Energy-efficient data collection in strip-based wireless sensor networks with optimal speed mobile data collectors

Computer Networks 156 (2019) 33–40

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Energy-efficient data collection in strip-based wireless sensor networks with optimal speed mobile data collectors R. Vishnuvarthan a, R. Sakthivel b,∗, V. Bhanumathi c, K. Muralitharan d a

Department of Electronics and Communication Engineering, Anna University Regional Campus, Coimbatore 641046, India Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India c Department of Electronics and Communication Engineering, Anna University Regional Campus, Coimbatore 641046, India d Department of Mathematics, Anna University Regional Campus, Coimbatore 641046, India b

a r t i c l e

i n f o

Article history: Received 19 November 2018 Revised 1 February 2019 Accepted 30 March 2019 Available online 6 April 2019 Keywords: Wireless sensor network Strip-based WSNs Mobile data collector Energy consumption Network lifetime

a b s t r a c t Energy consumption and network lifetime are the major concerns in wireless sensor networks (WSNs). In particular, WSNs use radios for communication, which are the major energy consumers. Due to frequent data forwarding process, the sensors near the sink especially in strip-based network deplete more energy, which causes energy hole problem and network lifetime reduction. In this work, as a first attempt, an energy efficient data collection process is proposed for strip-based WSNs to solve the aforementioned issues. More precisely, an optimal speed for the mobile data collector (MDC) with accurate data transmission range for each cluster is determined through an analytical approach. In addition, to reduce the energy usage of the sensor nodes, the transmission range of the sensors is adjusted automatically. With this proposed methodology, the network can avoid energy hole problem. Simulations are carried out to validate the proposed method, where it is shown that the network lifetime is significantly extended when compared to the existing methods. © 2019 Published by Elsevier B.V.

1. Introduction A set of homogeneous or heterogeneous tiny sensors are grouped together to perform a particular task called wireless sensor network (WSN) which can sense, process and perform short range communications [1,2]. These sensors are spatially deployed over a particular domain for monitoring or measuring the environment changes periodically. Usually, sensors are operated with low powered battery and WSN lifetime is limited to it. The applications include target tracking, environment monitoring, space surveillance, battlefield surveillance, weather forecasting, etc., [3–6]. The abilities of WSNs have been expanded significantly because of the micro-electro-mechanical systems and in advancements of the Internet of things (IoT). Deployment of large number of sensors in the hostile environment creates faulty and unreliable networks due to limited battery resource. Every sensors consume energy for its data transmission and reception. The gathered data are forwarded or routed to the sink via multi-hop transmission [7,8]. Hence, the sensors closer to sink dissipate their energy faster when compared to other sensors because of their frequent data forwarding activity. Hence, the exist∗

Corresponding author. E-mail address: [email protected] (R. Sakthivel).

https://doi.org/10.1016/j.comnet.2019.03.019 1389-1286/© 2019 Published by Elsevier B.V.

ing network suffers a problem around the sink called energy hole problem [9,10]. If energy hole problem occurs in the sensor network, no more data can be transferred to the sink. Consequently, other sensors cannot deliver their collected data to the sink. Thus, data loss occurs in the network and considerate energy is wasted by disconnected sensors, which opens the way to the premature death of sensors. Further, the energy hole and data loss issues degrade the network lifetime as well as the quality of service [11]. The strip-based WSNs are the network where the length of the network is larger than the height of the network. Some real-time applications for the strip-based network include bridges, pipelines, rivers, metros, roads, etc. Here, the sensors are arranged linearly and hence, the data transmission would follow many-to-one pattern. As a result, the number of data transmission to be handled by the nodes near the sink is huge which an causes energy hole problem. Most of the existing methodologies were applied only to spiral or circular network scenarios and it cannot be applied to strip-based network [12–16]. In the existing literature, several approaches have been proposed to improve the network lifetime, see [17–22] and the references cited therein. It can be achieved via different techniques such as deployment, localization, data fusion, clustering, transmission range adjustment, routing and energy scheduling. Therefore, it is very essential and an important task to extend the network

