

a mobile sink is governed by application deadline. They also

consider obstacles that restrict the movement of a mobile sink

along a predefined path. The objective is to find a set of RPs on

the fixed path such that the length of data forwarding paths from

sensor nodes to RPs is minimized and that the traveling time

between RPs is limited to the required packet delivery time.

2) Unconstrained: In [33], a WSN with a static sink node

and a mobile element (ME) is assumed to collect data from

RPs. Moreover, RPs perform data aggregation. An algorithm

called RD-VT is proposed with the objective of identifying atraveling path that is shorter in duration than the packet delivery

time. The algorithm first constructs a Steiner minimum tree

(SMT) rooted at the sink node. RD-VT then starts from the

sinks position and traverses the SMT in preorder until the

shortest distance between visited nodes is equal to the required

packet delivery time. Since, in an SMT, a Steiner point may

be a physical position and does not correspond to the position

of a sensor node, RD-VT replaces these virtual RPs with the

closest sensor nodes. A major limitation of RD-VT is that

traversing the SMT in preorder leads to the selection of RPs

that in turn results in long data forwarding paths to sensor nodes

located in different parts of the SMT. As a result, RD-VT causes

nodes to have an unbalanced data forwarding load and energyconsumption.

Xing et al. [31] propose rendezvous planning with a con-

strained ME path (RP-CP). Similar to RD-VT, the authors

consider a WSN with a fixed sink node and a ME. The RP-CP

first constructs a routing tree that is rooted at the sink node and

connects all sensor nodes. Then, each edge of the routing tree is

assigned a weight that corresponds to the number of nodes that

use that edge to forward their data to the sink node. The ME isrestricted to moving only on the edges of the tree. To construct

the MEs traveling path, RP-CP first sorts all edges according

to their weight. It then selects the edges with the highest weight

until the length of the selected edges becomes equal or less than

the required packet delivery time. The problem with RP-CP is

that the traveling path of the ME is restricted to routing tree

edges. This also means that the ME will visit the sensor nodes

on the selected edges twice.

In [31], the authors propose an improvement to RP-CP, which

is called the RP-UG algorithm. Initially, a geometric tree, which

is rooted at the fixed sink node, is constructed, and all edges on

the tree are split into multiple short intervals, which are denoted

as Lo. All points that join two edges with length Loare consid-ered RP candidates. RP-UG starts from the sinks position and,

in each step, adds the RP that minimizes the distance of sensor

nodes from selected RPs and also results in the shortest trav-

eling tour between RPs. RP-UG uses a TSP solver to calculate

the tour length. To finalize the tour, RP-UG replaces virtual RPs

with the closest sensor nodes and marks them as RPs. RP-UG

does not balance the energy consumption rate of sensor nodes,

which has a significant impact on network lifetime. Specifically,

the network lifetime is determined by the sensor node with the

highest energy consumption rate, e.g., n, assuming all nodeshave the same initial energy level. In this regard, RP-UG does

not aim to minimize the energy consumption rate of node n. Inaddition, when using RP-UG with a small Lovalue, the numberof RPs increases significantly, and the complexity of RP-UG

grows exponentially. The algorithm uses a TSP solverN timesin each iteration, where Nis the number of RPs. Hence, RP-UGhas a running time complexity ofO(N2 O(TSP)).

A CB algorithm is proposed in [32], in which a binary search

procedure is used to select RPs. Fig. 3 shows how CB works

in a network with ten nodes where the maximum allowed tour

length is 90 m. In the first iteration, using binary search on a

range from 0 to 10, CB selects five random cluster heads. In this

case, we have nodes 2, 3, 4, 5, and 7 [see Fig. 3(a)]. Other nodes

then establish a path to their closest cluster head in terms of hopcount. After the clusters are determined, CB starts from the sink

nodes position and selects one node from each cluster as an RP,

which is the closest node to the set of selected RPs. Fig. 3(b)

shows that node 8 fromcluster{7, 8},whichis theclosest node to

the sink, is selected as an RP and also node 6 from cluster {5, 6}

and so forth. Fig. 3(b) shows the final tour that have a length

of 127 m, which is larger than 90 m. Therefore, CB reduces the

number of clusters to two. According to Fig. 3(c), nodes 7 and 1

are selected randomly as new cluster heads. Fig. 3(d) shows that

the shortest possible tour between clusters is a tour including

nodes 2 and 9 that has a length of 55 m. CB therefore increases

the number of clusters to three because the tour length is less

than 90 m. Fig. 3(e) shows that nodes 4, 3, and 10 are selectedas new cluster heads, and the final tour length is 128 m, which is


