Clustering Energy Efficent for Larger Area

7/29/2019 Clustering Energy Efficent for Larger Area

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EEMC: An Energy-Efficient Multi-tier Clustering Algorithm for

Large-Scale Wireless Sensor Networks

Yan Jin LingＷang Yoohwan Kim*

Xiaozong Yang

Department of Computer Science and Technology *School of Computer Science

Harbin Institute of Technology, Harbin, China University of Nevada, Las Vegas, USA Email: {jinyan, lwang}@ftcl.hit.edu.cn Email: [email protected]

Abstract

Wireless sensor networks can be used to collect surrounding data by multi-hop. As sensor networks have the

limited and not rechargeable energy resource, energyefficiency is an important design issue for its topology. In this paper, we propose a distributed algorithm, EEMC (Energy-

Efficient Multi-tier Clustering), that generating multi-tier clusters for long-lived sensor networks. EEMC terminates in

O(log logN) iterations given N nodes, incurs low energyconsumption and latency across the network. Simulationresults demonstrate that our proposed algorithm is effectivein prolonging the large-scale network lifetime and achieving more power reductions.

Keywords: wireless sensor networks, energy efficient, multi-

tier, clustering, algorithm

1. Introduction

Wireless sensor network (WSN) is a type of special

wireless network whose important target is to gather thesensed data from surrounding environment. The nodes inwireless sensor networks are untethered and unattended.

Because of the compact form factors of sensor nodes,wireless sensor nodes are severely energy constrained, whichrestricts sensor networks from being used for broader

applications. Furthermore, it is impractical to replace the batteries on thousands of nodes in a possibly harshenvironment. Hence, energy efficiency is an important design

consideration for the wireless sensor networks. Clusteringtechnique has been proposed by lots of researchers to reduceuseful energy consumption. This approach can group a

number of nodes, usually within a geographic neighborhood,to form a cluster. By this way sensors can be managed locally

by a cluster head (CH), a node elected to manage the cluster and be responsible for communication between the cluster and the sink node.

In [1] the first energy-efficient cluster-based hierarchicalrouting scheme LEACH is proposed for sensor networks, andit has been proved to adapt to the large-scale networks and be

scalable for future application such as multimedia datatransmissions. Since then, there are lots of routing protocolsderived from [1], such as PEGASIS and Hierarchical-

PEGASIS, TEEN and APTEEN etc [2]. Besides, Seema et al.[3] give the selected optimal probability when the sink node

is located in the center of the network and the regular node isfar away from its CH at most K-hop. The disadvantages of itare that [3] brings out unforeseen latency and complexity

computation for the parameters of probability and the optimalvalue of K, as well as ignoring the overhead of receivingenergy, which is an important factor in designing the energy-

efficient algorithm [4].

In this paper, firstly we give the optimal value of cluster heads and the probability to be a cluster head by probabilitytheory. Secondly, both transmission energy and receivingenergy have been considered to design a distributed energy-

efficient multi-tier clustering algorithm (EEMC). At last,

comparing with existing clustering algorithm, simulationresults show that our algorithm achieves better performance(lower energy consumption and latency) than others.

2. Energy analysis for clustering schemes

Some notations are given as followings: N : The total number of sensor nodes in a WSN

R: The area radius of a WSN Ri: The area radius of ith-tier cluster

L: The distance between a 1st-tier CH to a sink node

N i: The number of sensor nodes in an ith

-tier cluster N CHi: The number of ith-tier CHs that belongs to a (i-1)th-

tier CH

r : The number of bits transmitted per secondIn this paper, we adopt the Radio Energy Model [1]:

Psend(n1 , n2)=(α11+α2d(n1 , n2 )k )r (1)

Preceive=α12r (2)where Psend(n1 , n2) is the energy consumed by node n1 when it

transmits data to node n2, Preceive is the energy consumed bynode n2, d(n1 , n2 ) is the distance between the two nodes n1

and n2, k is the path loss exponent depending on thesurrounding environment. Here α11, α12, α2 are radio parameters, typical values for radio parameters are

α11=α12=50nJ/bit, α2=100pJ/bit/m2 (k =2) or 0.001pJ/bit/m4

(k =4) [1].In this paper, it is assumed that all nodes are located in a

circle uniformly and there is only one sink node without

constrained energy resources, which is far away from all

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nodes. The regular nodes (non-CHs) can reach corresponding

CH directly by one hop.