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R. Vishnuvarthan, R. Sakthivel and V. Bhanumathi et al. / Computer Networks 156 (2019) 33–40

lifetime by reducing the energy consumption using the aforementioned techniques. Here, instead of forwarding the sensed data blindly to the network, the sensors are grouped together called clusters. Each cluster is assigned with a periodically changing cluster head (CH) and this process of grouping is called as clustering [23,24]. In general, all the sensors need to perform the data transmission. By applying the clustering approach, most of the data forwarding can be done through CH and sinks [25]. Hence, clustering is one of the important methodologies to extend the network lifetime. Radio is the main energy consumer in the sensor unit. Here, the energy consumption is determined by how far the data has to be transmitted during the communication over the wireless medium. As transmission distance plays an important role in the energy usage, proper adjustment of transmission range in the radio device maximizes the network lifetime [26–28]. Recently, researchers found a new idea to avoid the conventional multi-hop transmission over the fixed sinks and used a mobile device or robot which travels over the network to collect the data from the sensors or cluster heads [29–31]. MDC is used because of two main reasons: (1) MDC can collect data over spatially separated regions and (2) minimal energy consumption requirement. In general, MDC aims to optimize the node energy consumption, network reliability and data latency [12]. Moreover, the conventional data forwarding mechanism for a longer distance from the sensor can be avoided [32]. The suggested approach provides the balanced network and increases the network lifetime significantly because of effective data collection. Authors in [33] did a comparative study on various topologies and data collection/dissemination schemes of sink mobility. In [34], the authors proposed optimization-based mobile data collector for general WSN. But these works consider corona network model where they cannot be applied for strip based network model. In [35], authors have considered strip-based WSN with static sink. Though the work maximizes the network lifetime by adjusting the communication range, the energy hole problem is not solved completely. 1.1. Motivations Most of the existing works considers multi path transmission model and consumes more energy due to longer travel distance of data causing energy hole problem. So, mobile data collectors were deployed to alleviate this issue. But still operating the MDC at optimal speed for data collection is not explored. Also, many data transmission protocols adjust the sensor transmission distance in the closer area of the sinks [36], but optimal speed MDC with transmission range adjustment is one of the areas to be well explored. 1.2. Contributions

in WSN. Speed of the MDC has to be operated for a particular cluster depends on the size of cluster, the data transmission rate and the amount of data to be transmitted by CH to MDC. Lastly, CH transmission ranges are adjusted to reduce the energy consumption and to increase the network lifetime. Therefore, the proposed approach can prevent the network from energy hole problem and can avoid data loss. The main contributions of this paper can be summarized as follows: • MDC-based data collection approach with optimal speed and dynamic transmission range adjustment is proposed in WSNs as a first attempt to extend the network lifetime. • The speed of MDC depends on the length of the cluster and the number of packets to be transmitted by the cluster. So, the proposed variable speed MDC-based scheme increases the network lifetime significantly and avoids the energy hole problem and packet loss. • In this work, a novel heuristic algorithm is proposed for data collection with MDC, which helps in construction of energy efficient strip-based WSN. • It is revealed from the numerical simulations that the proposed approach considerably improves the network lifetime than the existing approaches. 2. System model 2.1. Network model Stationary sensor nodes are deployed uniformly in linear fashion. Generally, in strip-based network L > > H, where L is length and H is the height of the strip as shown in Fig. 1. In this work, the sink acts as MDC which traverses over the network to collect the data. If all the nodes communicate directly with the sink, the total energy consumption will be huge. In order to avoid that, the network is divided into n number of clusters denoted as C1 , C2 , C3 , . . . , Cn and each Ci has a cluster head CHi which communicates with the mobile sink. Each cluster has ρ nodes and each generates b bits of data. The main tasks of CH are: collect the data from its members, fuse them together at the fuse rate of 1/β and transfer them to MDC in single hop when it comes to its vicinity. The length of any cluster Ci is denoted as li and it satisfies 0 < li < L  and ni=1 li = L. 2.2. Radio model In this work, the most common radio model [38] is considered and the energy consumption for transmitting k bit message over distance d for free space and multi path model is given by



ET x (k, d ) =

kEelec + kE f s d2 ,

d < d0 ,

kEelec + kEamp d ,

d ≥ d0 ,

4

(1)

and the energy consumption to receive this message is given by This work is focused on using MDC for data collection in stripbased network to optimize the energy consumption of the node and to enhance the network lifetime. To the endeavor of our knowledge from the literature, the proposed approach is the first attempt for strip-based WSN with the integrated implementation of clustering, accurate transmission range adjustment of nodes and velocity adjustment of MDC. The proposed approach has the following phases: Firstly, the network is partitioned into number of equal sized clusters and a CH is elected for each cluster based on the LEACH protocol [37]. Periodically the CH is rotated to maintain the energy balance in the network. Secondly, the transmission ranges of cluster members are adjusted in accordance with CH to reduce the energy consumption for intra cluster communication. Thirdly, MDC is enforced for effective data collection from the CH