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Fig. 3. Tour finding steps in CB.

larger than 90 m. This causes CB to reduce the number of

clusters to two again. However, given that, CB has already

found a tour for two clusters, it stops and outputs {2, 9} as

the final tour. Note that this tour does not pass through dense

parts of the network consisting of nodes with a larger number of

neighbors such as nodes 10, 6, and 7. This problem causes longdata forwarding paths from sensor nodes to the RPs and nonuni-

form energy depletion, which reduces the lifetime of the WSN.

C. Contributions of This Paper

In this paper, we propose a hybrid unconstrained movement

pattern for a mobile sink with the aim of balancing the energy

consumption of sensor nodes. Our approach makes the follow-

ing contributions, as compared with the work reported in the

literature.

We prefer nodes that have a high degree. This is critical as

sensor nodes in dense parts of a WSN generate the highestnumber of packets. Hence, giving priority to sensor nodes

in these parts during tour computation will help to reduce

congestion points, and in turn, reduces energy consump-

tion and improves WSN lifetime. In addition, it helps to

mitigate the energy-hole problem.

We consider hop distance between sensor nodes and RPs

as fewer hop counts reduce multihop transmissions. RP-

UG [31] minimizes network energy consumption by re-

ducing the physical distance between sensor nodes and

RPs. However, due to the existence of obstacles, physical

distance is not a reliable indicator of energy consumption.

Apart from node density and hop count, when using an

SMT, we use virtual RPs in the final tour to increaseperformance, and we do not replace them with real sensor

nodes. Replacing a virtual RP with a real sensor node in

RD-VT [33] and RP-UG [31] effectively approximates

an SMT with a shortest-path tree (SPT). We will show

through simulation that, when SMT is used and virtual

nodes are in the final tour, the energy consumption of

nodes can be reduced considerably, as compared with

using an SPT.

III. PROBLEM F ORMULATION

Let us consider a WSN in which sensor nodes generate data

packets periodically. Each data packet must be delivered to the

sink node within a given deadline. There is a mobile sink that

roams around a WSN to collect data from a set of RPs. The

objective is to determine the set of RPs and associated tour that

visits these RPs within the maximum allowed packet delay.

A. Assumptions

Before describingDEETP,we firstoutline someassumptions.

1) The communication time between the sink and sensor

nodes is negligible, as compared with the sink nodes

traveling time. Similarly, the delay due to multihop com-

munications including transmission, propagation, and

queuing delays is negligible with respect to the traveling

time of the mobile sink in a given round.

2) Each RP node has sufficient storage to buffer all sensed

data.

3) The sojourn time of the mobile sink at each RP is suffi-

cient to drain all stored data.

4) The mobile sink is aware of the location of each RP.5) All nodes are connected, and there are no isolated sensor

nodes.

6) Sensor nodes have a fixed data transmission range.

7) Each sensor node produces one data packet with the

length ofb bits in time intervalD.

B. Notation

We model a WSN as G(V, E), where Vis the set of homoge-neous sensor nodes, andEis the set of edges between nodes inV(see Table I for a summary of each notation). If sensor node

isendsb bits to nodej , its energy consumption is [23]

ETX(i, j) =b

1+ 2 di,j

(1)

where di,jis the physical distance between sensor node i andj,and1 is the energy consumption factor indicating the powerper bit incurred by the transmitting circuit. The expression

2di,j indicates the energy consumption of the amplifier per

bit, where2 is the energy consumption factor of the amplifiercircuit. Here,is the path-loss exponent, which usually rangesbetween 2 and 4, depending on the environment. Moreover, the

power consumption incurred by node i to receive b bits fromnodej is

ERX(i, j) =b (2)


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TABLE ISUMMARY OFN OTATION

where is a factor that represents the energy consumption perbit of the receiving circuit.

