A Stable Clustering Algorithm Based on Battery Power for Mobile Ad Hoc Networks

A Stable Clustering Algorithm Based on Battery

Power for Mobile Ad Hoc Networks

Pi-Rong Sheu* and Chia-Wei Wang

Department of Electrical Engineering, National Yunlin University of Science & Technology,

Touliu, Yunlin 640, Taiwan, R.O.C.

Abstract

Recently, extensive research efforts have been devoted to the design of clustering algorithms to

organize all the hosts in a mobile ad hoc network into a clustering architecture. However, due to the

dynamic nature of the mobile hosts, their association with and dissociation from clusters disturb the

stability of the network, making reconfiguration of cluster heads unavoidable. Re-computation of

cluster heads and frequent information exchange among the participating hosts will suffer high

computation overheads. Therefore, it is obvious that a more stable clustering architecture will directly

lead to the performance improvement of the whole network. In this paper, we will propose an efficient

clustering algorithm that can establish a stable clustering architecture by keeping a host with weak

battery power from being elected as a cluster head. Computer simulations show that the clustering

architectures generated by our clustering algorithm are more stable than those generated by other

clustering algorithms.

Key Words: Ad Hoc Network, Battery Power, Clustering Algorithm, Clustering Architecture

1. Introduction

A mobile ad hoc network (MANET) is formed by a

group of mobile hosts (or called mobile nodes) without

an infrastructure consisting of a set of fixed base stations

[1]. A mobile host in a MANET can act as a general host

as well as a router; i.e., it can generate as well as forward

packets. Two mobile hosts in such a network can com-

municate directly with each other through a single-hop

route in the shared wireless media if their positions are

close enough. Otherwise, they need a multi-hop route to

finish their communications. In a multi-hop route, the

packets sent by a source are relayed by multiple interme-

diate hosts before reaching their destination. MANETs

are found in applications such as short-term events, bat-

tlefield communications, disaster relief activities, and so

on. Undoubtedly, MANETs play a critical role in situa-

tions where a wired infrastructure is neither available nor

easy to install.

The research of MANETs has attracted a lot of atten-

tion recently [1]. Since host mobility causes frequent un-

predictable topological changes, efforts have been devo-

ted in particular to the design of clustering strategies to

organize all the hosts in a MANET into a clustering ar-

chitecture. This way, the transmission overheads for the

update of routing tables after topological changes can be

reduced [2�5]. In fact, research has demonstrated that

routing on top of clustering architectures is much more

scalable than flat routing [2�5]. In addition, a clustering

architecture can facilitate spatial reuse of resources to in-

crease network capacity [6,7]. For example, under a non-

overlapping clustering architecture, two clusters may use

the same frequency or code set if they are not adjacent.

Furthermore, in a clustering architecture, when a mobile

host changes its position, it is sufficient only for the hosts

within its cluster to update their topology information,

but not for all the hosts in this network.

In appearance, a clustering architecture is similar to a

Tamkang Journal of Science and Engineering, Vol. 9, No 3, pp. 233�242 (2006) 233

*Corresponding author. E-mail:[email protected]

single-hop cellular architecture [6,7]. Figure 1 shows a

clustering architecture for a MANET. There exists a link

between two nodes if the two nodes are within the trans-

mission range of each other. The black nodes denote the

cluster heads of the clustering architecture. Nodes within

a circle belong to the same cluster. Each node in a MANET

is assigned a unique identifier (ID) that is a positive inte-

ger. We assume a cluster’s ID to be the same as its cluster

head’s ID. For example, the ID of the cluster with node

15 as its cluster head is C15. Nodes 3, 8, 13, 15, and 16 all

belong to cluster C15. A cluster head in each cluster acts

as a coordinator to resolve channel assignment, perform

power control, maintain time division frame synchroni-

zation, and enhance spatial reuse of bandwidth. The ma-

jor characteristics of a clustering architecture are as fol-

lows. Firstly, there is only one cluster head in each clus-

ter. Secondly, each node in a clustering architecture is ei-

ther a cluster head or adjacent to one or more cluster he-

ads. A node belonging to two or more clusters is called a

gateway. Communication between any two adjacent clu-

sters has to rely on their common gateway. Thirdly, any

two cluster heads are not adjacent to each other. Finally,

any two nodes in the same cluster are at most two hops

away from each other.