ERx (k ) = kEelec ,

(2) × 10−9

10 × 10−12

J/bit/m2 ,

where Eelec = 50 J/bit, E f s = Eamp = 1.3 × 10−15 J/bit/m4 and d0 = 87 m. In this work, we assume that, the nodes follow free space model, i.e. li < d0 .

Fig. 1. Network model.

R. Vishnuvarthan, R. Sakthivel and V. Bhanumathi et al. / Computer Networks 156 (2019) 33–40

35

2.3. Formal definition of the problem Consider a WSN with N sensors deployed linearly which is divided into n clusters. Communication range of each node is adjusted and MDC is operated at an optimal speed above the network so that the total energy consumption of each node (Ei ) is minimized. Mathematically it can be given as, N 

Minimize

Ei

i=1

Fig. 3. The distance between MDC and CH.

3. Transmission scheme based on accurate distances

given by

In the considered network, two types of communications are performed, which are: (1) intra-cluster communication, i.e. cluster members transmit data to its CH which adopts single hop communication since li < d0 ; and (2) communication between CH and MDC, which also adopts single hop. Theoretical energy depletion calculation is given as follows:

Since L > > H, the distance between any two nodes in the cluster and the distance between their projection points are same as in Fig. 2. For example, the distance between the nodes X and Y is same as their projection X and Y . Thus the expectation of distance square between any two points in layer Ci is given by

=



li



0

li 0

 li  0

( x − y )2 li2

dxdy



l2 li y2 + − y dy = i , 3 li 6

(3)

which is approximately equal to the average distance square from any node of the cluster to its CH. In any cluster Ci , the energy consumption for intra cluster communication Eicluster includes two parts: (1) EiCM−tr , energy consumed for data transmission by the cluster members to CHi ; and (2) EiCH−re energy for data reception by the CH of the cluster Ci . Any cluster Ci with ρ nodes can generate b bits of data. Therefore, the total data generated and transmitted by cluster members are T CM = bρ . To transfer all these data, the energy consumed by the cluster members, according to Eq. (1) is given by



EiCM−tr = T CM Eelec + E f s E[d2 ]



= bρ Eelec + E f s

 2

li 6



= bρ Eelec +

6





Efs bρ li2 + bρ Eelec 6

= 2bρ Eelec +

E f s bρ li2 . 6

(6)

MDC moves in a particular direction at a constant velocity vi and distance dM over the network (dM < li /2), so the distance between MDC and CH varies with respect to time as shown in Fig. 3. The communication between them proceeds as the MDC moves along its path. Let m be the total number of packets to be transmitted by cluster CHi to MDC. The path is divided into m time slots, where total time slot tm = L/m and each time slot tj is the maximum time required to transmit packetj . According to Fig. 3, the current and new distances square between MDC and CH of the cluster Ci at time tj for sending ( j + 1 )th packet is given by



d2j

li = − vi t j 2

d2j+1 =

m 

d2j =



bρ li2 .

= R Eelec = bρ Eelec . CH

li − vi t j+1 2

(7)

2 + ( dM )2 .

(8)



mli2 2 + v2i t12 + t22 + · · · + tm 4

=

Therefore, the total energy consumption for intra-cluster communication in cluster Ci is computed by adding Eqs. (4) and (5) and is

+ ( dM )2 ,

− vi li [t1 + t2 + · · · + tm ] + m(dM )2

(4)

(5)

2

For calculation purpose, the above equations are generalized as (7). Further, the average distance square between the MDC and CHi is calculated as follows: Sum of the distances from t = 0 to m is given by

j=1

 Efs

Data received by the CH are equal to the data sent by the ordinary nodes of its cluster and they are given by RCH = bρ . Based on Eq. (2), the energy consumed for data reception by the CH of the cluster is

EiCH−re

= bρ Eelec +

3.2. Energy depletion for MDC and CH communication

3.1. Energy depletion in intra cluster communication

E (d 2 ) =

Eicluster = EiCM−tr + EiCH−re

m m   mli2 + v2i t 2j − vi li t j + m ( dM )2 . 4 j=1

(9)

j=1

Average of the distances square between MDC and CHi is given by m 

di2

=d2j =

li2 4

= +

j=1

v

d2j

m m 

2 i

m

j=1

t 2j −

m vi li 

m

t j + ( dM )2 .