The mobile-sink node moves with a constant speed v. Hence,the maximum length of the traveled path l is

lmax= D v. (3)

A mobile-sink node starts its movement from a node m0Vand before timeD returns to its starting point. Each sensornode sends its generated data packets to the closest RP through

multihop transmissions. We define a function called H(i, M)that returns the closest RP in terms of hop count to the sensornodei, whereMis the set of RPs. Specifically

H(i, M) ={hi,mj | mk M, hi,mj hi,mk} (4)

wherehi,j is the hop distance between nodesi andj .For each RPmi, our algorithm constructs a data forwarding

tree Tmi comprising of the closest sensor nodes to said RP. Thenumber of data packets NFD(i) that sensor nodei forwards tothe closest RP mi in each time interval D is equal to its owngenerated data packet plus the number of its children in the data

forwarding treeTmi . Specifically

NFD(i) =C(i, Tmj ) +1 (5)

where C(i, Tmj ) is a function that returns the number ofchildren that node i has in the data forwarding tree rooted atits corresponding RPmj .

C. Delay-Aware Energy-Efficient Traveling Path

The objective is to find a tour M=m0

, m1

, m2

, . . . ,mn, m0, wheremi V, such that 1) the tour Mis not longerthan lmax, and 2) the energy consumption for sending senseddata from sensor nodes to the tour M, as defined by (ETX+ERX)

iVH(i, M), is minimized within time interval D.

DEETP is NP-hard by a reduction from TSP. Note that the

minimum energy consumption occurs when all sensor nodes

are designated as an RP. This is because they do not incur any

energy expenditure related to the forwarding of packets from

other nodes. In this case, the goal is then to determine whether

there is a tour that is not longer than lmax. Henceforth, in thefollowing, we propose a novel heuristic method to approximate

the optimal solution.

IV. WEIGHTEDR ENDEZVOUS P LANNING

WRP preferentially designates sensor nodes with the highest

weight as a RP. The weight of a sensor node is calculated by

multiplying the number of packets that it forwards by its hop

distance to the closest RP on the tour. Thus, the weight of sensor

nodei is calculated as

Wi= NFD(i) H(i, M). (6)

Based on (6), sensor nodes that are one hop away from an RP

and have one data packet buffered get the minimum weight.

Hence, sensor nodes that are farther away from the selectedRPs or have more than one packet in their buffer have a higher

priority of being recruited as an RP.

From (1) and (2), the energy consumption is proportional

to the hop count between source and destination nodes, and

the number of forwarded data packets. Hence, visiting the

highest weighted node will reduce the number of multihop

transmissions and thereby minimizes the energy consumption.

In addition, as dense areas give rise to congestion points due to

the higher number of nodes, energy holes are more likely to oc-

cur in these areas. Hence, a mobile sink that preferentially visits

these areas will prevent energy holes from forming in a WSN.

Algorithm 1 shows how WRP works. It takes as inputG(V, E), and it outputs a set of RPs. WRP first adds the fixedsink node as the first RP (see line 6). Then, in lines 917, it

adds the highest weighted sensor node. After that, WRP calls

TSP() (see line 21) to calculate the cost of the tour. If the tourlength is less than the required length lmax, the selected nodefrom lines 917 remains as an RP (see lines 2232). Otherwise,

it is removed from the tour (see lines 3337).

After a sensor node is added as an RP, WRP removes those

RPs from the tour that no longer receives any data packets

from sensor nodes(see lines 2730). This is because adding a

sensor node to the tour may reduce the number of data packets

directed to these RPs. Consequently, this step affords WRP

more opportunities to add other nodes into the tour. Note thatthe variable removed is used to guarantee that an RP will be


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deleted from the tour only once. If a removed RP is added to

the tour for the second time, because its corresponding variable

removed is true, it will not be removed from the tour again.

In this way, all sensor nodes will be added to the tour when the

required tour length for a mobile sink is bigger than the time to

visit all sensor nodes.

Fig. 4 shows an example of how WRP finds a traveling tour

for a mobile sink. The maximum tour length islmax= 90 m.WRP starts from the sink node and adds it to the tour, i.e., M=[Sink]. Then, an SPT rooted at the sink node is constructed

[see Fig. 4(a)]. In the first iteration, WRP adds node 10 to thetour because it has the highest weight, yielding M= [Sink, 10].

Fig. 4. Example of WRP operating in a WSN with ten nodes.

As Fig. 4(b) shows, the tour length of M is smaller thanthe required tour length (56< 90), meaning node 10 staysin the final tour (lines 2232). In the second iteration, WRP

recalculates the weight of sensor nodes because node 10 is now

part of the tour. In this iteration, WRP selects node 6 as the

next RP, which has the highest weight. As Fig. 4(c) shows, the

tour length ofM= [Sink, 10, 6]is larger than the required tourlength(119> 90). Consequently, WRP removes node 6 fromthe tour M = [Sink, 10](lines 3337). In the third iteration, theweight of sensor nodes will not change because node 6 is not

selected as an RP but it stays marked and will not be selected.