2.1. One-tier clustering scheme

Assume that a cluster with N 1 nodes (which is called OneT ier C lustering S cheme-OTCS). The radius of this cluster is

R1. The figure is shown in Figure 1. Sink node

2R1

CH node

regular node

L

d i

Figure 1. Cluster with radius R1 (OTCS)

According to the energy model mentioned previously, we

have: Lemma 1: The expected energy consumption of OTCS with N 1 nodes and radius R1 is:

11 1 2 11 2

2[ ] ( 1)( ) ( )

2

k k

sum OTCS

R E P N r L r

k α α α α

−= − + + +

+

(3)

Proof : From Figure 1, Eq. (1) and Eq. (2), the total energy

consumption of OTCS is:1 1

11 2 12 11 2

1

( ) ( ) N

k k

sum OTCS i

i

P d r L r α α α α α

−

−

=

= + + + +∑ (4)

The first part of Eq. (4) is the sum of the energy required by

all regular nodes for transmission and the energy required by

the CH for receiving, and the second part of Eq. (4) is the

energy required by the CH for transmitting the aggregated

result to the sink node. In Eq. (4), d ik

can be calculatedas

12

1

2

10 0

21dθ dl

2

R k k R

l l R k

π

π

=+

∫ ∫ . The desired result now

immediately follows. ■ Theorem 1: Given the parameters R, L, k (=2) and the

number of sensor nodes N in all, the optimal value of N CH 1

is: 21 2

2 12

1

2

opt

CH N R N L

α

α α

=

−

Proof : We skip the proof due to space limitations. ■

2.2. Two-tier clustering scheme

T wo-T ier C lustering S cheme (TTCS) is developed bydividing OTCS into N CH2 sub-clusters. The figure is shown inFigure 2. After gathering the data from regular nodes, thesecond-tier CHs transmit the aggregated data to the

responding first-tier CH. Then all first-tier CHs send theresults to the sink node directly after they gather all the datafrom the second-tier CHs.

Sink node

The first-tier CH node

The second-tier CH node

L

2R1

Figure 2. Cluster with radius R1 (TTCS)

Lemma 2: Given the same parameters ( N 1 and R1) in Lemma1, the expected energy consumption of TTCS is:

11 2 1 2

2

2[ ] ( 1)( )

2 ( )

k

sum TTCS CH k

CH

R E P N N r

k N α α

−= − − + +

+

2 1 2 1 11 2

2( ) ( )

1

k k

CH N R r L r k

α α α α + + +

+

(5)

Proof : The proof of Lemma 2 is similar to that of Lemma 1.

We skip the detailed proof due to space limitations. ■

Note that in Eq. (5), when N CH 2 is small, some sensors willhave to transmit for a longer distance to reach the

corresponding CH. On the contrary, when N CH2 is large thereare fewer data to be aggregated in the second-tier CHs.Therefore, there is a tradeoff with N CH2 in minimizing the

total communication energy of TTCS. This observation leadsto Theorem 2: Theorem 2: Under TTCS, the energy consumption is

minimal if and only if N CH2 (called2

opt

CH N ) satisfies:

4 N CH2k+2- N CH2

2(k -2)2+2kN CH2( N 1-1)(k -2)-k 2( N 1-1)2=0 (6)

Proof : We skip the proof due to space limitations. ■

According to Theorem 2,2

opt

CH N =

11 N − when k =2.

Theorem 3: The energy required of TTCS is less than that of

OTCS with same N 1, R1 and L. Proof : This fact can be obtained by comparing Eq. (3) and

Eq. (5): (3)-(5)= 12 1 2

2

2 1( 1)[1 ( ) ] 0

1

k k

CH

CH

R N N r

k N α − − − >

+

. It implies

the energy consumption of TTCS is less than that of OTCS.■ Finally, an example is given when k is 2. Suppose there

are 100 sensor nodes divided into 5 clusters (i.e., every

cluster has 20 nodes on average) in OTCS. We can further divide each cluster into N CH 2=4(≈19

1/2) sub-clusters to form

TTCS to minimize the energy consumption (i.e., every sub-

cluster has 5 nodes on average) following Theorem 2.