(10)

j=1

When CHi receives bρ bits from its members, then with fusion rate of 1/β , the data transmitted by CHi to MDC are given by Fig. 2. The approximate distance between two nodes in a cluster.

T CHi =

bρ

β

,

(11)

36

R. Vishnuvarthan, R. Sakthivel and V. Bhanumathi et al. / Computer Networks 156 (2019) 33–40

which is equal to the data received by MDC

RMDC =

bρ

β

3.4. Optimal velocity of MDC for each layer

.

(12)

According to Eq. (1), the energy consumption for data transmission of CH of Ci is given by



EiCH−tr = T CH Eelec + E f s di2 = =



bρ

β

bρ

Eelec + E f s di2

Eelec +

β

bρ







m m li2 v2  vi li  + i t 2j − t j + ( dM )2 , 4 m m j=1

j=1

(13) and according to (2), the energy consumption for data reception of MDC from cluster Ci is

bρ

EiMDC−re = RMDC Eelec =

β



j=1

vi =

=

β

bρ

β

Eelec + Eelec +

bρ

β

bρ

Eelec .

β



m m li2 v2i  vi li  + t 2j − t j + ( dM )2 . 4 m m j=1

at

3:

EiTotal = Eicluster + EiCH−MDC

β

li2 + 4

v

−

vi li m

m 

9:



10: 11:

t j + ( dM )2

j=1

  m 1 2 E f s bρvi  = E f s bρ + l − t j li 6 4β i βm j=1   m v2i E f s  E f s ( dM )2 Eelec 2 + bρ 2Eelec + + t + , β β m j=1 j β

12: 13: 14: 15: 16:

(16)





21: 23:

j=1

 m v2i E f s  E f s ( dM )2 2 + b 2Eelec + + t + . β β m j=1 j β

19: 20: 22:

1 m EiTotal 1 2 E f s bvi  = E f sb + li − t j li Ni 6 4β βm Eelec

17: 18:

and the number of nodes in cluster Ci is Ni = ρ . So, the average energy consumption of individual nodes of the cluster is given by



6:

8:

1

Ei =

4: 5:

7:

E f s bρ li2 bρ = 2bρ Eelec + + E 6 β elec Efs

Eelec



3l

i vi = and 4m + 2  l2 v2 vi li di = i + i ( m + 1 ) − (m + 1 )(2m + 1 ) + (dM )2.

2

6

(20)

Algorithm 1 Proposed Algorithm. 2:

According to Eqs. (6) and (15), the total energy consumption of cluster Ci and MDC is

bρ



j=1

3.3. Average energy depletion of individual nodes

+



Algorithm 1 works with the single hop strategy between CH and MDC with two packets datareq and datareply . Initially, cluster

1:

m 2  i t 2j m j=1



1 2 bvi E f s l − m + 1 li 4β i 2β

3.5. Data collection model with MDC

(15)



6

+

E ( dM )2 v2 E f s + b 2Eelec + + i (m + 1 )(2m + 1 ) + f s β 6β β

4



(19)

1



(14)

E f s di2 + 0

Efs ×

3li . 4m + 2

Then, the minimum average energy consumption of a node for cluster Ci is expressed as

EiCH−MDC = EiCH−tr + EiMDC−re bρ

(18)

j=1

dE i = 0 to find the optimal vi for dvi the cluster Ci . Here, it is assumed that CHi requires unit time to transmit a packet to MDC. Therefore, the optimal velocity vi at which the MDC should travel over the cluster Ci with minimal energy consumption is

E imin = bE f s

But, MDC has enough energy capacity and are rechargeable. So, we neglect the energy consumed by MDC for this work, i.e. EiMDC−re = 0. Therefore, total energy consumption for CH and MDC communication is given by

=



m m ( 2vi )E f s  E f sb  dE i =− t j li + b t 2j . dvi βm βm

Set the derivative value as zero

Efs ×

β

We compute the first derivative of Eq. (17) to find the minimum energy consumption value for cluster Ci .