WRP selects node 8 because it has the highest weight and is

not marked [see Fig. 4(d)]. The TSP function returns 76 m for

M = [Sink, 10, 8], which is less than 90 m. Therefore, node 8is added to the tour. The process continues, yielding a final tour

ofM= [Sink, 8, 7, 10, 9] with a tour length of 81 m, which isless than the required tour length [see Fig. 4(e)].

As shown in Fig. 4, the final tour computed by WRP always

includes sensor nodes that have more data packets to forwardthan other nodes as RPs. This ensures uniform energy con-

sumption and mitigates the energy-hole problem. This is the key

advantage of WRP over CB, RD-VT, and RP-UG. In Section V,

we will show that this feature of WRP allows it to save 30%

more energy than CB.

A. Analysis

The time complexity of our algorithm is dependent on how

many times WRP calls the TSP solver to calculate a tour that

visits all RPs. The worst case is when all sensor nodes are

marked but not selected as an RP, which means WRP will iterate

for |V| times to check the possibility of adding nodes into a tour.After a node is selected as an RP, WRP again unmarks other


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sensor nodes and restarts the search process (see lines 1237).

This means our algorithm uses the TSP solver for a maximum

of n2 times, where n= |V|. Therefore, the time complexityof WRP is O(n2 O(TSP)). Hence, if we use Christofidessheuristic [39], which has time complexity ofO(n3), the result-ing time complexity is O(n5). In our experiments, we used a

local-search-based heuristic TSP solver [40].We like to point out that WRP always finds a tour when there

is at least one possible tour in the network. This is because

WRP checks the possibility of adding all sensor nodes to the

tour. This is significant when compared with CB and RD-VT

because the latter two algorithms fail in the following scenario.

In CB, if the only possible tour consists of only the sink and a

neighbor in the same cluster, CB will not be able to find this tour

because two sensor nodes from the same cluster cannot be in the

final tour. As for RD-VT, it will return no tour if the distance

of the first sensor node in the SMT, as it starts its depth-first

traversal, exceedslmax.We now prove that visiting the most weighted nodes by a mo-

bile sink results in the least energy consumption, as compared

with visiting any other nodes.

Theorem 1: Visiting sensor nodePwith weightwp reducesenergy consumption more than visiting sensor node Q withweightwq , wherewp> wq .

Proof: Recall that sensor node P forwards NFD(P) datapackets to its closest RP. Therefore, the energy consumption of

sensor nodes on the path from nodePto the closest RP is

Ep= (ETX+ ERX)(NFD(P) H(P, M)) . (7)

However, if sensor node P becomes an RP, the energy con-sumption incurred by data packets at

Pis zero. Similarly, for

sensor node Q that forwards NFD(Q)data packets to its closestRP, we have

Eq = (ETX+ ERX)(NFD(Q) H(Q, M)) . (8)

From (6), the weight of sensor node P iswp= NFD(P)H(P, M), and the weight of sensor node Q is wq =NFD(Q)H(Q, M). We know that wp> wq; therefore, it can be con-cluded thatEp> Eq , which means selecting sensor node P asan RP, which has a higher weight thanQ, leads to less networkenergy consumption.

We now show the difference between WRP and the optimal

solution. We first prove the following lemma.Lemma 1: Let WRPop be a version of WRP that uses an

optimal TSP solver. If there is an optimal tour namedC withlength Lc lmax comprising of all sensor nodes as RP, thenWRPopis guaranteed to find tourC.

Proof: Assume there are n sensor nodes in a WSN andtour C=m0, m1, m2, . . . , mn, m0, where m0is the sink node.Then

Lc=n10

dmi,mi+1+ dmn,m0 . (9)

WRPop, after picking the sink, will select node mi=1 to

include in the tour as it has the highest weight before runningTSP() (see line 21 of Algorithm 1). The returned cost will be

less than Lc as the tour connecting the set of nodes cannotbe longer than the tour containing all nodes by the triangle

inequality. Hence, WRPop will add mi=2 and so forth untili= n. WRPopthen terminates asTn= |V|.