Clustering architectures can be classified into two cat-

egories: overlapping and non-overlapping. In overlap-

ping clustering architectures [6], a node which is not a

cluster head may belong to more than one cluster; such a

node is named a gateway. Nodes which belong to only

one cluster are ordinary nodes. For example, in Figure 1,

nodes 8, 12 and 13 are gateways; the other white nodes

are ordinary nodes. In non-overlapping clustering archi-

tectures [8�11], a node which is not a cluster head be-

longs to only one cluster; such a node is named an ordi-

nary node. No gateway exists in this kind of architecture.

In fact, even in overlapping clustering architectures, a ga-

teway is not necessarily existent between any two clus-

ters (e.g., no gateway exists between cluster C2 and clus-

ter C6 in Figure 1). To support the function of a gateway,

the concept of distributed gateway (DG) has been pro-

posed [6]. A DG is a linked pair of ordinary nodes yet be-

longs to different clusters. In Figure 1, for example, the

pair of nodes 9 and 10 forms a DG. One of the advantages

of using DGs is that the hop counts of a route may be re-

duced. Take again Figure 1 for example. The route from

node 2 to node 6 will be {2, 8, 15, 13, 5, 12, 6} if DGs are

not introduced. On the other hand, when nodes 9 and 10

form a DG, the route can be reduced to {2, 9, 10, 6}. To

simplify our discussion, only non-overlapping clustering

architectures are considered in this paper.

Due to the dynamic nature of the mobile hosts, both

their integration and disintegration will disrupt the stabil-

ity of the network, calling for reconfiguration of cluster

heads. This feature needs attention, since re-computation

of cluster heads and frequent information exchange among

the participating hosts will result in high computation

overheads. Worse, frequent cluster head changes adver-

sely affect the performance of other dependent protocols

such as scheduling, routing, and resource allocation. In

fact, in a MANET that uses scalable cluster-based ser-

vices, the network performance metrics such as through-

put and delay are coupled with the frequency of cluster

reorganization. Therefore, it is obvious that a more stable

clustering architecture will directly lead to a better per-

formance of the whole MANET. In light of this, this pa-

per aims to build a stable clustering architecture.

In this paper, we will propose an efficient clustering

algorithm that can establish a stable clustering architec-

ture by keeping a node with weak battery power from be-

ing elected as a cluster head. A clustering architecture is

more stable if it can be held for a longer period of time.

To be more specific, a stable clustering architecture has a

longer clustering architecture lifetime, which is defined

in this paper as the duration from the time when the clus-

tering architecture is constructed until any cluster head in

the architecture runs out of its battery power (Another

metric used frequently to evaluate the stability of a net-

work is the so-called network lifetime, which is defined

in this paper as the duration during which the clustering

234 Pi-Rong Sheu and Chia-Wei Wang

1

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C5C15

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17Distributed gateway

Figure 1. A clustering architecture.

architecture is constructed until any node in the network

runs out of its battery power. We will also use this metric

to measure our clustering algorithm). Computer simula-

tions show that the clustering architectures generated by

our clustering algorithm are more stable than those gen-

erated by other clustering algorithms.

The rest of this paper is organized as follows. In Sec-

tion 2, related researches are reviewed. In Section 3, our

proposed stable clustering algorithm is presented. In Sec-

tion 4, the performance of our clustering algorithm is eva-

luated by computer simulations. Finally, in Section 5,

some conclusions will be drawn.

2. Related Researches

In this section, the related researches will be summa-

rized.