(17)

{L: Length of the network} {n: Number of sensor nodes} {i: Cluster ID } {mi : Number of packets to be transmitted by clusteri } {dcur : Current distance between MDC and CH} {dnew : Distance between MDC and CH after the successful packet transmission} {dtran : Transmission Distance} Deploy sensors uniformly in linear fashion Cluster formation using LEACH while dis := L do MDC broadcasts datareq ( pos, v ) packet to the sensors within its vicinity if CH receives datareq then Respond with datareply ( pos, li , mc ) message end if Adjust the velocity of MDC to vi (using Equ. 19) loop j := 1 to m MDC calculates dcur and dnew Find dtran = max(dcur , dnew ) MDC sends datareq (ack, dtran ) CH adjusts transmission distance to dtran CH sends datareply (data ) end loop end while

is formed in the WSN with the help of LEACH protocol. MDC starts moving from one end of the cluster and broadcasts datareq packet. If any CH receives datareq packet from MDC, then it replies with datareply packet and starts its data transmission process.

R. Vishnuvarthan, R. Sakthivel and V. Bhanumathi et al. / Computer Networks 156 (2019) 33–40

Algorithm Description: When MDC arrives to the vicinity of the cluster head, it sends its location information to the CH with the current distance dcur in the datareq packet. The CH in turn replies the MDC with datareply packet with the cluster length li and the number of packets m to be transmitted. MDC calculates v through Eq. (19) and adjusts its speed. Before transmitting each packet, using Eqs. (7) and (8), CH calculates the current distance dcur and the new distance dnew that the MDC will be at after transmitting the packet. The transmission distance is adjusted with the maximum of two values max (dcur , dnew ). 4. Performance evaluation via numerical simulation

which has a direct impact on network lifetime. It is clear that, the number of clusters should be minimized as much as possible in order to extend the network lifetime. 4.2. Comparison on average energy consumption Fig. 5–8 compare the average energy consumption of a node against different cluster IDs. In stationary sink network model, if the cluster ID is larger, it implies that cluster is farther from the sink. It is clearly noticed in these figures that, DT consumes more energy as the cluster IDs number increases. It is because, the energy consumption of the node increases when the transmission distance increases. To overcome this, mobile sink is deployed in

In this section, the obtained results are evaluated with different network sizes. The proposed work is compared over the existing linear network models such as accurate-distances-based transmission scheme (ADTS) [35], energy efficient geographic routing protocols (EEGR) [39], energy-balanced data gathering protocol (EBDG) [39] and direct transmission scheme (DT) [39]. The parameters’ values for the simulations are listed in Table 1. 4.1. Impact on energy consumption with variable cluster size Fig. 4 shows the average energy consumption of a node for the network (L = 10 0 0) with different cluster sizes. The cluster size should not exceed d0 (i.e. li < d0 ) in order to be in free space model. The result implies that, if the cluster size is small, then the number of clusters in the network is more. When the number of clusters is more, then the average energy consumption is high Table 1 Simulation parameters. Parameters

Description

Value

b

Generated data Node density Height of the network Length of the network Data fusion rate Node’s initial energy Height at which MDC is operated

500 bits/round 1 node/m2 10 m 40 0 m–10 0 0 m 1/50 5J 1m

ρ H L 1/β E0 dM

Fig. 4. Energy consumption for L = 10 0 0.

37

Fig. 5. L = 400.

Fig. 6. L = 600.

38

R. Vishnuvarthan, R. Sakthivel and V. Bhanumathi et al. / Computer Networks 156 (2019) 33–40

Fig. 9. Alive nodes Vs rounds. Fig. 7. L800.

Fig. 8. L = 10 0 0.

Fig. 10. Network lifetime.

the proposed model. Moreover, in the proposed model, with transmission range and speed adjustment of MDC, the network achieves less average energy consumption of a node than the existing models and the load is balanced well throughout the network.

different methods. As the network size increases, the network lifetime decreases because the data to be transmitted are more. When compared to the existing works, the network lifetime through the proposed work is significantly higher as the average energy consumption of the entire network is minimal. This is because of operating the MDC at optimal speed and with optimal transmission range adjustments.