Note that, in Lemma 1, the requirement on there being an

optimal TSP solver can be relaxed if we assume that|E|i=0 i

lmax. In other words, the sum of all distances between nodes isless than the required tour length.

Note that, intuitively, it would seem that the maximum differ-

ence in energy consumption occurs when the final tour returned

by WRPop is not composed of any sensor nodes while the

optimal tour visits all sensor nodes. However, as per Lemma 1,

this will not happen.

Theorem 2: Assume a sensor node Pthat has the longest hopdistance from the sink, and the average hop distance between

sensor nodes and the sink is k ; then, the maximum differencebetween the network energy consumption of WRPop and the

optimal is within((2 K(|V| 1) +1)/(|V|+2)).Proof: The network energy consumption when the mobile

sink visits only sensor node P is

ENetwork(p)= (ETX+ ETX((|V| 1) k))

+ (ERX((|V| 1) k)) . (10)

On the other hand, the minimum amount of energy consumed

by visiting all sensor nodes except node P is

ENetwork(|V|1)= ETX(|V|+1) + ERX. (11)

This means sensor node P has to send all its data packetsto the closest RP, whereas other sensor nodes send their data

packets directly to the mobile sink. From (10) and (11), the ratio

of energy consumption in WRP in comparison to the optimal

model is

Ratio

= ETX(1+ (|V| 1) k) + ERX((|V| 1) k)

ETX(|V|+1) + ERX.

(12)

If we considerETX=ERX, (12) is equal to

Ratio= 2 K(|V| 1) +1

|V|+2 . (13)

V. EVALUATION

We compare WRP against three existing methods that have

the same objective as ours, namely CB, RD-VT, and RP-UG,

using a custom simulator written in C++.1 We consider a

connected WSN where nodes are placed uniformly on a sen-

sor field of size 200200 m2. We note that interconnectingdisconnected sensor nodes using a mobile node is a well-

known and separate problem. Having said that, we remark that

WRP can be also made to interconnect disconnected nodes if

the required delivery time for data packets is greater than the

1Our simulator is available upon request.


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TABLE IISIMULATION PARAMETERS

shortest traveling tour to visit all sensor nodes. The reason that

we have assumed uniform sensor-node distribution is because

energy holes are more likely to form when nodes are distributed

uniformly [41]. Experimental results in [13] demonstrated that,

if sensor nodes are distributed uniformly, up to 90% of residual

energy is unused when the first sensor node dies. In addition,

we adopt uniform distribution to ensure fair comparison withRD-VT, CB, and RP-UG.

Similar to [42], we have set the radio parameters as per the

CC1000 radio, which is used by Mica2 Motes [43]. Each sensor

node generates one data packet every T time, which is thenforwarded to an RP via an SPT. We assume nodes are aware of

the mobile sinks movement and, hence, arrival time. We record

and compare the network energy consumption every T time.Moreover, there are a maximum of 200 sensor nodes, which

is reasonable for most applications (see [44, Tab. I]).

To measure network lifetime, we assume that all sensor

nodes have a fully charged battery with 100 J of energy. Other

parameters are summarized in Table II. We set the mobile sinksspeed to 1 m/s. We further assume that it visits each RP. Given

a transmission range of 20 m, which is feasible for Mica2 [43]

or TelosB [45] nodes, the mobile sink will be in a sensor nodes

transmission range for 20 s. Assuming a data transmission rate

of 40 Kb/s, each sensor node will be able to send 3413 data

packets with a length of 30 b to the mobile sink in 20 s. This

means that the mobile sink has sufficient time to drain the buffer

of all sensor nodes even when there are 200 sensor nodes. To

reduce the run time of RP-UG, we set L0 to 20 m, whichcorresponds to the transmission range of sensor nodes.

We use standard deviation (SD) to measure the imbalance

between the energy consumption of sensor nodes, i.e., a wide

variation means some parts of a WSN is likely to exhaust its

energy sooner. The metric SD is calculated as follows:

SD=

iV (EN[i] )

2

|V| (14)

where EN[i] is the energy consumption of node i,V is the setof sensor nodes, and is the average energy consumption ofsensor nodes.

In our evaluation, we consider two scenarios involving an

SPT and an SMT for the RD-VT model: RP-UG and WRP.

In WRP, we find the Steiner points and treat them as real

nodes. This means that Steiner points have a weight and arenot replaced with real sensor nodes in the final tour.

Fig. 5. Network energy consumption between brute force and WRP.

