UHEED

An Unequal Clustering Algorithm for Wireless Sensor Networks

E. Ever

, R. Luchmun

, L. Mostarda

, A. Navarra

and P. Shah

CCM Department, School of Engineering and Information Sciences, Middlesex University, London NW44BT, U.K.

Department of Mathematics and Computer Science, University of Perugia, 06123 Perugia, Italy

Keywords:

Clustering, Multi-hop, Power Management, Residual Energy.

Abstract:

Prolonging the lifetime of wireless sensor networks has always been a determining factor when designing and

deploying such networks. Clustering is one technique that can be used to extend the lifetime of sensor networks

by grouping sensors together. However, there exists the hot spot problem which causes an unbalanced energy

consumption in equally formed clusters. In this paper, we propose UHEED, an unequal clustering algorithm

which mitigates this problem and which leads to a more uniform residual energy in the network and improves

the network lifetime. Furthermore, from the simulation results presented, we were able to deduce the most

appropriate unequal cluster size to be used.

1 INTRODUCTION

Wireless Sensor Networks (WSNs) are usually self-

forming, self-healing networks that interact with their

environment to monitor or sense physical parame-

ters such as temperature, acoustics, vibration and hu-

midity among others. They are usually composed of

ﬁxed, spatially distributed sensors and a base station

(BS). The main functions of a sensor node in a WSN

are sensing the environment, processing the raw val-

ues and transmitting them to a nearby node until they

reach the base station. The role of the base station

is to collect all those data received over time, analyse

them and ultimately make decisions based on whether

certain thresholds have been exceeded or not.

WSNs can operate in two modes: continuous peri-

odic sensing and transmission or event-triggeredsens-

ing followed by transmission. To decide on which

mode of operation to use is highly application de-

pendant. WSN, being a relatively new technology,

leads to many challenges, some of which have still not

been met completely. These are the real time, power

management, security and privacy factors (Karl and

Willig, 2005). The energy challenge is considered

to be very important because in most typical us-

ages, WSN nodes are deployed with a limited, non-

renewable source of energy, on which the lifetime of

the network will depend. One of the solutions put for-

ward by researchers is clustering.

In the clustering operation of WSNs, nodes are pa-

rtitioned into a number of small groups called clus-

ters. Each cluster has a coordinator, known as a Clus-

ter Head (CH), and a number of member nodes which

communicate only to their CH in order to transmit

data. Clustering offers some advantages such as data

aggregation done at the CH level, distribution of load

across all nodes since the role of the CH is not per-

manently ﬁxed to one particular node; hence rotation

of CH is present. CH handles two types of trafﬁc:

intra-cluster and inter-cluster communication; the for-

mer being communication between member nodes of

a cluster and the CH and the latter being the transmis-

sion/relay of packets from CH to CH until it reaches

the BS. Inter-cluster communication can make use of

either single hop or multi-hop forwarding (Zhao and

Wang, 2010). In single hop forwarding, each CH di-

rectly transmits to the BS, which can cause excessive

use of energy for the CH furthest away from the BS

making them critical nodes. However, in multi-hop

clustering, nodes nearest to the BS tend to deplete

their energy the fastest since they are burdened with

heavy relay trafﬁc from the rest of the network in ad-

dition to their own intra-cluster trafﬁc share. Those

nodes closer to the BS tend to die earlier than the rest

and as a result, sensing coverage gets reduced and

network partitioning becomes apparent, (Zhao and

Wang, 2010; Li et al., 2005; Xuhui et al., 2009; Kim

et al., 2008) which is deﬁned as the hot spot problem.

Nevertheless multi-hop data transmission from source

to BS is usually more energy efﬁcient due to the na-

185

Ever E., Luchmun R., Mostarda L., Navarra A. and Shah P..

UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks.

DOI: 10.5220/0003804001850193

In Proceedings of the 1st International Conference on Sensor Networks (SENSORNETS-2012), pages 185-193

ISBN: 978-989-8565-01-3

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Residual energy of cluster heads (r=20m).

ture of the wireless channel (Zhao and Wang, 2010).