4.3. Comparison on network lifetime Network lifetime is the amount of time that a WSN is fully operative. There are many methods to measure network lifetime, such as when the first node or the last node dies in the network, break in the network link etc. In this work, network lifetime is measured when the last node dies. Fig. 9 shows the number of alive nodes after each round for L = 10 0 0 and Fig. 10 shows the maximum rounds before the death of last node in the network for

5. Conclusion In this paper, an energy efficient data collection model with MDC has been considered for linear WSNs. Specifically, a novel algorithm has been developed for finding the optimal speed of MDC to collect the data based on the amount of data to be transmitted

R. Vishnuvarthan, R. Sakthivel and V. Bhanumathi et al. / Computer Networks 156 (2019) 33–40

and the length of the cluster. In addition to that, the communication range of the nodes has been adjusted to improve the network lifetime further. Thus, by operating the MDC at optimal speed and adjusting the communication range of the nodes, the nodes consume minimal energy for data transmission. Overall, the proposed algorithm significantly increases the network lifetime and the simulation results confirm that the proposed algorithm is a good solution for data collection in linear WSNs. It would be an interesting topic to extend the proposed work with multiple mobile sinks, which will be our future research direction. Acknowledgment The work of first author was supported by the University Grant Commission (UGC), Government of India [UGC NET-JRF]. References [1] O. Cayirpunar, E. Kadioglu-Urtis, B. Tavli, Optimal base station mobility patterns for wireless sensor network lifetime maximization, IEEE Sens. J. 15 (11) (2015) 6592–6603. [2] M. Krishnan, S. Yun, Y.M. Jung, Dynamic clustering approach with ACO-based mobile sink for data collection in WSNs, Wirel. Netw. (2018), doi:10.1007/ s11276- 018- 1762- 8. [3] B. Rashid, M.H. Rehmani, Applications of wireless sensor networks for urban areas: a survey, J. Netw. Comput. Appl. 60 (2016) 192–219. [4] K. Muralitharan, R. Vishnuvarthan, R. Sakthivel, Performance evaluation of sensor deployment using optimization techniques and scheduling approach for k– coverage in wsns, Wirel. Netw. 24 (3) (2018) 683–693. [5] J. Yan, M. Zhou, Z. Ding, Recent advances in energy-efficient routing protocols for wireless sensor networks: a review, IEEE Access 4 (2016) 5673–5686. [6] V.C. Gungor, G.P. Hancke, Industrial wireless sensor networks: Challenges, design principles, and technical approaches, IEEE Trans. Ind. Electron. 56 (10) (2009) 4258–4265. [7] J. Huang, D. Ruan, W. Meng, An annulus sector grid aided energy-efficient multi-hop routing protocol for wireless sensor networks, Comput. Netw. 147 (2018) 38–48. [8] Z. Zhang, Y. Wang, F. Song, W. Zhang, An energy-balanced mechanism for hierarchical routing in wireless sensor networks, Int. J. Distrib. Sen. Netw. 11 (10) (2015) 1329–1550. [9] J. Lin, M.A. Weitnauer, Range extension cooperative MAC to attack energy hole in duty-cycled multi-hop WSNS, Wirel. Netw. 24 (5) (2018) 1419–1437. [10] C. Song, M. Liu, J. Cao, Y. Zheng, H. Gong, G. Chen, Maximizing network lifetime based on transmission range adjustment in wireless sensor networks, Comput. Commun. 32 (11) (2009) 1316–1325. [11] P.V. Kallapur, V. Geetha, Article: research challenges in using mobile agents for data aggregation in wireless sensor networks with dynamic deadlines, Int. J. Comput. Appl. 30 (5) (2011) 34–38. [12] M.D. Francesco, S.K. Das, G. Anastasi, Data collection in wireless sensor networks with mobile elements: a survey, ACM Trans. Sens. Netw. 8 (1) (2011) 1–31. [13] N. Sabor, S.M. Ahmed, M. Abo-Zahhad, S. Sasaki, ARBIC: an adjustable range based immune hierarchy clustering protocol supporting mobility of wireless sensor networks, Pervasive Mob. Comput. 43 (2018) 27–48. [14] X. Liu, An optimal-distance-based transmission strategy for lifetime maximization of wireless sensor networks, IEEE Sens. J. 15 (6) (2015) 3484–3491. [15] J.A. Torkestani, An energy-efficient topology control mechanism for wireless sensor networks based on transmit power adjustment, Wirel. Pers. Commun. 82 (4) (2015) 2537–2556. [16] S.T. Cheng, M. Wu, Optimization of multilevel power adjustment in wireless sensor networks, Telecommun. Syst. 42 (1) (2009) 109–121. [17] Y. Yun, Y. Xia, Maximizing the lifetime of wireless sensor networks with mobile sink in delay-tolerant applications, IEEE Trans. Mob. Comput. 9 (9) (2010) 1308–1318. [18] Y. Gu, Y. Ji, J. Li, B. Zhao, ESWC: efficient scheduling for the mobile sink in wireless sensor networks with delay constraint, IEEE Trans. Parallel Distrib.Syst. 24 (7) (2013) 1310–1320. [19] G. Huang, D. Chen, X. Liu, A node deployment strategy for blindness avoiding in wireless sensor networks, IEEE Commun. Lett. 19 (6) (2015) 10 05–10 08. [20] H. Yang, X. Wang, ECOCS: energy consumption optimized compressive sensing in group sensor networks, Comput. Netw. 146 (2018) 159–166. [21] K. Kalaivanan, V. Bhanumathi, Reliable location aware and cluster-tap root based data collection protocol for large scale wireless sensor networks, J. Netw. Comput. Appl. 118 (2018) 83–101. [22] W. Zhang, Z. Zhang, H. Chao, Y. Liu, P. Zhang, System-level energy balance for maximizing network lifetime in wsns, IEEE Access 5 (2017) 20 046–20 057. [23] N. Mittal, U. Singh, B.S. Sohi, A stable energy efficient clustering protocol for wireless sensor networks, Wirel. Netw. 23 (6) (2017) 1809–1821.