Two sets of experiments are carried out. Initially, the numberof nodes is limited to 20, and WRP is compared against a brute-

force approach that yields the optimal tour with 2.5 min as

the required tour length. In the second experiment, the number

of nodes is increased to 200, and WRP is compared against

RD-VT and CB with 5 min as the required tour length. In all

experiments, we designate the node with the highest ID as the

sink node, and the results are an average of ten simulation runs

over different topologies.

A. Performance Under SPT

Fig. 5 shows the energy consumption of sensor nodes forWRP versus brute force. Both algorithms yield higher energy

consumption when the number of sensor nodes increases as

the length of data forwarding paths from sensor nodes to RPs

increases. The energy consumption of WRP is very close to

the brute-force approach. In particular, brute force only outper-

forms WRP by 5%.

Fig. 6 shows the difference, as per SD, between sensor nodes

energy consumption. A small SD value means uniform energy

consumption and longer network lifetime. The performance of

WRP is only 16% less than the optimal or brute-force approach.

This is because, in WRP, sensor nodes that forward more

data packets and cause more multihop transmissions than othersensor nodes are likely to be designated as an RP.

Fig. 7 shows the energy consumption for WRP, CB, RD-

VT, and RP-UG with a large number of sensor nodes. RD-

VT leads to the highest energy consumption because of its

preorder traversal of the SPT and long data forwarding paths

from sensor nodes to the RPs. WRP recorded 47% reduction in

energy consumption, as compared with RD-VT. CB has better

performance than RD-VT because, in its finalization process, if

the required delivery time is not violated, it replaces the selected

RP in each cluster with a node closer to the cluster head to re-

duce the number of multihop transmissions. CBs performance

is 28% better than RD-VT in terms of energy consumption.

Recall that in Section II-B2, CB does not consider node densityor hop counts when selecting RPs. As a result, WRP achieves


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Fig. 6. Standard deviation of sensor nodes energy consumption.

Fig. 7. Network energy consumption for WRP, CB, RD-VT, and RP-UG.

a 10% reduction in energy consumption, as compared with CB.

RP-UG and WRP have nearly the same performance; WRP

reduces energy consumption by an additional 6%, as compared

with RP-UG.

The ability of the four algorithms to uniformly distribute

energy consumption is shown in Figs. 8 and 9. WRP distributesenergy more uniformly than the other approaches, specifically,

12% more than RP-UG, 28% more than CB, and 53% better

than RD-VT. Similarly, RP-UG does not aim to balance the

energy consumption rate of sensor nodes. RP-UG adds sensor

nodes that are close to the sink as RPs, which may not nec-

essarily have the highest energy consumption rate. Moreover,

although RP-UG considers nodes that are on many routing

paths, WRP preferentially selects nodes with high energy con-

sumption rate and hop count from the sink. As shown in Fig. 9,

WRP improves network lifetime by 13%, as compared with RP-

UG. With regard to CB, as shown in Fig. 3, the random cluster-

head selection process causes nonuniform energy consumption.

Moreover, two sensor nodes from the same cluster cannot be inthe final tour. Hence, when there are a large number of sensor

Fig. 8. Standard deviation of sensor nodes energy consumption for WRP,CB, RD-VT, and RP-UG models.

Fig. 9. Network lifetime for WRP, CB, RD-VT, and RP-UG.

nodes, energy holes are likely to occur around the RP for a

given cluster. In contrast, WRP avoids this scenario by having

the mobile sink visits dense parts of a WSN, which helps to

reduce the number of multihop transmissions. In RD-VT, long

forwarding paths are observed from sensor nodes to RPs, which

results in nonuniform energy consumption and 25% reductionin network lifetime, as compared with CB.

In this experiment, we simulated the algorithms in a network

with 110 sensor nodes and data packets with a packet delivery

time ranging from 100 to 300 s. Figs. 10 and 11 show network

energy consumption and network lifetime for WRP, CB, RD-

VT, and RP-UG. Consistent with the result shown in Fig. 7,

WRP yields the best performance among all algorithms. The

energy consumption for RD-VT reduces by 21% when the

required packet delivery time is changed from 100 to 300 s,

whereas WRP, RP-UG, and CB observed a reduction of 41%,

33%, and 37%, respectively. WRP observed a superior perfor-

mance, as compared with other algorithms, even with small

packet delivery times. This is because WRP always checks thepossibility of adding the node with the highest weight first.


