An Efficient Cluster Update Model in MANET

Dongsheng Chen, Alireza Babaei and Prathima Agrawal

Dept. of Electrical and Computer Engineering

Auburn University, Auburn, AL 36849

Abstract—In hierarchical networks, the efficient choices of

cluster-head as well as the cluster update interval is important

to keep the established cluster structure stable and improve the

communication quality. In this paper, we establish a cluster

update interval model and use this model to determine a

reliable update interval for the cluster structures in MANETs.

This update interval is affected by two main factors: nodes’

relative mobility and transmission range. We establish a

cluster update interval model which uses the expected link

lifetime with respect to the cluster-head (CH) as the update

interval. The proposed model takes all of the above mentioned

factors into consideration and no weights combination is

needed. Simulation results shows that our proposed model can

help to determine a dynamic cluster update interval adapting

to various scenarios and achieve better stability in the cluster

structure.

Keywords-area-based; cluster update; expected link lifetime;

stability;

I. INTRODUCTION

MANETs (Mobile Ad hoc Networks) have attracted research interest for a long period. In MANETs, wireless hosts communicate with each other in the absence of fixed infrastructure. Examples include battlefield scenarios, disaster relief, mobile conferencing, and short-term scenarios such as public events and so on. In the case of large MANETs, a flat structure is not the most efficient one for routing between nodes especially in the multicast mesh networks like ODMRP [1], in which each mobile host broadcasts control packet to search receiver and establish route. It is likely that the broadcast results in packet explosion when the number of hosts is large. The hierarchical architecture has been proven effective in addressing the scalability problems in MANETs. However, nodes mobility becomes the biggest challenge for keeping relative stability of the cluster structure. Due to mobility, network topology dynamically changes which incurs frequent communication interruptions, larger communication delay and lower packet delivery ratio. Therefore a suitable cluster-head election and update interval of cluster structure are very important in networks with hierarchical architecture.

In this paper, our proposed cluster update interval algorithm utilizes nodes’ velocity and transmission range to identify different update intervals for the cluster-heads. During this update interval, cluster structure can remain relatively stable. It means the rate of member exchange between different clusters is low and unnecessarily fast update of the cluster-head is avoided. Therefore, link (route) stability can be enhanced and communication delay can be reduced.

The rest of paper is organized as follows. Section II reviews the related work. Section III introduces the model used for determining the cluster update interval for the cluster-head. In Section IV, we first introduce the simulation configuration in Ns-2.34; then we define two metrics and compare the performance of our proposed algorithm and constant update interval in three well-known algorithms (LID, HD, WCA). Finally, we conclude the paper in Section V.

II. RELATED WORK

Many cluster-head election algorithms have been

proposed to solve the scalability problem in MANETs and

achieve relative stability of cluster structure. Here, we list

some of the well-known clustering algorithms:

1) LID (lowest ID algorithm): LID [2] is a typical

algorithm in identifier-based clustering. Each node is

assigned a unique ID, and this ID is broadcast to its

neighbors using Hello messages. In the LID algorithm, the

node with minimum ID is selected as cluster-head. When a

node has more than one cluster-heads in its neighbor table, it

serves as gateway. LID is simple to implement but the

number of cluster-heads may become undesirably high.

Furthermore because of exhaustive energy consumption by

the cluster-heads, the network lifetime becomes low.

2) HD (highest-degree clustering algorithm): the goal of

the HD algorithm [2] is to reduce the number of clusters. The

nodes’ degrees are regarded as the metric for determining

cluster-head. Node with largest degree (largest number of

neighbors) is elected as cluster-head (CH). If two nodes have

the same degree, the node with smaller ID is selected as CH.

Even though HD algorithm can reduce the number of cluster-

heads in the network, it neglects the impact of mobility on

the stability of clustering structure.

3) WCA (weighted clustering algorithm): WCA [3] has

been widely studied and modified as in [4, 5]. In WCA

algorithm, the cluster-head is chose by striking a balance

between few factors including: sum of relative distance of

nodes to their neighbors, degree difference, mobility and

power left. This algorithm needs to assign the appropriate

weights to each of these factors before selecting or updating

CH. One drawback of WCA is that it is very likely that one

or two factors in selecting the CH prevails no matter what

weights combination is assigned. Also it is not easy to find

the best weights combination for these factors especially in

unknown environment. Therefore WCA takes relatively

more time to set up clusters and reform cluster structure.