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R. Sakthivel received the B.Sc., M.Sc., M.Phil., and Ph.D. degrees in mathematics from Bharathiar University, Coimbatore, India, in 1992, 1994, 1996, and 1999, respectively. He was a Lecturer with the Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore, from 20 0 0 to 20 01. From 20 01 to 20 03, he was a Post-Doctoral Fellow with the Department of Mathematics, Inha University, Incheon, South Korea. He was a Visiting Fellow with the Max Planck Institute, Magdeburg, Germany, in 2002. From 2003 to 2005, he was a Japan Society for the Promotion of Science Fellow with the Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Kitakyushu, Japan. He was a Research Professor with the Department of Mathematics, Yonsei University, Seoul, South Korea, until 2006. He was a Post-Doctoral Fellow (Brain Pool Program) with the Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, South Korea, from 2006 to 2008. He was an Assistant Professor and an Associate Professor with the Department of Mathematics, Sungkyunkwan University, Suwon, South Korea, from 2008 to 2013. From 2013 to 2016, he was a Professor at the Department of Mathematics, Sri Ramakrishna Institute of Technology, India. He is currently a Professor with the Department of Applied Mathematics, Bharathiar University, Coimbatore, India. He has published over 250 research papers in reputed science citation index journals. His current research interests include systems and control theory, optimization techniques, and nonlinear dynamics. He has been on the Editorial Board of international journals, including the IEEE Access, the Journal of the Franklin Institute, Neurocomputing, Advances in Difference equations, and the Journal of Electrical Engineering and Technology.

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R. Vishnuvarthan, R. Sakthivel and V. Bhanumathi et al. / Computer Networks 156 (2019) 33–40 V. Bhanumathi received the B.E degree in electronics and communication engineering from Madras University, M.E. degree in communication systems and Ph.D in Information and Communication Engineering from Anna University, Chennai. She is currently working as an assistant professor in the Department of Electronics and Communication Engineering, Anna University, Regional Campus, Coimbatore. She has published her works in various International Journals and conferences. Her areas of interest are Wireless Communication, VLSI Design, Network Security, and Digital Communication.

K. Muralitharan received the B.Sc. degree in electronics and M.C.A. degree in computer science from Bharathiar University, Coimbatore, Tamilnadu, India, in 2001 and 2004, respectively. He was a Senior Software Engineer in Nilgiri Networks Pvt Ltd., [TeNet group (I.I.T Madras)], Tamilnadu, India from 2004 to 2009 and worked as a Senior Engineering Research Fellow (SERF) in the Department of Computer Applications, Anna university of Technology, Coimbatore, India from 2009 to 2012. He received his Ph.D. degree from Anna University, Chennai, India in 2016. His current research interests include smart grid networks, wireless sensor networks and optimization techniques.