2.1 Stability in Clustering Algorithms

Because each host in a MANET is mobile and the

MANET works mainly on battery power, the topology

may change dynamically and the power may be exhaust-

ed. In order to reduce the cluster maintenance overheads

and to provide a more stable architecture for upper layer

protocols [11], stability of clustering architectures should

be taken seriously. Like many existing stable routing pro-

tocols, whose objective is to find routes consisting of

links and nodes with higher stability [12�15], clustering

algorithms must also deal with link stability as well as

node stability. In general, a link with higher received pow-

er is considered to have higher link stability. Similarly, a

node with higher battery power is considered to have

higher node stability [16,17]. Due to the limitation of

space, in the following we will only consider node stabil-

ity, which is measured only according to its battery pow-

er. When a node uses up its battery power, the communi-

cation between itself and any other node will be termi-

nated. Similarly, when a cluster head exhausts its battery

and becomes inactive, the cluster which it belongs to will

beak up. Obviously, the battery power of a node is very

important in keeping a MANET functioning. Since a

cluster head acts as a coordinator in a cluster, it will take

more tasks, which in turn will cause its battery power to

consume more rapidly. When a cluster breaks up for this

reason, the clustering architecture has to be reconfigured,

which will bring in high computation overheads. Intuiti-

vely, to reduce such overheads, we should always choose

nodes with larger battery power as cluster heads so that

the lifetime of the clustering architecture may be extend-

ed. However, in our study, we discover that a more effi-

cient way to form a stable clustering architecture is to avo-

id as much as possible choosing a node with little battery

power as a cluster head.

2.2 Related Clustering Algorithms

Before elaborating on our idea, let us first review four

existing clustering algorithms. The first three do not take

the factor of stability into consideration while the last

does. In the lowest-ID clustering algorithm [6], each no-

de is assigned a distinct ID. A node with ID lower than

those of its neighbors will be elected as a cluster head.

The lowest-ID neighbor of a node is its cluster head. In

the highest-connectivity clustering algorithm [6], a node

that has not chosen its cluster head is an “uncovered”

node; otherwise, it is a “covered” node. A node is elected

as a cluster head if it is the most highly connected node

among its “uncovered” neighbors (if there is a tie, the

node with the lowest ID prevails). To reduce clustering

and maintenance overheads, the access-based clustering

protocol (ABCP) [11] relies on the feature of MAC layer

to do the clustering. The ABCP can provide a rapidly de-

ployed clustering architecture for upper layer protocols.

The cluster head election criterion of the ABCP is based

on its multiple-access scheme on control channel. Each

node accesses the control channel to declare its intention

to be a cluster head. A node which successfully sends a

cluster head declaration before its one-hop neighbors do

will become the cluster head.

The distributed and mobility-adaptive clustering al-

gorithm (DMACA) [8�10] is a generalization of the low-

est-ID clustering algorithm. In the DMACA, each node

is assigned a weight, which becomes the criterion of ele-

cting a cluster head. The weight of a node can be given

according to its some qualities such as its mobility, its

processing power, and so on. Obviously, if the weight of

each node is set to its ID (degree), the DMACA will be-

come the lowest-ID (the highest-connectivity) clustering

algorithm. At first glance, the DMACA seems to be able

to successfully solve the stability problem. This is be-

cause if the battery power is taken as the node weight,

nodes with larger battery power will have a higher proba-

bility of becoming cluster heads. Thus, the stability of

A Stable Clustering Algorithm Based on Battery Power for Mobile Ad Hoc Networks 235

the whole clustering architecture seems to become high-

er. However, this is not always true. As an example, let

us consider the MANET in Figure 2. The number within

each node represents its battery power while the number

beside each node represents its ID; e.g., the battery pow-

er of node 1 is 4, the battery power of node 2 is 1, and so

on. When the weight of a node in the DMACA is set to its

battery power, the resulted clustering architecture is shown

in Figure 3, where nodes 1, 2, 3, 7, 8, and 10 have been

elected as cluster heads. Observe that among these clus-

ter heads, nodes 2 and 3 have low battery power. There-

fore, the resulted clustering architecture will be very un-

stable.

3. Our Proposed Clustering Algorithm

In this section, we will propose a new clustering al-

gorithm to form a stable clustering architecture. We de-

fine a bottleneck node to be a node with battery power

lower than a predefined value Ethreshold (the value of Ethresh-

old is determined by computer simulations and will be dis-

cussed in Section 4). When a bottleneck node is elected

as a cluster head, it is named a bottleneck cluster head.

We think that if a clustering architecture has fewer bottle-

neck cluster heads, it may have a longer lifetime. Thus,

the basic idea behind our clustering algorithm is that a

node will have a higher probability to become a cluster

head if it has more neighboring nodes that are bottleneck

nodes.