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Fig. 10. Network energy consumption for WRP, CB, RD-VT, and RP-UGunder different required delivery times for data packets.

Fig. 11. Network lifetime for WRP, CB, RD-VT, and RP-UG under different

required delivery times for data packets.

Finally, we recorded the simulation time of each algorithm

(see Fig. 12). For RP-UG, we set L0= 20 m, i.e., the transmis-sion range of sensor nodes. The value of 20 m is the maximum

possible for L0 because otherwise, edges bigger than L0 aresplit into edges with length L

0. Virtual nodes are then added

as necessary to connect these new edges. Consequently, this

process, depending on the value of L0, increases run timesignificantly. In fact, even with L0 set to 20 m, the runningtime of RP-UG is six times bigger than WRP, 36 times more

than CB, and 72 times longer than RD-VT. This is because,

in each iteration, RP-UG calculates the utility of each sensor

node by calling a TSP solver. RD-VT has the lowest run-

ning time because it only calls the TSP solver once in each

iteration.

B. Performance Under SMT

We have also considered using the SMT for RP-UG, RD-VT, and WRP; this tree is constructed using the function in

Fig. 12. Simulation time for WRP, CB, RD-VT, and RP-UG.

[46]. Specifically, the Steiner tree function uses the principal

of an equilateral triangle, a circle, and a line to construct a

Steiner point for a set containing three points on the minimum

spanning tree (MST). When an SMT is formed, there are two

types of Steiner points. The first type corresponds to real sensor

nodes, which are called real Steiner points, and the other type

is simply a physical position with no sensor nodes, which are

called virtual Steiner points.

For each Steiner point in WRP, a neighbor set is assigned

after the formation of the SMT. In RP-UG, RD-VT, and WRP,

virtual Steiner points that are not in the final tour are deleted

from the SMT. On the other hand, we handle virtual Steiner

points that are part of a tour in the following manner. In RD-VTand RP-UG, virtual RPs are replaced with the closest physical

sensor nodes. In WRP, when a sensor node notices that the

succeeding hop destination for its data packets is a virtual RP,

the sensor node stores its data until the mobile sink arrives at the

virtual RPs position. Upon arrival, the sensor node forwards its

data to the mobile sink.

Fig. 13 shows a comparison between WRP, RP-UG, RD-VT,

and CB when the SMT is used for data forwarding. The results

show that the SMT has a better performance than the SPT. This

is because a Steiner point is the shortest interconnection point

between neighboring nodes. As a result, the total length of the

SMT in comparison to the SPT is shorter. This causes RD-VT-SMT and RP-UG-SMT to visit more RPs, and causes nodes

to have 29% and 8% less energy consumption than RD-VT-

SPT and RP-UG-SPT, respectively. Moreover, RD-VT-SMT

outperforms CB. For the same reason, WRP-SMT conserves

13% more energy than WRP-SPT and 22% more than CB.

Moreover, WRP has 24% better performance than RD-VT and

14% better performance than RP-UG when they all use the

SMT. This is because WRP does not replace virtual RPs with

the closest physical sensor nodes. Instead, as stated previously,

a mobile sink is programmed to visit virtual RP positions and

to collect data from nearby sensor nodes.

Figs. 14 and 15 show the difference between the energy

consumption of sensor nodes and the network lifetime for SMTexperiments. In particular, the SD recorded is less than those


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Fig. 13. Network energy consumption for WRP, CB, RD-VT, and RP-UG inSMT scenarios.

Fig. 14. Standard deviation of sensor nodes energy consumption in SMTscenarios.

Fig. 15. Network lifetime for WRP, CB, RD-VT, and RP-UG in SMTscenarios.

when using the SPT. This is because virtual Steiner points,

which are in the final tour, do not receive data from other sensor

nodes. Instead, these points are visited by the mobile sink. In

comparison, when we use the SPT, RPs have a higher energy

consumption, as compared with other sensor nodes. However,

for the SMT case, when virtual points are in the final tour, we

observe fewer RPs; thus, actual nodes that act as RPs reducesand thereby reduces consumed energy. Moreover, the energy

consumption between sensor nodes is distributed uniformly.

