In wireless sensor networks, a large number of nodes are [631251]

1
Abstract

In wireless sensor networks, a large number of nodes are
dispersed in a region for monitoring purpose and the ba se
station (BS) is used to collect the observations of the nodes.
As the batteries of the nodes are limited and non –
rechargeable, the use of node’s power must be in an
energy -efficient manner to prolong the network lifetime.
For this purpose, many approach es have been p resented
for saving the energy and most of the approaches are based
on the clustered architecture. Some researchers have
mentioned the mobile BS as a way to reduce the energy
consumption and used some rendezvous points (RNs) to
store the data for the mobile BS. This work ’s aim is to
provide a new approach which will increase the network
lifetime b y using clustering, mobile BS, and RNs
collectively. The simulation results show that the proposed
scheme increases the network lifetime as compared to the
LEACH (using static BS) and the Optimizing LEACH
(using mobile BS and RNs) protocols, especially for the
large scale WSNs.
Keywords: Rendezvous nodes, LEACH, mobile BS, Wireless
sensor networks (WSNs).

I. Introduction
Wireless sensor networks (WS Ns) have been widely employed
in many applications such as monitoring war territories, sea
searching and tide monitoring, patient monitoring and disease
analysis. A WSN inheres a large number of tiny embedded
(sensor nodes) devices with sensing, low powe r, limited
memory and transmission capabilities [1]. Placement of these
nodes is generally random and without planning. In such
circumstances, nodes must be self -configurable to
communicate with the whole network. Nodes are usually
deployed in a natural en vironment and are vulnerable to harm.
The disablement of the sensor nodes due to such harm turns to
change in the network topology regularly. A WSN uses a
base station (BS) to gather the observations of the nodes. The
BS aggregate the data and send it to the end user for the further
processing. Each node is able to send it s data using a single hop
[2]. But long distance transmission requires more energy as
compared to the shor t distance transmission. Therefore , the
small distance transmission can save the energy and the
lifetime of the network can be increased . A multi -hop
transmission is utilized to reduce the distance, where each node
transmits its data to a neighboring node who is one hop near to
the base station. This method exhausts the energy of those
nodes quickly, which are situated near to the sink and reduce
the network lifetime.
The clustering is another method to limit the energy
consumption. In this method, cluster head (CH) receives data
from its member nodes and transmit the collected data to the
BS. Clustering provides network scalability, resource A New Clustering Approach for Increasing Network
Lifetime of a WSN with Mobile BS and Rendezvous
Nodes



apportion ing and efficient use of limited resources that grant
stable network topology and energy – saving aspects [3]. This
method offers the reduced communication overhead and
effective resourc e sharing, thus results in lower energy
consumption.
Recent studies have proven the relevancy of the mobile sink
(BS) for receiving the data from the nodes as compared to the
multi -hop transfer to a base station [4]. The motion of the BS
may be controlled or uncontrolled in a given trajectory or BS
may also move randomly in the network. A mobile BS can
collect data directly from all the nodes which are situated 1 -hop
away from the trajectory of the mobile BS or with reduced
hops if nodes are situated furth er. This method avoids long
distance transmissions and minimizes the energy consumption
of the nodes situated close to the BS [5 -7]. But in the mobile
BS method, BS has to update all the nodes regarding its current
position and this process consumes high e nergy.
Since a WSN composes many nodes in the sensing field and
hence it is not possible for mobile sink to entertain each node
separately in a dedicated time. Therefore, an idea has been
presented, which is known as rendezvous points (RPs). The
RPs are th ose points (nodes) in the network, which are close to
the trajectory of the mobile BS. Nodes which are situated far
away from the trajectory communicate their data to the RPs
(close to it), The RPs wait for the BS arrival to their regions and
when the BS p asses over to it they hand over all the data [8 -9].
This method has proposed the RPs near the trajectory and
hence the nodes situated far apart from the trajectory have to
transmit their data through a long multi -hop path. Therefore,
energy consumption in such transmissions is higher . The
literature studies show that the clustering methods, mobile BS
and RPs have significantly improved the network lifetime,
overall energy consumption and reporting delay in the WSNs.
The presented research has focused to fi ll the above discussed
gaps along with improved network lifetime and reporting delay
using proposed clustering, RP selection and routing method.
This paper is organized as follows: In section 2 related work is
discussed. The system model and detail of the proposed
approach is given in the section 3. Simulation results are
discussed in the section 4 and section 5 concludes the paper.