The outline of our whole clustering algorithm is as

follows. Each node in a MANET broadcasts its beacon

packets periodically to declare its existence. The beacon

packet of a node carries its battery power and cluster ID.

Thus, each node can obtain the number of non-clustered

neighbors who are bottleneck nodes (we name these ne-

ighbors bottleneck neighbors) by its received beacons.

Next, nodes with more bottleneck neighbors will be ele-

cted as cluster heads. However, different nodes may have

the same number of bottleneck neighbors. In this case,

ties may arise. Therefore, a secondary election criterion,

the battery power of a node, needs to be introduced to

solve such ties. The second election criterion is also help-

ful in maintaining a longer lifetime of the elected cluster

head. Finally, if a tie still happens, the node with lower

ID is preferred.

Before describing our clustering algorithm in detail,

we make the following assumptions, which are common

in designing clustering algorithms for MANETs [6�10]:

1. The network topology is static during the execu-

tion of the clustering algorithm.

2. A packet broadcasted by a node can be received

correctly by all its one-hop neighbors within a fi-

nite time.

3. Each node has a unique ID and knows its degree

(the number of its one-hop neighbors). At the same

time, each node knows the ID and the degree of its

every one-hop neighbor.

Next, in addition to the beacon packet, we will define

three different kinds of packets and two types of tables

used in our clustering algorithm. The most important pa-

cket in our clustering algorithm is the CRITERION (#_

of_bottleneck, battery_power, id) packet, which is broad-

casted by each node. Parameter #_of_bottleneck is the

number of non-clustered bottleneck neighbors of the no-

de, battery_power is the battery power of the node, and

id is the node’s ID. The CH (cid) packet is used by a node

to declare itself as a cluster head. Parameter cid is a no-

de’s cluster ID and is initially zero. The JOIN (cid, id)


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Figure 2. A MANET with battery power in each node.

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Figure 3. A clustering architecture established by DMACAfrom Figure 2.

packet is used by a node to inform the cluster head which

it wants to join, where cid is the cluster ID of the cluster

which it wants to join and id is its own node ID. Each

cluster head uses a Member_Table to record its cluster

members. Each node uses an NC_Neighbor_Table to re-

cord its non-clustered neighbors. Each time a beacon pa-

cket with cid equal to zero is received, a node will update

its NC_Neighbor_Table.

Our clustering algorithm:

� Each node broadcasts its own a CRITERION (#_

of_bottleneck, battery_power, id) packet to all its

neighboring nodes and receives multiple CRITE-

RION (#_of_bottleneck, battery_power, id) pack-

ets from its neighbors.

� If a node discovers that it has a larger #_of_bottle-

neck than those of the received CRITERION (#_

of_bottleneck, battery_power, id) packets, then it

sets its cid to its own ID and broadcasts a CH (cid)

packet to declare itself as a cluster head. If there is

a tie, then the cluster head will be the one with the

largest battery_power. If there is still a tie, the

node with the highest ID will be the final winner.

� When a node receives multiple CH (cid) packets

and dose not belong to any cluster (i.e., its cid = 0),

it will select the cluster head with the highest bat-

tery_power as its cluster head and set its cid to that

of the received CH (cid) packet from its selected

cluster head. Next the node broadcasts a JOIN (cid,

id) packet to join the cluster.

� When a cluster head receives a JOIN (cid, id) pa-

cket with cid equal to its own cid, it will record the

id in the received JOIN (cid, id) packet in its Mem-

ber_Table.

� When a non-clustered node receives a JOIN (cid,

id) packet, it will remove the node with id equal to

the id of the received JOIN (cid, id) packet from its

NC_Neighbor_Table.

� Each time a non-clustered node removes a node

from its NC_Neighbor_Table, it will check whe-

ther its NC_Neighbor_Table becomes empty or

not. If empty, it sets its cid to its own node id and

broadcasts a CH (cid) packet to declare itself as an

orphan cluster.

� A node will terminate the clustering algorithm when

it has joined or formed a cluster (i.e., its cid � 0).

Now, let us use the MANET in Figure 2 as an exam-

ple to illustrate the operation of our clustering algorithm.