For these reasons, the SD for WRP-SMT is 16% less than

WRP-SPT and 39% less than CB (see Fig. 14). The SD for RD-

VT-SMT is 28% less than RD-VT-SPT, and for RP-UG-SMT,

it is 5% less than RP-UG-SPT. This is because visiting more

RPs leads to shorter data forwarding paths and, thereby, better

network lifetime. The difference between the SD of WRP-SMT

and RD-VT-SMT is 44%, and between WRP-SMT and RP-UG-

SMT, it is 22%, which is less than the results recorded in SPT

experiments. This thus confirms that the better performance

gained by WRP in the SMT scenario is due to the use of

virtual RPs.

VI. CONCLUSION

In this paper, we have presented WRP, which is a novel algo-

rithm for controlling the movement of a mobile sink in a WSN.

WRP selects the set of RPs such that the energy expenditure of

sensor nodes is minimized and uniform to prevent the formation

of energy holes while ensuring sensed data are collected on

time. In addition, we have also extended WRP to use an SPT

and an SMT. Apart from that, we have also considered visiting

virtual nodes to take advantage of wireless coverage. Our re-

sults, which are obtained via computer simulation, indicate that

WRP-SMT reduces the energy consumption of tested WSNs by

22% in comparison to CB. We also benchmarked WRP against

existing schemes in terms of the difference between sensor-

node energy consumption. Our simulation results show that

WRP uniformly distributes energy consumption by 39% and

44% better than CB and RD-VT, respectively.

As a future work, we plan to enhance our approach to include

data with different delay requirements. This means a mobile

sink is required to visit some sensor nodes or parts of a WSN

more frequently than others while ensuring that energy usage is

minimized, and all data are collected within a given deadline.

Moreover, we plan to extend WRP to the multiple mobilesinks/rovers case. This case, however, is nontrivial as it involves

subproblems such as interference and coordination between

rovers. Having said that, we note that WRP remains applicable

if a large WSN is partitioned into smaller areas where each

area is assigned a mobile sink. WRP can be thus run in each

area. We defer the evaluation of such an approach to a future

paper.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for pro-

viding constructive comments that have improved this papersignificantly.


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Hamidreza Salarian received the B.S. degreein computer engineering (hardware major) from

Ferdowsi University of Mashhad, Mashhad, Iran, in2005 and the M.S. degree in computer architecturefrom Isfahan University of Technology, Isfahan, Iran,in 2008. He is currently working toward the Ph.D.degree with the School of Electrical, Computer,and Telecommunications Engineering, University of

Wollongong, Wollongong, Australia.His research interests include energy consumption

in wireless sensor networks and wireless sensor actu-ator networks, particularly the effect of mobility in increasing system lifetime.

Kwan-Wu Chinreceived the B.S. degree (with firstclass honors) and the Ph.D. degree (with distinctionand the vice chancellors commendation) from theCurtin University of Technology, Perth, Australia.

He then joined Motorola Research Laboratory asa Senior Research Engineer, where he developedzero-configuration home networking protocols anddesigned new medium-access-control protocols forwireless sensor networks. Since 2004, he has beenwith the University of Wollongong, Wollongong,Australia, first as a Senior Lecturer and then pro-

moted as an Associate Professor in 2011. He is a holder of four U.S. patents and

the author of more than 65 articles in numerous conferences and journals. Hiscurrent research interests include medium-access-control protocols for wirelessnetworks, routing protocols for delay-tolerant networks, radio-frequency iden-tification anticollision protocols, and discrete optimization problems related tocomputer communications.

Fazel Naghdy was born in Tehran, Iran. He receivedthe B.Sc. degree from Tehran University in 1976;

the M.Sc. and Ph.D. degrees from the University ofBradford, Bradford, U.K., in 1972 and 1982, respec-tively; and the M.Edu. degree from the University ofWollongong, Wollongong, Australia.

He has a demonstrated track record and lead-ership in research, teaching, and management. He

is currently a Professor of robotics and intelligentsystems and the Director of the Center for IntelligentMechatronics Research with the University of Wol-

longong. He is the author of more than 250 papers in international journalsand conferences and several book chapters. His research has had its focuson machine intelligence and control, particularly in embedded mechatronicsand robotics systems. His current research interests include haptically renderedvirtual manipulation of clinical and mechanical systems and intelligent control

and learning in nonlinear and nonstructured systems.Dr. Naghdy has served on a large number of international scientific com-

mittees of various international conferences. He is a Contributing Editorto the IEEE TRANSACTIONS ON MECHATRONICS ENGINEERING and the

International Journal of Intelligent Automation and Soft Computing.

an energy efficient mobile sink path selection.pdf

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