II. Related Work
The limited power of the nodes makes it essential that the
power of the each node must be utilized in an eff icient way. For
this purpose, many researchers have been proposed different
methods for saving the power. But clustering is the most
popular technique in the WSNs. The concept of the clustering
is introduced in [10] by introducing low energy adaptive
clustering hierarchy (LEACH) protocol. In LEACH, network
is divided into many small parts and a leader (cluster head) is
selected for each part. The remaining nodes in each region
transmit their data to a CH and the CHs are responsible for
transmitting the data to BS. This method reduces the number of
transmissions towards the BS and hence it reduces the total energy consumption in the network. Selection of the CHs is a
random process and hence the selected CHs may be close to
each other (CHs are not uniform) an d hence many regions may
have to spend more energy to transmit their data to the CH.
This type of cluster formation increases the inter -cluster energy
consumption. The TL -LEACH provides two CH layers to
reduce the inter -cluster energy consumption [11]. The EECS
protocol r enders a balanced distribution of the CHs in the
network [12]. In EECS, many nodes assume themselves as CH
candidates and advertise this information to other nodes. Now
each CH candidate compares its residual energy with the newly
announced CH candidate’s residual energy. If the new CH
candidate has high residual energy than the other candidates, it
considers itself as a CH. Non -CHs nodes select a CH which is
closer to them for transmitting their data and the selected CH
must have the minimu m distance from the BS than other CHs.
The HEED protocol chooses the CHs on the basis of the
residual energy and the minimum power for its member nodes
to transmit their data to the corresponding CH [13]. SEECH
protocol provides uniform CHs throughout the network and
control the inter -cluster energy by reducing the distance
between the CHs and the member nodes [14]. SEECH selects
CHs on the basis of residual energy and the number of
neighboring nodes. The CH candidate who has the residual
energy greater tha n a threshold value and maximum
neighboring nodes is considered as the first CH. Next
candidates are also selected with the same procedure. SEECH
also provides the total number of CHs required to complete the
task in an energy efficient way.
The mobile BS method is also highlighted in the WSNs for
saving the energy. A static BS overloads the nodes with high
volume data those are situated close to it. A mobile BS is able
to distribute the traffic uniformly in the network and enhances
the network lifetime [5 -7,15-17]. The mobile BS may
approach each node and gather its data [2] or may approach
only selected locations of the network and the nodes situated in
the nearby region send their data using multi -hop transmission
towards mobile BS [18]. However, the firs t solution provides
direct (one -hop) data collection and save energy. But the time
required for data collection from all the nodes is very large. In
the second solution, the time required for the data collection is
reduced, but energy consumption is higher due to multi -hop
data transmission. An alternative method is that the nodes send
their data to some nodes (RPs) which store the data and wait
for the BS arrival to the nearby region. When BS comes to its
communicating range the RPs will hand over all the stored data
[19-20] or when RPs get a query from the BS about the stored
data.
The above mentioned techniques wait for the mobile BS tour
for their data transmission. In such situations, the data reporting
time is large, because until the BS reaches to the RPs region,
the data is only stored in the RPs and not handed over to the
mobile BS. Additionally, most of the studies did not mention
the time span when RPs and mobile are in their
communicating range and this time is sufficient for RPs to
hand over all the data to BS or not. The storing capacity of the

3
RPs (nodes) is also an important issue, because data may be
overflows if mobile BS does not pass through the RPs region
for a long time.
In the proposed technique, the RPs are only used for storing the
mobile BS position and they are connected with the CHs to
update them regularly about the mobile BS position. Now CHs
can send their data directly to mobile BS using multi -hop
transmission. This technique is found to be energy -efficient and
enhances the netw ork lifetime with different node densities.

III. System Model
A large number of static sensor nodes are randomly deployed
in a defined area (Figure1) . All nodes are homogenous with
unique ID number and a BS is supposed to move in the middle
of the network are a. We consider some assumptions for the
successful working the proposed method and they are given
below:
a. The energy of the BS is assumed to infinite.
b. It is also supposed that the positions of the nodes and
BS can be calculated for each round.
c. Nodes are a ble to adjust their transmitting powers
according to the destination distance.
d. The links are supposed to be symmetric and the nodes can
estimate their distance from the neighboring nodes by
using received signal strength if the transmitting power
of the no de is known.
In this paper, a basic energy model [21] is used to calculate the
energy consumption while sending (E tx)/receiving ( Erx) per bits
(l) of messages to a distance d meter (refer equations (1) and
(2)).