All of the above clustering algorithms utilize a constant

cluster update interval and none of them provide an

44th IEEE Southeastern Symposium on System TheoryUniversity of North Florida, Jacksonville, FLMarch 11-13, 2012

978-1-4577-1493-1/12/$26.00 ©2012 IEEE 73

analytical model to determine the cluster update interval. By

utilizing a constant cluster update interval, the impact of

cluster update interval on stability of cluster structure and

communication quality had been neglected. The case

becomes worse when the node’s velocity distribution and

transmission range change. Our proposed model not only

considers the impact of nodes’ velocity distribution and

transmission range, but also no weights combinations are

needed to find the update interval based on these factors.

III. CLUSTER UPDATE INTERVAL MODEL

In this section, we establish a model for cluster-head

update interval. The model mainly considers two factors:

nodes’ velocity distribution and transmission range. We

determine the specific update interval for each cluster-head

locally based on the local nodes’ velocity distribution and

transmission range of cluster-head. We realize that the cluster update interval, let us denote it

by �, is very important parameter in designing clusters. If � is too long, it is likely that a cluster becomes unstable because of high mobility of its member nodes, which results in frequent exchange of nodes between different clusters. Consequently, more control packets are needed to reestablish the disconnected links (routes). Also being a cluster-head for a long time leads to exhaustive energy consumption and thereby reducing the average lifetime of the network. If � is too short, cluster reformation procedure is conducted too frequently. As a result, more energy is wasted in choosing a new cluster-head and transmission delay may increase.

In many protocols such as those considered in [6], the

cluster update interval is considered to be constant. These

papers do not provide analytical results for the cluster update

interval and the effects of node velocity and transmission

range on cluster update interval are not analyzed. In this

section, we establish a model for determining the cluster-

head update interval T to avoid unnecessary fast update and

improve stability of cluster structure. We consider the

expected link-life time as the cluster update interval T as it

is reasonable to conduct cluster update procedure before an

average link disconnects. Let us introduce our assumptions used in our derivations:

1. Nodes are uniformly distribution in the networks.

2. Both nodes’ speed magnitude and angle satisfy uniform

distribution; i.e. � is uniformly distributed in (0,a] (a is

maximum speed), and � is uniformly distributed in ���, �. Also speed and angle are uncorrelated random variables.

3. We first focus on a typical node with random angle and

distance of and � respectively where and � are

independent.

4. A link can be established between two nodes if they are in

the transmission range of each other.

In [7], the authors have established an expected link lifetime model. This model is used to describe the interval between link generation and termination; therefore the

expected link lifetime is based on assumption of long time observation. However, this assumption is not correct for describing the link lifetime with respect to cluster-head during the cluster-head update interval as we only consider the current existing links while conducting cluster formation or reformation. It is more reasonable to assume cluster members randomly distributed within transmission range of the cluster-head.

Before establishing the expected link lifetime model with

respected to certain node; we take the example of link (0,1)

connected by node 0 and node 1 to derive relative velocity

and velocity direction based on the acquired information. We

define following variables:

• �� and � are current velocities of nodes 0 and 1,

respectively.

• (��, ��) and (� , � ) are current updated locations

of nodes 0 and 1, respectively.

• ������� and � ����� are the velocity vectors, and �� and �

are the velocity directions of nodes 0 and 1

respectively; also the relative velocity is ���, � ≜|� ����� � ������� |, and � � � � ��.

• ∅ is the angle of relative velocity of ����, � Next let us assume that node 0 is fixed and calculate the

relative velocity ��(0,1)of node 1 with respect to node 0, and

the relative distance d between node 0 and node 1. Imagine

a Cartesian coordinate system with orthogonal unit vectors: ı� along the moving direction of node 0 and ȷ� on its

orthogonal direction respectively as shown in Fig. 1. Then � ����� can be expressed as: � �����= � cos�� � ��� ��+ � sin�� ���� ��; and ��(0,1) =� �����-�������=� (cos�� � ���-��)��+ � sin�� � ��� ��.