Figure 4 shows the resulted clustering architecture when

Ethreshold = 1.5 and our clustering algorithm is applied to

the MANET in Figure 2. Observe that node 6 has two

bottleneck neighbors, that each of node 4 and node 5 has

one bottleneck neighbor individually, and that each of

the other nodes has no bottleneck neighbors. Thus, node

4, node 5, and node 6 will have higher priorities to be-

come cluster heads. Although both node 1 and node 9

have no bottlenecks, node 1 rather than node 9 is elected

as a cluster head because the former has larger battery

power than the latter. Note that no bottleneck cluster he-

ad exists in Figure 4 while two bottleneck cluster heads

(node 2 and node 3) appear in Figure 3.

4. Computer Simulations

In this section, we will evaluate the stability of our

clustering algorithm and compare it with those of ABCP

and DMACA. We select ABCP as a representative of

clustering algorithms that do not take the stability into

consideration. The choice of ABCP over the lowest-ID

and highest-connectivity clustering algorithms is based

on the fact that the last two clustering algorithms are in-

deed special cases of DMACA. For DMACA, a node’s

battery power is adopted as its node weight.

4.1 Power Model

According to the path-loss model [18,19], the trans-

mission power consumption of a link can be expressed as


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Figure 4. A clustering architecture established by our cluster-ing algorithm from Figure 2.

a function of the distance between its endpoints. To be

more specific, the power required to transmit a packet

along link (vi, vj) is approximately equal to di j,

2 � �, where

di j,

2 denotes the distance between node vi and node vj, � is

a constant. The path-loss model also indicates that the

power required to receive a packet does not depend on

the length of the link, and can be modeled by a constant

�. In our computer simulations, for simplicity, we only

consider transmitting power and set � to 1. Thus, if node

vi transmits � packets to node vj, it will consume di j,

2 � �

units of power.

4.2 Simulation Environments

The environment of our simulations is assumed to be

a static network. Each mobile host is randomly distrib-

uted in 1200 � 1200 m2 physical area. The transmission

range of each mobile host is the same and fixed value 200

m. Five different network sizes are taken into account:

40-node, 60-node, 80-node, 100-node, and 120-node.

Each numerical value is obtained from an average value

of 100 times of simulations. In the beginning, each node

is given 10000~100000 units of battery power. The dis-

tribution of node’s initial battery power is based on two

different kinds of battery power distributions. In the first

scenario, 25% of the total nodes have battery power low-

er than 50000. In the second scenario, 50% of the total

nodes have battery power lower than 50000.

In a cluster, we assume that each ordinary node vi

will consume � i id� 2 units of battery power to transmit

or relay �i packets to its cluster head, where di denotes

the distance between node vi and its cluster head. The

transmission rate of each ordinary node is between 1 and

10 packets per second. Because a cluster head plays a

role as a coordinator in its cluster, it is feasible to assume

that a cluster head must process more tasks and thus

needs to consume more battery power than an ordinary

node. In our computer simulations, the power consump-

tion of a cluster head is assumed to be � � i id � 2,

where � � i is the number of packets per second from

all its ordinary nodes to the cluster head and di denotes

the average distance between the cluster head and its mem-

bers.

4.3 Performance Metrics

The performance metrics we will observe are 1) the

lifetime of clustering architecture, 2) the lifetime of net-

work, 3) the battery power of each cluster head, and 4)

the number of cluster heads. Recall that the clustering ar-

chitecture lifetime is defined as the duration from the

time when the clustering architecture is constructed until

any cluster head in the architecture runs out of its battery

power. The network lifetime is defined as the duration

from the time when the clustering architecture is con-

structed until any node in the network runs out of its bat-

tery power.

4.4 Determining Proper Values for Ethreshold

It is not hard to see that the stability of our clustering

algorithm largely depends on the value of the bottleneck

battery power Ethreshold. Therefore, before starting our sta-

bility evaluation, we need to determine proper values for

Ethreshold. Figure 5 shows the clustering architecture life-

times obtained by our clustering algorithm as different

values from 10000 to 100000 units are adopted for Ethresh-

old. Figure 5(a) is for our first scenario. We can observe

that when Ethreshold is set to 40000 units, our clustering al-


Figure 5. Determining proper values for Ethreshold.

gorithm can generate maximal average clustering archi-

tecture lifetimes for all the networks with different sizes.