2
4elec f
Tx
elec mlE l d
E
lE l d
 (1)

rx elecE lE (2)
Based on the distance between sending node and receiving
node, free space ( ɛf) or multipath fading ( ɛm) channel model are
used. The electronic energy E elec is used to perform digital
coding and modulation techniques. λ is a threshold distance.
We consider that the information collected by a CH is highly
correlated hence CH s perform data aggregation operation and
then transmit the data to the BS. It is assumed data CH
consumes E DA (nJ/bit/signal) energy for the data aggregation.
1. The Proposed Model
The operation of the proposed model is divided into many
phases like LEACH. Each node prod uces data with equal
frequency and transmits once in every round. Each round
initiates with t he setup phase and pursues with a steady -state
phase. The setup phase is further divided into three stages. In the first stage, cluster heads (CHs) and rendezvous nodes
(RNs) are specified. In the second stage, clusters are formed
and next stage includes g eneration of the TDMA schedule for
the member nodes of the CHs so that they can send their data
in a non -conflicted way. The second phase of the model
includes the data transmission between CHs and mobile BS.

A. Selection of the Rendezvous nodes (RNs)
Initially, each node is considered as an ordinary node (ON) and
all nodes check the ir eligibility to become a RN. If the node
fulfills the eligibility criteria, it can label itself RN. The nodes
which are labeled as RN will not participate in the cluster he ad
(CH) selection process. The selection of the RN must be near
the trajectory and the condition to become the RN is given in
the equation (3).

max max1 (1 )22x i xyyP y P    (3)
Where, y max is the width of the network area and y i is the
position of the i -th node in y direction. P x is a constant value
less than 1.

B. Selection of Cluster Heads (CHs) and Clusters
After the RNs node selection, each node calculate its two -hops
neighboring nodes and also calculate the weight of the each
node. Ea ch node broadcast a message which includes its ID
number, residual energy (E res) and a TTL (time to live) value.
The TTL is set to value 2 in the beginning. The TTL value is
decremented by one when the message is received by a
neighboring node and this nod e further transmits the packet to
its neighboring node if TTL value does not reach 0. The node
who has received the message with TTL value 0, it doesn’t
forward the message. Thus, the TTL message will only be
broadcasted within two -hops neighboring nodes.
After broadcasting, each node counts its 1 -hop (H 1) and 2 -hop
(H2) neighboring nodes. Meanwhile, a node (i) can calculate
the average residual energy of its 1 -hop neighboring nodes
using equation (4).

1
1 1
1H
reshop
iE
EH (4)
The weight of the each node can be calculated using equation
(5).

1
2 /H
i i i iW H E E Z   (5)
Ei represents the residual energy of the node i, and Z i represents
its distance from the BS which can be determined by its
coordinates.
Each node share its weight information with the 1 -hop and 2 –
hop neighboring nodes. Now each node forms a list of weights d ≥ λ
d ≤ λ

of its 2 -hop neighboring nodes. Each node checks the list and
compare its weight with the available information. The node
who found that its weight is highest among 2 -hop neighbors,
that node will announce itself a CH and broadcast this
information to 2 -hop neighboring nodes with a TTL value 2.
This procedure is followed to select all CHs (Figure 2) . Only 2 –
hop neighboring nodes are involve d in the CH selection
procedure, because it had been demonstrated that in order to
make a tradeoff between energy saving and data gathering
latency, relay hops should be obliged to small level (2 or 3)
[22].
All selected CHs broadcast their roles in th e network and then
all nodes (including RN nodes) aware about the CHs with their
position s. This message is also received by all the CHs and
they also get the information of about other CHs present in the
network. Now each CH estimate its distance from the
remaining CHs. The nodes which are situated within the 2 –
hops region of the CH becomes its member nodes by sending a
joining request. The CH rep lies to each member node with a
message with TDMA slot information for data transmission.
C. Updating Mobile BS Position by the CHs through RN
nodes
After receiving the broadcast messages from the CHs, each RN
node acknowledges to the CHs with a message which include
ID number, residual energy and role in the network. The RN
node which is closer to the mobile BS send a BS location
information to each CH when a new round is started for the
data collection.
D. Data T ransmission
After the CHs have been generated and the TDMA schedule is
confirmed, the data transmission may begin. It is assumed that
all nodes generate data with equal rate and send once in each
round to the respective CH during the assigned time slot. The
CHs gather data from all the member nodes and aggregated it
to reduce the number of transmissions towards the BS. Then
CH can relay data to a cluster head (CH) which is one hop
closer to the BS or it can directly relay data to the BS if it is in
the range of the BS. The CHs are not allowed to relay their data
to RN nodes because the energy of the RN nodes is only
reserved for circulating the mobile BS position updates in the
network.