Figure 1. Example of link between node 0 and node 1

In Fig. 1, we can derive:

• ∅ ≜atan2( !" #$% #&'(/'*) ;

• ��+,�� ≜|��(0,1)| =,�� - � � 2��� cos �;

In addition, we need to derive the probability density

function (PDF) of relative speed � and ∅. Let us define /'(,'*,#���, � , �� ≜ 0',∅��, ∅�. where 0',∅��, ∅� is the joint pdf of � and ∅ . Using the

assumptions above, we know:

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0'(���� � 0'*�� � � �1, and 0#��� � � 2; Therefore, it is

easy to conclude: /'(,'*,#���, � , �� � 0'(���� ∙ 0'*�� � ∙ 0#��� � 12�5

Next, we use an auxiliary variable �� in the Jacobian’s

transform. We get 0',∅,'(��, ∅, ��� � /'(,'*,#���, � , �� ∙ �|7�'(,'*,#�|. Also

8���, � , �9�=::;''( ;''* ;'#;<'( ;<'* ;<#;'('( ;'('* ;'(# ::=='*>'(*> ''(?@A<' ��, ��, C�

where Λ��, ��, ∅� � D E=� - �� - 2��� cos∅F � D�=� - �� - 2��� cos∅ � 5� and D�G�is the unit step function. Then 0',∅��, ∅� � H /','(,∅��, ��, ∅� ∙ ���'(

(2)

Now we can analyze the expected link lifetime

(maximum cluster-head update interval) based on the

derived 0',∅��, ∅�. Based on the assumptions 1 and 3 in this section, we can

show the PDF of random variables �, as

0I��� � J2�K LMNO� ∈ Q0, K0SGMNTLUVN

0W�� � J 12� LMNOT ∈ Q0,2��0SGMNTLUVN

Figure 2. Expected link lifetime model for cluster member with respect to

cluster-head

In Fig. 2, we illustrate the location of a typical node

within transmission range R of the cluster-head. In this

figure, � and are used to describe the location of this

typical node. Variable � indicates relative distance, and

indicates relative angle. Using this notation, we can get:

�XYZ[ � ,K � ��. VUO]� � �. ^SV] � ,K � ��. sin� � _�� � �. cos�� _�

where �XYZ[ is the estimated as the estimated length of

movement of typical node while it is in the transmission

range of the cluster-head. Also, we have GXYZ[ � I`abc' . We

can therefore write

dvddddfdfvfttETv d

dvlinklink ⋅⋅⋅⋅⋅⋅⋅== ∫ ∫ ∫ ∫ ϕγγϕ

ϕ γ

γϕ)()(),()( ,

dvddfdddfd

vvf

d

dlink

v

v ⋅⋅⋅⋅⋅⋅⋅⋅= ∫ ∫∫ ∫ ϕγγϕγ

γϕ

ϕ})(])([{

1),(,

dvddxxRx

Rvvf

R

v

v ⋅⋅⋅−⋅⋅⋅⋅= ∫∫ ∫ ϕπ

ϕ

ϕ

ϕ}

4

12{

1),( 22

2

0 2,

dvdv

vfR

v

v ⋅⋅⋅= ∫ ∫ ϕϕπ

ϕ

ϕ

1),(

3

8,

1

11

22

1

2

2

1

|cos

sin|(ln

2

1

3

8dvd

vv

vaa

a

R

v

⋅⋅+

−+⋅⋅= ∫ ∫ ϕ

ϕ

ϕ

ππϕ

The above equation cannot be simplified further. Meanwhile the formula (3) is very important in our algorithm, since it can be used to dynamically and adaptively chooses cluster update interval � in the following section. We can obtain expected link lifetime under varied transmission ranges or velocity distributions. Fig. 3 and 4 show the numerical results of expected link lifetime under scenarios with different maximum node velocities (i.e. a in (3)) and transmission ranges (i.e. R in (3)).

Figure 3. Expected link lifetime with varied maximum node speed a (m/s)

Figure 4. Expected link lifetime with varied transmission range R (m)

In the Fig. 3, we can observe that the expected link lifetime decreases with increasing node velocity; while in Fig. 4, the expected link lifetime � is linearly proportional to transmission range R which can also be seen from (3).