In this paper, an unequal clustering algo-

rithm (UHEED), based on the HEED algorithm (You-

nis and Fahmy, 2004), is proposed. HEED is a hy-

brid energy efﬁcient distributed algorithm which uses

2 parameters to form equal sized clusters: residual en-

ergy of a node and node degree or the node proximity

to its neighbours. HEED does not make any assump-

tions about network topology, size and distribution or

density of nodes. UHEED creates unequal sized clus-

ters based on the distance of the CH from the BS. The

further away a cluster head is from the BS, the larger

will be its competition radius and hence the cluster

size will be bigger compared to those clusters formed

nearer to the BS. By creating unequal sized clusters,

the amount of intra-cluster trafﬁc is considerably re-

duced for the CH’s nearer to the BS.

We also attempt to ﬁnd the right cluster size based

on distance from the BS. We ﬁrst demonstrate that

the hot spot problem actually exists in equal size clus-

ters (HEED) and use this as a comparison basis with

UHEED. From the analysis of the simulation results;

UHEED effectively mitigates the hot spot problem

of equal sized clusters and thus balances the energy

levels of CHs in the network, provided appropriate

sized cluster have been formed. Our simulation re-

sults also indicate that the network life-time is signiﬁ-

cantly improved when compared with HEED (Younis

and Fahmy, 2004), LEACH (Heinzelman et al., 2000)

and unequal LEACH (Ren et al., 2010) based cluster-

ing algorithms.

The rest of this paper is organised as follows: Sec-

tion 2 presents most recent research within the area of

clustering algorithms in WSNs; Section 3 describes

the HEED algorithm and how we changed it to de-

velop UHEED; Section 4 describes the UHEED al-

gorithm, the radio and the network models used, the

competition radius formula and the simulator built in

Java to test this algorithm. Section 5 presents the sim-

ulation study conducted for different test cases and

a comparison of the results with recent advances in

clustering in WSNs. Finally, the paper is concluded

along with an opportunity to extend the work further

in Section 6.

2 RELATED WORKS

There have been a number of (equal and unequal)

clustering algorithms proposed for wireless sensor

networks in recent years. Existing studies on unequal

clustering approaches are considered in this section.

An unequal clustering model was ﬁrst proposed

in (Soro and Heinzelman, 2005) based on unequal

clustering size (UCS) in order to balance the energy

level or energy consumption of cluster heads due to

heavy inter-cluster relay trafﬁc. Their simulations

assumed that cluster heads were located at prede-

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186

Figure 2: Residual energy of cluster heads (r=50m).

termined locations and involved using heterogenous

node structure. In the case of multi-hop networks, it

was demonstrated that UCS was 10-30 % better than

existing equal clustering models.

In the energy efﬁcient unequal clustering (EEUC)

algorithm (Li et al., 2005), the authors propose

another unequal clustering algorithm where nodes

join clusters of unequal size. However, according

to (Gong et al., 2008), EEUC may produce lone

nodes since the cluster head election is probabilis-

tic. Zhao et al. propose an unequal layered clus-

tering approach for large scale wireless sensor net-

work (ULCA) (Zhao and Wang, 2010) which assumes

a BS at the centre of the grid and creates layers. The

layers closer to the base station are smaller in size

giving the inner layers more residual energy for inter-

cluster trafﬁc. When compared to EEUC (Li et al.,

2005), ULCA has a better network lifetime and the

overhead for clustering the network is much lower be-

cause of the inherent local join and local broadcast

mechanism.

In (Gong et al., 2008), a Multi-hop Routing

Protocol with Unequal Clustering (MRPUC) is pro-

posed which bears similar characteristics of the al-

gorithm mentioned in (Karl and Willig, 2005; Li

et al., 2005). A comparison study conducted in (Gong

et al., 2008) demonstrates that MRPUC outperforms

an equal clustered version of itself by extending the

network lifetime by 34.4%.

In (Heinzelman et al., 2000), the Lower Energy

Adaptive Clustering Hierarchy (LEACH) protocol is

presented. The algorithm elects cluster heads solely

based on probability. No residual energy is taken into

account. Moreover, cluster heads use the single hop

communication model to forward packets to the base

station. A reﬁned version of LEACH can be found

in (Xuhui et al., 2009). The lifetime of the sensor net-

works is maximised by ﬁrst forming unequal clusters,

and then a new threshold algorithm, based on residual

energy, is used to elect cluster heads.