IV. Simulation Results
1. Simulation setup and parameters
The various parameters used for conducting the simulation are
stated in Table 2 . The network consists of 100 nodes and they
are randomly dispersed in the sensing area s (150 m×150 m,
250 m×250 m, 350 m×350 m and 450 m×450 m). Initially the
BS is placed at x = 0 and y = (y max/2 ) where y max is the width
of the network. The BS moves in the x direction. The BS is
supposed to return the initial position after 100 rounds for all
network sizes. The simulation work is conducted in the MA TLAB tool. The simulation is conducted 20 times to
analyze each case and results are averaged to reduce the effect
of the randomized network.
2. Performance metrics
The various metrics used to eval uate the performance of the
proposed method is given below:
A. Network lifetime
This paper is focused to reduce the total energy consumption in
the network. To evaluate the proposed method from the
energy aspect, we considered lifetime criterion. Literat ure
consists many definitions for life time. But first node dies in the
network is the specific definition for periodic data collection
scenarios . The effect of the node density and network size on
the network lifetime is also analyzed.
B. Average energy remaining per node
The proposed method uses a new scheme to select the CHs and
gives uniform CH density throughout the network. To validate
the effectiveness of the uniform density of the CHs, the average
energy remaining per node is monitored throughout the
experiments. Additionally, the first 25% dead nodes are also
observed for different node density regions.
3. Simulation results and discussion
Figure 3 and Figure 4 show that, in the 150 m × 150 m and 200
m × 200 m network sizes, the number of dead nodes are large
and earlier for all mobile BS protocols as compared to the static
BS. But, the proposed method achieved well for the large
regions. Figure 5 shows that the proposed protocol is
performing well in the sensing region 350 m × 350 m. The
results sho w that the proposed method provides dead nodes in
the later stage compared to the static BS (LEACH) and
optimized LEACH protocols [19]. Figure 6 showing that the
results are improving regularly with the increase in network
area (For comparison refer Table 1).
The remaining energy in the network is an important factor for
WSNs. The remaining energy in the network after performing
k rounds is given by equation (6).
Total remaining energy (E) =
1()n
k
NEN
 (6)
Where E k (N) is the ene rgy of Nth node in the kth round.
Figure 7 shows that the remaining energy of the proposed
method is greater as compared to other protocols and hence the
proposed method increases the network lifetime.
Average energy remaining per node in kth round is calculated
by the equation (7).

Eavg (i) =
1()
()N
k
iEi
N dead k
 (7)
Ek(i), total remaining energy in kth round and dead (k )
number of dead nodes till kth round.

5

Fig.1. 400 node distribution in a square of 200 m * 200 m (yellow nodes are CHs and Black nodes are RN)

Fig. 2. Flow chart for CH selection process

0 200 400 600 800 1000 1200020406080100Number of dead nodes
Rounds Optimizing LEACH [19]
Static LEACH [10]
Proposed

100 200 300 400 500 600 700 800 900020406080100Dead nodes
Rounds Optimizing LEACH [19]
Static (LEACH) [10]
proposed

Start
Deploy nodes randomly in a given region
Each node calculates number of its 2 -hop
neighboring nodes
If a node (n(i)) has
maximum neighboring
number of node in 2 – hop
region AND
High energy than threshold
energy
Choose Cluster head (CH) to it
Stop Y es No
Fig.3. Number of dead nodes Vs Rounds (150 m × 150 m)
Fig.4. Number of dead nodes Vs Rounds (200 m × 200 m)

100 150 200 250 300 350 400 450 500020406080100Number of dead nodes
Rounds Optimizing LEACH [19]
Static (LEACH) [10]
proposed