3. EEMC algorithm

The algorithm works in an up-bottom fashion and the path

loss exponent (k ) considered is 2 for simplicity. Given N nodes in all, these nodes first elect the first-tier CHs, then thesecond-tier CHs, and so on. For example, the first-tier

(OTCS) CHs are chosen with the probability p1=

1

opt

CH N

N

where1

opt

CH N is determined by Theorem 1. Thus there

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are N 1 (=1/ p1) nodes in every OTCS. The second-tier (TTCS)

CHs are chosen as follows: Each regular sensor node decideswhether to become a second-tier CH or not by using the

probability p2 (= 1

1 1

1 1

1 1

N

N N

−

=

− −

). A sensor node generates a

random number (rand ) and decides to become a CH if rand <

p2. Then it advertises itself as a second-tier CH to the sensors

within its radio range. Each regular sensor that receives anadvertisement joins the cluster of the closest second-tier CH

by sending a notify message. Thus, all the second-tier CHsget to know the size of the cluster, i.e. N 2

(=1 1 N − approximately). The second-tier CH then sends a

command message to its members to repeat the election process at the third-tier. The members decide to be a CH with

a certain probability p3 (=

2

1

1 N −

) and broadcast their

decisions. CHs at tiers 4, 5,…,T are chosen in a similar fashion, with probabilities p4, p5, . . . pT respectively. Thisgenerates a multi-tier clustering scheme. Certainly, any ith-

tier CH is in charge of data aggregation for (i+1)th

-tier CHs.A pseudo code of the algorithm is given below. Without

loss of generality, we only describe the procedure of forming

the ith

-tier topology from the existing (i-1)th-tier topology.

I. InitializeSuppose there are N i-1 nodes in one of the (i-1)th-tier clusters

and pi is calculated as11/ 1i N

−−

1. Set current_tier = i-1, Q = 0

II. Main_Processing ( i : Tier)1. If this node is not a CH yet 2. { Generate a random number rand 3. If rand is less than pi 4. { Broadcast a i

th-tier CH message

5. Set this node as a ith-tier CH

6. If receive a “join” message and it’s a CH

7. Increase Q until1 1 1i N

−− −

8. If Q≤2 Exit Main_Processing

9. Broadcast a “dividing (i+1)th-tier” message }

10. Else

11. { If receive a ith-tier CH message

12. Send a “join” message to this CH if it isnon-CH

13. ElseIf receive a dividing message

14. Main_Processing(i +1:Tier) } }

III. Wrap up

1. If not receive any CH message2. If this node hasn’t been a CH yet3. Set the node as a forced CH

Figure 3. EEMC algorithm for ith-tier forming

Note in Figure 3, the line of 8 in phase 2 demonstrates thatwe should avoid a cluster at most including 3 regular nodes

to continue plotting out, which brings out trigonometric phenomenon unfortunately.

Proposition 1: EEMC is a completely distributed algorithm.

A node can either elect to become a CH according to aspecific probability or join a cluster according to overheardCH messages within its cluster range. Hence it is scalable for

large-scale sensor networks. Proposition 2: EEMC algorithm terminates in N iter =O(log logN) iterations.

Proof : Note that a node does not execute the phase II of EEMC again if it becomes a CH, so we only consider thecase where a node still remains a regular node when it

completes phase II. The maximum number of iterations isthus equal to the number of tiers (T ). According to the line 8of phase II, the number of nodes within a cluster must be

equal or greater than 3. Also according to Theorem 2, thenumber of CHs is proportional to the square root of thenumber of sensor nodes within the cluster. Therefore thefollowing condition holds: T can be calculated approximately

as:1

2 3T

N ≥ . Therefore, the maximum number of iterations

(= N iter =T ) in EEMC algorithm is2 3

log ( log ) N , which is

O(log log N). ■ Proposition 3: At the end of phase III of the EEMC, a node iseither a cluster head for some tier or a regular node that belongs to a cluster.

Proposition 4: EEMC has a worst-case message exchangecomplexity of O( N

1/2) per node and O( N ) in the whole

network, where N is the number of nodes in the network.

We skip the proof of Proposition 4 due to spacelimitations. Based on Proposition 4 we have the samemessage complexity of EEMC as that of HEED [5], which isgiven in Lemma 4 of [5].

Proposition 5: EEMC has a worst-case processing time

complexity of O( N ), where N is the number of nodes in the

network.

4. Simulations and conclusions

A square region of 500*500m2 is generated and 100 nodes

are placed in the network randomly. The initial energy of allnodes is allocated with 2J to 5J uniformly. Other network parameters involved are: radio communication radius is 50m,

data packet size and control packet size are 2000bytes and 20 bytes respectively, and bandwidth is 1Mbps. We simulate

three cases, OTCS (here OTCS equals to LEACH where thenumber of CHs is 5% of all nodes), energy-efficient multi-tier K -hop (EEMK) algorithm (where K =3) [3] and our

EEMC algorithm. Each algorithm is executed 10 times to getmore reliable results. The results from those 10 executionswere then averaged and plotted. A more efficient scheme is

signified by a lower value in the energy-dissipation metric, aswell as a higher value in the lifetime of network.