In (Yu et al., 2011), an energy-driven unequal

clustering (EDUC) algorithm is proposed which dis-

cusses the rotation of the role of CH based on either

time-driven CH rotation or energy-drivenCH rotation

approach. In EDUC, it is discussed that the energy-

driven CH rotation is better since a new CH is elected

only when the energy of the current CH has fallen be-

low some set threshold value and since the election is

local, this avoids global topology reconstruction and

downtime. In EDUC unequal clusters are formed by

having unequal competition ranges and each node can

be a cluster head only once during the sensor net-

work lifetime. One drawback of EDUC is that it

uses single-hop inter-cluster transmission and accord-

ing to (Zhao and Wang, 2010), multi-hop is better.

A totally new approach is proposed in (Jaichan-

dran et al., 2010) to mitigate the hot spot problem in

WSNs in which an area S is divided into N number of

UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks

187

Figure 3: Network lifetime for 500x500 grid with 1000 nodes.

cells, each having at least 1 sensor node and the sen-

sor nodes cooperate with neighbour nodes to forward

sensed data to the base station. Sensor nodes near the

base station act as gateway nodes (G nodes) which

tend to die earlier as they have to relay heavy trafﬁc.

The novel approach in (Jaichandran et al., 2010) is to

introduce additional sensor nodes in the gateway area

to help in the relay of trafﬁc to the base station. Al-

though, results indicate that adding an arbitrary num-

ber of G nodes does not improve performance, instead

a calculation of optimal number of G nodes is ﬁrst re-

quired which, then needs to be added to improve and

extend the lifetime of the network.

Recent research in (Bagci and Yazici, 2010) pro-

poses an energy aware fuzzy unequal clustering al-

gorithm (EAUCF) which uses 2 parameters in or-

der to calculate the competition range of the clus-

ter head. From the results obtained, EAUCF out-

performs EEUC (Li et al., 2005), ULCA (Zhao and

Wang, 2010) and LEACH (Xuhui et al., 2009) for all

the performance measures.

In (Pin et al., 2010), the authors propose IEEUC,

which is similar to the study in EEUC (Li et al., 2005),

since it creates unequal sized clusters as they are fur-

ther away from the base station, to mitigate the hot

spot problem. The main difference between IEEUC

and EEUC lies in the competition radius calculation.

IEEUC uses the node degree factor, which is based

on the number of hops to the base station, to calcu-

late the competition radius. In EEUC, even clusters

equidistant from the BS may have different number

of member nodes, either too many or too few. On the

other hand in IEEUC, we do not have this problem.

The authors of (Nam et al., 2010) propose a vari-

ant of the LEACH algorithm by including the residual

energy parameter in the calculation of the threshold T.

In the original LEACH algorithm, a node generates a

random valueU ∈ [0, 1] and if that value is less than T,

it becomes a cluster head and also, if p is the ratio of

cluster heads, a node can be a cluster head only once

during the 1/p round. In (Nam et al., 2010) a new

threshold formula is used to allow a cluster head to

be re-elected based on residual energy and it is shown

that this new threshold increases the network lifetime.

In (Ren et al., 2010), yet another version of LEACH is

presented. Two parameters are used in the setup phase

of electing cluster heads: energy ratio (current energy

to initial energy) and competition radius. Similar to

the study in (Nam et al., 2010), this technique allows

cluster heads with more residual energy to be elected.

In addition, (Ren et al., 2010) attempts to solve the

hot spot problem by creating unequal sized clusters

by varying the competition radius. Smaller clusters

will be formed near the base station while larger ones

will be created as they are further away from it.

In this paper, we introduce an unequal variant of

HEED (UHEED). While HEED deﬁnes an equal clus-

ter size, UHEED makes use of a competition radius

formula which creates unequal clusters. We com-

pare UHEED with the HEED, LEACH and unequal

LEACH algorithms described in (Younis and Fahmy,

2004), (Heinzelman et al., 2000), and (Ren et al.,

2010), respectively.

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Figure 4: Network lifetime for 100x100 grid with 300 nodes.

3 FROM HEED TO UHEED

Hybrid Energy Efﬁcient Distributed (HEED) is a dis-

tributed clustering algorithm in which two parameters

are used to determine the eligibility of a node to be-

come a cluster head. Since prolonging the network

lifetime is the main goal, residual energy is used as the

ﬁrst parameter, which allows those nodes with higher

residual energy to become cluster heads, thus balanc-

ing the overall energy of the network. The second

factor intra communication cost, which can be clus-

ter density, allows a node to join a CH with the least

number of nodes so as to reduce the load of the intra-

cluster trafﬁc on the CH. HEED does not make any

assumption about the network such as density or size.