0 200 400 600 800 1000 1200020406080100Number of dead nodes
Rounds Optimizing LEACH [19]
Static BS (LEACH) [10]
Proposed

0 50 100 150 200 250 300 350 400 450 500051015202530Remaining energy (mJ)
Rounds Optimizing LEACH [19]
Static (LEACH) [10]
Proposed

0 50 100 150 200 250 300 350 400 4500.000.050.100.150.200.250.300.350.40Average enegy per node (mJ)
Rounds Static (LEACH) [10]
Optimizing LEACH [19]
Proposed

0 50 100 150 200 250 300 350 400 450 50050100150200250300350400450500Rounds
Number of nodes Optimizing LEACH [19]
Static (LEACH) [10]
Proposed

The remaining energy at the end of the static BS technique was
large as compared to the mobile BS techniques. This is because
the nodes situated at the boundary of the network didn’t
utilized their energy completely, while the rest of the nodes
have exhausted their power and now these nodes are not able
to communicate with the network (the static BS case).
Therefore, the static BS case showing remaining energy even
at the end of the simulation.
Figure 8 shows that, in the 350 m × 350 m region, the prop osed
method has maximum average energy nodes in majority of
rounds. The remaining energy of the nodes and the number of
alive nodes are large as compared to the other protocols.
Figure 9 shows the effect of node density on the network
performance. The res ults show that the proposed method has
improved the network lifetime with higher node density. The
effect of node density can be more significant in large regions
as compared to the smaller one. The first 25% node died in the Fig.5. Number of dead nodes Vs Rounds (35 0 m × 350 m)

Fig.6. Number of dead nodes Vs Rounds (450 m × 450 m)

Fig.7. Nodes remaing energy (350 m × 350 m area) Fig.8 . Average energy per nodes Vs Rounds (350 m × 350 m area )
Fig.9. The effect of node density on 25 % dead nodes (350 m × 350 m )

7

later stage as compared to the other techniques. We observe
that as node density increases, the 25% dead node’s situation
shifts to later stage.
The node death curve for the proposed scheme has a more
steeper slope than other techniques. This slope shows that all
the nodes performing together and utilizing the maximum
energy of the network. This causes the lifetime of the network
is increased as compared to the other techniques.

V. Conclusions
An efficient use of power is the primary aspect in the WSNs.
This work proposed a new approach that uses a mobile BS and
rendezvous nodes (RNs) for collecting data in an energy –
efficient way. The orientation of the CHs remains uniform
throughout the network and it reduces the total in ter-cluster
energy consumption by reducing the distance between the CH
and member nodes for each cluster using the proposed approach. The simulation results show that the death of the first
node and the death of 25% nodes occur in the later round as
compa red to the LEACH (using static BS) and optimizing
LEACH (using mobile BS and RNs) protocols. These results
are further improving with the increase in the node density and
sensing area.