Thus, we will let Ethreshold = 40000 for our first scenario.

Figure 5(b) explains our second scenario. It shows when

Ethreshold is set to 30000 units, our clustering algorithm

can generate maximal average clustering architecture

lifetimes. Thus, we will let Ethreshold = 30000 for our sec-

ond scenario. Note that the clustering architecture life-

times of our second scenario are shorter than those of our

first scenario under the same network size and the same

Ethreshold value. This is expected because there exist more

nodes with battery power below 50000 in the second sce-

nario than in the first scenario.

4.5 Performance Analyses and Comparisons

Figure 6 presents the minimum battery power among

all the cluster heads when a clustering architecture is es-

tablished by the three clustering algorithms, respectively.

It can be observed that the minimum battery power of a

cluster head generated by our clustering algorithm is al-

ways larger than those obtained by the other two clus-

tering algorithms. The results justify our assumption

that keeping a node with weak battery power from being

elected as a cluster head is more efficient than DMACA,

in which nodes with larger battery power will have a

higher probability of becoming cluster heads.

Figure 7 shows the average clustering architecture li-

fetimes obtained by the three different algorithms. Figure

7(a) illustrates the first scenario and Figure 7(b) explains

the second scenario. These curves indicate that the aver-

age clustering architecture lifetime obtained by our clus-

tering algorithm is about 30% longer than that of DMACA,

and about 33% longer than that of ABCP. Thus, the clus-

tering architecture constructed by our clustering algori-

thm is more stable. In other words, it takes longer for our

clustering architecture to reconfigure.

Figure 8 shows that the average network lifetime ob-

tained by our clustering algorithm is about 32% longer

than that of DMACA, and about 44% longer than that of

ABCP. These results demonstrate an important fact that a


Figure 6. Comparisons on the minimum battery power of cluster heads.

Figure 7. Comparisons on clustering architecture lifetimes.

more stable clustering architecture may also lead to a

longer network lifetime. This is because in our clustering

algorithm, most nodes with lower battery power will be-

come ordinary nodes, which have fewer tasks and con-

sume lower battery power. Thus the lifetimes of ordinary

nodes will be longer. On the other hand, in DMACA, no-

des with lower battery power still have a high probability

of becoming cluster heads, which have more tasks and

consume more battery power. This situation will shorten

not only the clustering architecture lifetime but also the

network lifetime.

Finally, during our computer simulations, we disco-

ver an interesting phenomenon that the number of cluster

heads formed by our clustering algorithm is fewer than

those formed by the others. Figure 9 reveals such a phe-

nomenon. In [20], the performance of a clustering archi-

tecture with fewer cluster heads has been demonstrated

to be more efficient. This is because the overheads of

broadcasting task, where packets initiated at a source are

retransmitted by only cluster heads and gateways, can be

significantly reduced when the number of cluster heads

and gateways is decreased. Therefore, the results in Fig-

ure 9 indirectly imply our clustering algorithm can estab-

lish clustering architectures with better performance in

addition to higher stability.

5. Conclusion

In this paper, we have proposed an efficient cluster-

ing algorithm to establish a stable clustering architecture.

In our clustering algorithm, the node with the largest #_

of_bottleneck is first elected as the cluster head. If there

is a tie, then the node with the largest battery_power will

become the cluster head. If a tie still exists, then the node

with the highest ID prevails.

The computer simulations demonstrate the fact that

the stability of our clustering algorithm is better than tho-

se of DMACA and ABCP in terms of clustering architec-

ture lifetime and network lifetime. Furthermore, our com-

puter simulations show that the number of cluster heads


Figure 8. Comparisons on network lifetimes.

Figure 9. Comparisons on the numbers of cluster heads.

generated by our clustering algorithm is smaller. This

implies our clustering algorithm is capable of building

clustering architectures for better performance and high-

er stability.

Acknowledgements

This work was supported by the National Science

Council of the Republic of China under Grant # NSC 93-

2213-E-224-023.

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Manuscript Received: Jul. 2, 2005

Accepted: Nov. 29, 2005


Documents

A Stable Clustering Algorithm Based on Battery Power for Mobile Ad Hoc Networks