The HEED algorithm is run by each node and is

in 3 stages:

In the Initialisation stage, an initial percentage of

CH among N nodes is set (C

prob

) which has no impact

on the ﬁnal number of CH to be formed at the end of

the algorithm and as such is only necessary to limit

the initial number of broadcast. Each node calcu-

lates its probability (CH

prob

) of becoming a CH. The

prob

is not allowed to fall below a certain threshold

min

in order for the algorithm to terminate in O(1)

iterations.

In the Repeat stage, those nodes that could not join

a CH, elect to become a tentative CH and send an an-

nouncement. This phase iterates itself and each time

the CH

prob

value doubles until it becomes 1. During

the iterations, the node can also decide to ﬁnd a CH

instead of becoming one itself.

In the Finalise stage, a node decides its status to

become a ﬁnal CH for the current round or joins the

least cost cluster.

Once the clustering process is over, the network

enters a data transfer phase. Clustering will occur

again after some time in order to rotate the role of the

CH and thus balance the energy levels in the network.

In this phase, each node of a cluster forwards data to

the CH which in turn forwards the aggregated data of

its members in a multi-hop fashion (CH to CH) until

the base station (BS) is reached.

The problem here is that those nodes nearer to the

BS deplete their energy faster than those located fur-

ther away. This excessive inter-cluster trafﬁc near the

BS causes the nearby nodes to die earlier reducing the

overall network lifetime.

In UHEED, we attempt to solve the problem of

nodes nearer to the BS dying earlier. In HEED, each

CH uses the same competition radius, irrespective of

its distance from the BS, hence on average having the

same number of nodes. UHEED uses the competition

radius formula from EEUC (Li et al., 2005), which

UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks

189

creates smaller clusters as the BS is neared.

This overall can improve the network lifetime for

multi-hop WSNs which will be shown using simula-

tions. This allows less intra-cluster trafﬁc for the CHs

near the BS and hence more energy is allocated to the

inevitable higher load of relay trafﬁc.

4 UHEED

In this section, the proposed algorithm is described in

detail. Although uneven clustering methods have ex-

tensively been discussed in the related works, the un-

even clustering approach have not been used together

with the well known HEED algorithm. It is necessary

to analyse the system parameters in order to provide

right cluster sizes for the HEED algorithm with un-

even cluster sizes (UHEED).

4.1 Network Model

The network model introduced uses a two dimen-

sional representation of the environment and the

nodes are deployed randomly following a uniform

distribution. We make the following assumptions

about nodes: (i) all nodes are homogeneous in terms

of energy, communication and processing capabili-

ties;(ii) each node is identiﬁed with a unique ID; (iii)

nodes can transmit at various power levels depending

on the distance of the receivers; (iv) nodes are not mo-

bile that is they remain stationary after the uniformly

distributed deployment process; (v) communicating

nodes can establish the distance among them

; (vi)

all nodes know their distance from the base station.

The BS is located away from the sensing grid with

no energy concerns at all, and it is considered to be a

node with enhanced communication and computation

capabilities. The BS is not mobile. The data captured

in a cluster is highly correlated, therefore it can be ag-

gregated before being transmitted to the base station.

A network operation model similar to that of

(Younis and Fahmy, 2004) consisting of multiple

rounds is used. A round starts by triggering the

clustering mechanism and after clusters have been

formed, the network goes into a data exchange

phase. This includes intra-cluster communication

where each sensor node sends exactly one message

to its cluster head and inter-cluster communication

where each aggregated data is sent by the cluster head

to the BS (multi-hop data transmission among cluster

Usually nodes estimate the approximate distance by the

strength of the signal received, since the transmission power

level is known (unless there is multi-path fading problem).

heads is performed). The round ends when all aggre-

gated data sent by the cluster heads are received at the

base station.