References
[1] J. C. Cuevas -Martinez et al., “Knowledge -based duty cycle
estimation in wireless sensor networks: Application for sound pressure
monitoring,” Appl. Soft Comput ., vol. 13, no. 2, 2013, pp. 967 -980.
[2] Zheng J et al., “Wireless sensor networks a networking
perspective,” Wiley -IEEE Press, 2009.
[3] V . Kumar e t al., “Tiwari, S. Energy Efficient Mechanisms in
Wireless Sensor Networks: A survey,” International Journal
ofAdvanced Research in Computer Science, 2011, 2(5),p. 595 -604.
[4] Nazir et al.,"Mobile sink based routing protocol (MSRP) for
prolonging network lifetime in clustered wireless sensor
network," Computer Applications and Industrial Electronics (ICCAIE),
Kuala Lumpur, Malaysia, Dec. 2010, pp. 624 -629.
[5] N. A. Pantazis et al., “Energy -efficient routing protocols in
wirelesssensor networks: A survey ,” IEEE Communications Surveys
& Tutorials , vol. 15, no. 2, 2013,pp. 551 -591.
[6] G . Han et al., “Routing protocols for underwater wireless sensor
networks,” IEEE Communications Magazine , vol. 53, no. 11, 2015, pp.
72-78.
[7] C. Tunca et al., “Ring routi ng: an energy -efficient routing protocol
for wireless sensor networks with a mobile sink,” IEEE Transactions
on Mobile Computing , vol. 14, no. 9, 2015, pp. 1947 -1960.
[8] Xing G et al., “Rendezvous planning in mobility -assisted wireless
sensor networks,” I EEE Trans Mob Comput 2008,pp.1430 –43.
[9] Liang W et al., “Approximation algorithms for capacitated
minimum forest problems in wireless sensor networks with a mobile
sink,” IEEETrans Comput ,2013, pp.1932 –44.
[10] Heizelman WR et al., Energy -efficient comm unication protocol
for wireless micro sensor networks,” In: IEEE Hawaii international
conference on system sciences, Hawaii, USA, 2000. pp. 10 –20. Netw ork Size Round number of first dead node Round number of 25% dead
nodes
LEACH
[10] Optimize –
LEACH [19] Proposed LEACH Optimize –
LEACH [19] Proposed
150 m×150 m 527 315 382 692 727 756
200 m×200 m 279 177 208 538 628 669
250 m×250 m 131 171 200 317 514 598
350 m×350 m 38 147 177 114 332 405
450 m×450 m 14 24 46 49 45 189
Parameters V alues
Network size 150 m×150 m, 200 m×200 m
250 m× 250m, 350 m× 350 m
450 m × 450 m
E0 0.3J
ETX 50nJ/bit
ERX 50nJ/bit
EDA 5nJ/bit/signal
Eamp 0.0013pJ/bit/m4
Efs 10pJ/bit/m2
l 4000 bit
Px 16% 교 정: 초벌편집
파 일: 김수영 (12-21)
Table 2. Simulation parameters Table 1. Rounds of first dead node and 25% dead nodes

[11] Asaduzzaman et al., “Energy efficient cooperative LEACH
protocol for wireless sensor networks,” J. Commu n. Netw. , vol. 12, no.
4, 2010, pp. 358 –365.
12] V . Loscrì et al., “A two -level hierarchy for low energy adaptive
clustering hierarchy,” IEEE V eh. Technol. Conf. , vol. 3. Sep., Dallas,
TX, USA, 2005, pp. 1809 –1813.
[13] O. Y onnis et al., “HEED: A hybrid, e nergy -efficient, distributed
clustering approach for ad hoc sensor networks,” IEEE Trans. Mobile
Comput. , vol. 3, no. 4, 2004, pp. 366 –379.
[14] Mehdi Trahani et al., “ SEECH : Scalable energy efficient
clustering hierarchy protocol in wireless sensor netw orks, IEEE sensor
journal, V ol. 14 No. 11, November 2014, pp.3944 -3954.
[15] C. Tunca et al., Ersoy. Distributed mobile sink routing for wireless
sensor networks: A survey,” IEEE Communications Surveys Tutorials ,
vol. 16, no. 2, 2014, pp. 877 –897.
[16] Xi e, Guangqian, and Feng Pan. "Cluster -based routing for the
mobile sink in wireless sensor networks with obstacles." IEEE
Access 4, 2016, pp. 2019 -2028.
[17] Ang et al.,"Optimizing energy consumption for big data collection
in large -scale wireless sensor ne tworks with mobile collectors," IEEE
Systems Journal , vol. 99, 2017, pp. 1 -11.
18] Z. Vincze et al., “Adaptive sink mobility in event -driven densely
deployed wireless sensor networks,” Ad Hoc and Sensor Wireless
Networks, vol. 3, nos. 2/3, 2007, pp. 255 -284.
[19] Mottaghi, Saeid, and Mohammad Reza Zahabi. "Optimizing
LEACH clustering algorithm with mobile sink and rendezvous
nodes." AEU -International Journal of Electronics and
Communications , vol. 69 no. 2, 2015 pp. 507 -514.
[20] Konstantopoulos et al. "A r endezvous -based approach
enabling energy -efficient sensory da ta collection with mobile
sinks, " IEEE Transactions on parallel and distributed systems ,
vol. 23, no. 5, 2012, pp. 809-817.
[21] W . B. Heinzelman et al., “An application -specific protocol
archite cture for wireless microsensor networks,” IEEE Trans.
Wireless Commun. , vol. 1, no. 12, 2002, pp. 660 –670.
[22] M. Zhao et al., „Bounded relay hop mobile data gathering
in wireless sensor networks,'' IEEE Trans. Comput. , vol. 61, no.
2, 2012, pp. 265_277.