As shown in Figure 4, we can achieve the best energy

saving with EEMC. However, the difference between EEMCand EEMK is minor. Comparably, OTCS consumesconsiderably more energy than the algorithms EEMC and

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EEMK since it only considers one-tier clustering topology

and do not optimize the transmission distance. For example,when k is 2 and 80% nodes are kept active the lifetime is prolonged by 40% compared with the case of OTCS.

Similarly, when k is 4 and 80% nodes are kept alive; thelifetimes are prolonged by 87.5% respectively compared withthe case of OTCS. From these results, we observe that, with

the increase of k EEMC achieves more energy savingscompared with OTCS. Note we cannot make three-tier clustering topology because the number of second-tier only

has at most 2 regular nodes each, which limits dividingfurther as shown in Figure 3.

(a) (b)Figure 4. Lifetime comparison for OTCS, EEMK and EEMC withthe elapsed time. The figures (a) and (b) represent k =2 and 4respectively

(a) (b)Figure 5. The energy consumption of OTCS vs. N CH 2. The figures

(a) and (b) present k =2 and 4 respectively

In order to observe the impact of N CH 2 on energy

consumption, the total energy consumption for a selectedcluster formed by OTCS is drawn in Figure 5. In Figure 5,each cluster in OTCS is divided into different N CH 2 ranging

from 2 to 10. From the Figure 5(a), we find that the optimal

value of N CH 2 is 4(≈ 100/5 1− ) when k is 2, which validates

the Theorem 2 because the size of each cluster is 20 on

average in OTCS. Similarly we find the value2

opt

CH N to be 3

in Figure 5(b). This result is also consistent with thetheoretical values predicted by Theorem 2. However, in thiscase, two-tier clustering scheme excels on one-tier clusteringscheme.

The latency ratio of EEMC to EEMK is shown in Figure

6. In this particular case, when the time is between [0,850],

the latency ratio is stable with the average value of 0.35 (≈

1/ K ), which is expected. Although there are some nodesrunning out of energy after 850 seconds, it influences EEMK

rather than our EEMC. The reason is that some “unfortunate”sensors in EEMK must search for other alive sensors by some

“beacon” approach to transmit data packets to the nodes at K -

hop away from the corresponding CH. It takes time to find acorrect routing path, and thus the latency is increased. InEEMC, the latency is relatively stable because a regular node

reaches CH only by 1-hop, regardless of other node’slocation. Therefore, the latency ratio gets reduced after 850second. Besides we run EEMC with the changed number

(scale) of nodes, from 100 to 5000. The optimal number of tiers is shown in Table 1.

Figure 6. The latency ratio of EEMC to EEMK when k is 2

Table 1. Optimal number of tiers vs. number of nodes N

N Tiers

100~2300 22400~4800 3

4900~ 4

In summary, the simulation results in this section show

that our EEMC algorithm achieves smaller energydissipation, lower latency compared with other clusteringalgorithms (LEACH and EEMK). It implies that EEMC is an

energy-efficient algorithm to manage a large-scale clusteringscheme network.

5. References

[1] W. Heinzelman, A. Chandrakasan, and H. Balakrishnan,

“Energy-Efficient Routing Protocols for Wireless Microsensor Networks,” in Proceedings of 33rd Hawaii International Conference on System Sciences, Jan. 2000, pp. 3005–3014[2] K. Akkaya, and M. Younis, “A Survey on Routing Protocols for

Wireless Sensor Networks,” Ad hoc Networks, 3(3), May. 2005, pp.325-349

[3] B. Seema and J. C. Edward, “Minimizing Communication Costsin Hierarchically-clustered Networks of Wireless Sensors,”Computer Networks, 44(1), Jan. 2004, pp. 1-16[4] E. I. Oyman and E. Cem, “Overhead Energy Consideration for efficient routing in wireless sensor network”, Computer Networks,

46(4), Nov. 2004, pp. 465-478 [5] Y. Ossama and F. Sonia, “HEED：A Hybrid, Energy-Efficient,

Distributed Clustering Approach for Ad Hoc Sensor Networks,”

IEEE Trans. Mobile Computing , 3(4), Oct.2004, pp.366–37

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Clustering Energy Efficent for Larger Area