The radio model employed uses both the free

space and the multi-path channel model and assumes

error-free communication links.The simulation pa-

rameters used are similar to those in (Younis and

Fahmy, 2004). A sensor spends E

elec

= 50nJ/bit

(Younis and Fahmy, 2004) to run the transmitter or

receiver circuitry. The energy spent by the transmitter

ampliﬁer E

will depend on the distance d between

the sender and the receiver: E

= E

assuming a free

space model when d < d

and E

= E

assuming

a multipath model when d ≥ d

, where d

= 75m is

a constant distance. E

= 10pJ/bit/m

and E

0.0013pJ/bit/m

. In order to transmit a k-size packet

over a distance of d using the above radio model, the

amount of energy consumed for transmission E

, can

be calculated as:

= (E

elec

× k) + (E

× k × d

), (1)

where, n = 2 for the free space model and n = 4 for

the multipath model. The amount of energy E

spent

to receive a k-bit size message is:

= (E

elec

× k) (2)

4.2 Simulation Model

UHEED is based on the HEED algorithm (Younis

and Fahmy, 2004), however, unlike HEED it uses the

competition radius formula given below, in order to

create unequal clusters. Since the lifetime of the lead-

ers closer to the BS is more critical, the clusters fur-

ther away have larger sizes compared to the clusters

close to the BS.

comp



1− c



max

− d(s

,BS)

max

− d

min



comp

(3)

comp

is the maximum competition radius which

is predeﬁned. In this work it is deﬁned as the diagonal

distance of the sensing grid area divided by 10.

max

and d

min

are the maximum and minimum dis-

tance between sensor nodes and the base station; c is

a constant coefﬁcient between 0 and 1.

For the simulation we perform various consecu-

tive rounds (explained in Section 4.1). These are per-

formed until the network is dead. The network is

considered dead when all nodes have depleted 99.9%

of their energy. Network lifetime is based on rounds

rather than clock time, and the simulation model used

is event triggered. In other words, the simulation

clock is always set to the time of the next event un-

til the network dies.

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190

Figure 5: Network lifetime for 200x200 grid with 400 nodes.

Figure 6: Residual energy comparison unequal leach vs UHEED.

5 SIMULATION STUDY

In this study, a simulation program is employed in or-

der to evaluate the proposed UHEED algorithm. The

simulation program is ﬁrst validated by using the nu-

merical results presented in the existing literature

(Younis and Fahmy, 2004). For the validation, a grid

with dimensions 2000 × 2000 metres is considered

and 1000 nodes are deployed. The cluster radius is

taken from 20m to 400m and each experiment value

is obtained for an average of 100 runs. The numerical

results shows that our implementation of the HEED

UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks

191

algorithm exhibit similar behaviour as in(Younis and

Fahmy, 2004).

5.1 Existence of Hot Spot Problem in

Equal Size Clusters

The results presented in this section are related to the

HEED equal clustering algorithm. More speciﬁcally,

the HEED algorithm has been run for one round, and

ﬁgures 1 and 2 clearly show that cluster heads nearer

to the base station have lower residual energy com-

pared to that of cluster heads further away. The results

presented are for cluster radiuses of 20m and 50m,

however the behaviour is the same for different clus-

ter sizes as well.

5.2 Network Lifetime

In this section the lifetime of UHEED is evaluated by

running simulations with different parameters of grid

size and number of nodes.

When comparing UHEED and HEED the same

parameters from (Younis and Fahmy, 2004) have been

used. The base station is located at lower right side of

the grid, E

elec

= 50nJ/bit, E

=10pJ/bit/m

, num-

ber of nodes 300 to1000 and the initial Energy = 2J.

More speciﬁcally, we have used two settings: (A) a

grid size of 500m x 500m with 1000 nodes; (B) a grid

size of 100m x 100m with 300 nodes. We have en-

sured there is the same number of cluster heads in

both UHEED and HEED. This ensures that the two

algorithms perform the same number of hops in the

inter-cluster communication. Figures 3 and 4 show

the best and worst case scenario, for network life time,

for UHEED and HEED for:

Case(A): The results show that UHEED outper-

forms HEED in the best scenario with c = 0.8 for

UHEED and r = 35m for HEED; but for the worst

case, UHEED and HEED both follow a similar pat-

tern with the last node dying after around 500 rounds.

In the best case scenario, the last node for UHEED

dies after round 3325 and for HEED, it dies after 900

rounds which is evident in Figure 3. Overall, there is

a 250% increase in network lifetime for UHEED in

the best case scenario.