(1)

(3)

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IV. SIMULATION RESULTS

In this section, we first introduce basic parameter configuration in simulation; then define two main metric to evaluate the relatively stability of cluster structure. Finally the simulation results are discussed.

A. Configuration

Simulations are conducted on Ns-2.34, and two groups of simulations are considered. The first group studies the influence of maximum node velocity on the two defined metrics with constant wireless transmission range R. Specific parameter configuration for this group of simulations is available in Table 1. The second group studies the impact of varying transmission range, R, on the two metrics considered and simulation parameters configuration is presented in Table 2. Each simulation in each group was conducted 15 times. The results shown in each figure are the average of simulations results obtained from each simulation step.

Table 1. Parameter configuration for Group 1

Number of nodes: 50 (1000x1000)

Transmission range (R) 250 m

Mobility model: Random waypoint

Propagation model: TwoRayGround

Maximum node velocity interval: 5-50 m/s

Hello message broadcast interval: 2 s

WCA [0.6,0.2,0.1,0.1]

Simulation length 600s

Constant T interval 15s

Table 2. Parameter configuration for Group 2

Transmission range (R) 175-400 m

Maximum node velocity interval: 20 m/s

Other parameters: same as that in Table 1

B. Metric definition

In this section, two metrics are defined and their values

are utilized as the important signs when evaluating cluster

stability and communication quality.

• Cluster-head update rate: is defined as the rate of

cluster-head nodes changing status to cluster

member or cluster members changing status to

cluster-head. Frequent cluster-head update result in

larger delays and also can reduce performance by

decreasing packet delivery ratio.

• Member exchange rate: is defined as the rate of

cluster members moving in/out between different

clusters. Higher member exchange rate indicates

that cluster chosen is not very stable, which causes

frequent route disconnection and larger delay.

C. Analysis of Results

For each of the defined metrics, we conduct our simulations to compare the performance of LID, HD, WCA algorithms under constant interval and the adaptive update interval decided by our proposed expected link lifetime based model. In Fig. 5 and 6, we study the first metric which is the cluster-head update rate. We can observe that cluster-head update rate is relatively smaller compared with that

under constant cluster update interval. Also the update rate of different cluster-head election algorithms seems very close when the maximum node speed is high (about 30 m/s) or transmission range R is small (about 175 m). That is because the value of the cluster update interval determined by our proposed model approximates that of constant update interval, which can be shown in the Fig 3 and 4. Moreover when the mobility is high (5 f 35m/s), the value of cluster updater rate obtained by using adaptive cluster update interval is a bit higher than by using constant update interval, however in this case, the member exchange rate can be reduced. This means that adaptive cluster update interval model can achieve better link stability and route stability within clusters.

The second part is the analysis of member exchange rate. Through simulation results in Fig. 7 and 8, we can observer that the member exchange rate under constant cluster update interval and adaptive update rate is very close. In most of case, the cluster member exchange rate under the adaptive cluster update rate decided by our proposed model is a little smaller than that of constant cluster update rate. This is a good proof that adaptive cluster update period decided by expected link lifetime model can enhance the relative stability of cluster structure while improving efficiency of cluster update rate. Therefore, cluster update rate can be reduced and member exchange rate is not affected. It means that the adaptive cluster update approach can reduce unnecessary cluster updates which results in larger communication delay and smaller packet delivery ratio and decreases communication overhead by keeping relatively stable route or link.

Figure 5.Cluster-head update rate with varied maximum node speed

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Figure 6. Cluster-head update rate with varied transmission range

Figure 7. Member exchange rate with varied maximum node speed

Figure 8. Member exchange rate with varied transmission range

V. CONCLUSION

An important drawback of the well-known cluster-head election algorithms is that they lack mechanism for determining the cluster-head update interval adaptively based on the parameters of network, e.g., mobility and transmission range. To address this issue, in this paper we establish an expected link lifetime model which is used to determine reliable cluster update interval under different nodes’ velocity distributions and transmission ranges. Simulation results show that the unnecessarily fast update of the cluster structure with constant update interval is avoided and stability of cluster structure can also be enhanced. Moreover, communication quality in terms of communication delay and packet delivery ratio can be improved.

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