Case(B): UHEED outperforms HEED in both the

worst and best scenarios. In the best case scenario, the

last node in UHEED dies after 4750 rounds, where

as, in HEED, it dies after 3340 rounds, which can be

observed in Figure 4. Overall, there is an increase of

more than 40% network lifetime for UHEED in the

best case scenario.

When comparing UHEED, LEACH and unequal

LEACH the same parameters from (Heinzelman et al.,

2000) and (Ren et al., 2010) have been used. More

speciﬁcally, the base station is outside the grid, E

elec

= 50nJ/bit, E

=10pJ/bit/m

, number of nodes 400

and the initial Energy = 0.3J.

UHEED is compared to Unequal LEACH (Ren

et al., 2010) and results are shown in Figure 5. The

best and worst case for UHEED and Unequal LEACH

are considered. For Unequal LEACH we have used

the parameters found in (Ren et al., 2010) with a grid

size of 200 by 200 and 400 nodes. In order to com-

pare UHEED to Unequal LEACH, the data exchange

phase of UHEED has been modiﬁed to a single-hop

data transmission since Unequal LEACH is a single-

hop protocol.

In the simulation study between UHEED and Un-

equal LEACH, it can be observed from Figure 5 that

UHEED outperforms Unequal LEACH by a factor of

more than 100% when network lifetime is considered.

Figure 6 shows the residual energy for UHEED,

Unequal LEACH and LEACH with respect to First

Node Dead (FND) and Half Node Alive (HNA). The

residual energy is obtained by calculating the residual

energy of the entire network. As can be seen from

the Figure 6, in UHEED after the ﬁrst node is dead,

the overall residual energy level for all the cases from

c = 0.1 to c = 0.9 is much higher than LEACH or Un-

equal LEACH. Also, it is observed that when half of

the nodes are alive, the residual energy level in case

of UHEED is comparatively higher than LEACH and

Unequal LEACH. Hence, from the results seen in Fig-

ure 6 for residual energy levels and Figure 5 for the

network lifetime, it is seen that the lifetime degrada-

tion of UHEED is graceful. This means that not many

nodes die very quickly and then the network has very

few nodes which are alive for a longer duration, but,

as observed in Figure 6, after half the number of nodes

are dead in the case of UHEED, there is still higher

residual energy level availablefor the rest of the nodes

to continue operation with respect to LEACH and un-

equal LEACH.

It is worth mentioning that, for UHEED we have

used HEED together with the algorithm employed for

EEUC to compute the size of the clusters. More

speciﬁcally, the HEED clustering method has been

improved by implementing it together with the com-

petition radius formula of EEUC. The simulation re-

sults clearly show that this combination performs bet-

ter than HEED, LEACH and unequal LEACH. How-

ever, the EEUC algorithm was not considered for

comparison. In fact, in (Li et al., 2005), the numerical

results presented for the number of alive sensors show

that EEUC has very little improvement compared to

the HEED algorithm. Furthermore, when the energy

consumptionsare compared, results of two algorithms

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192

cross each other and they are better than one another

for various time intervals.

6 CONCLUSIONS

In this paper, we proposed an unequal cluster-

ing algorithm for wireless sensor network based on

HEED (Younis and Fahmy, 2004). A common prob-

lem in equal based cluster in sensor networks is the

hot spot problem. Our approach to provide a solution

was ﬁrst to implement the HEED algorithm, show

that the hot spot problem really exists, and ﬁnally at-

tempt to mitigate it by creating UHEED. This algo-

rithm uses a competition radius formula which cre-

ates unequal clusters as they are further away from

the base station. This effectively allows more inter-

cluster or relay trafﬁc and less intra-cluster commu-

nication for nodes nearer to the base station, hence

preventing their early death. Simulation performed

on the UHEED algorithm demonstrated that the life-

time of the network was increased in all test scenarios

compared to HEED, LEACH and Unequal LEACH.

An interesting study also conducted was regarding

the value of the constant c in the competition radius

formula. Simulation results showed that a value of

c = 0.8 achieved up to almost 250% improvement in

the network lifetime when compared to HEED and

almost 100% improvement when compared to un-

equal LEACH. During the course of this investiga-

tion, we found out that values like ﬁrst node dead

(FND), half node alive (HNA) and last node dead

(LND) are somewhat affected by the density of the

network. Hence, our future work will be to investigate

the relationship between the network density and the

aforementioned parameters. A mathematical model

will also be developed in order to support the simula-

tion results presented in this paper.

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