INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL
ISSN 1841-9836, 12(1):90-102, February 2017.

Initial Phase Proximity for Reachback Firefly Synchronicity in
WSNs: Node Clustering

M. Misbahuddin, R.F. Sari

Misbahuddin Misbahuddin*
Department of Electrical Engineering, Faculty of Engineering,
Universitas Indonesia, Depok, 16424, Indonesia
*Corresponding author: misbahuddin@ui.ac.id

Riri Fitri Sari
Department of Electrical Engineering, Faculty of Engineering,
Universitas Indonesia, Depok, 16424, Indonesia
riri@ui.ac.id

Abstract: Synchronicity is one of the essential basic services to support the main
duties of Wireless Sensor Networks (WSNs). Synchronicity is the ability to arrange
simultaneously collective actions in WSNs. A high-rate data sampling to analyze
the seismic structure and volcanic monitoring is the important applications requir-
ing a synchronicity. However, most of the existing synchronicity algorithm is still
executed in a flat network, so that it requires a long time to achieve a synchronous
condition. To increase the convergence rate, the synchronicity can be executed con-
currently through a clustering scheme approach. In this work, the such scheme is
called as the Node Clustering based on Initial Phase Proximity for Reachback Firefly
Synchronicity (NCIPP-RFS). The NCIPP-RFS solves in three steps: (1) constructing
the node clustering, (2) intra-cluster synchronicity, and (3) inter-cluster synchronic-
ity. The NCIPP-RFS method is based on the firefly-inspired algorithm. The fireflies
are a species in the natural system, which are able to manage their flashing for syn-
chronicity in a distributed manner. The NCIPP-RFS was implemented in NS-3 and
evaluated and compared with Reachback Firefly Algorithm (RFA). The simulation
results show a significant increase in the convergence rate. The NCIPP-RFS can
reach a convergence time shorter than the RFA. In addition, the NCIPP-RFS was
compared in the various numbers of clusters, where the least number of clusters can
reach the fastest convergence rate. Finally, it can also contribute significantly to the
increase of the convergence rate if the number of nodes is greater than or equal to 50
nodes.
Keywords: wireless sensor network, synchronicity, node clustering, phase proximity,
firefly-inspired algorithm.

1 Introduction

Wireless Sensor Networks (WSNs) is a set of spatially distributed autonomous sensor nodes
that could to interact locally, and some nodes of them interact with a sink node or Base Station.
A sensor node in WSNs is a device that has the limitations in the processing unit, communica-
tion resources, and sensing capabilities. The WSNs has been implemented in various applica-
tions for environmental monitoring, condition sensing, and process automation such as battlefield
surveillance, habitat monitoring, coordinated target detection and localization, chemical attacked
detection, ubiquitous healthcare, and home automation. The duties of the WSNs can be exe-
cuted properly when it is supported by robust basic requirements such as time synchronization,
synchronicity, self-configuration, and self-localization. For example, time synchronization is ex-
tremely required to ensure the high accuracy measurement for an event-driven measurement
application in an area where an event is detected [1]. Synchronicity inspired by the biological

Copyright © 2006-2017 by CCC Publications



Initial Phase Proximity for Reachback Firefly Synchronicity in WSNs: Node Clustering 91

principle of a firefly is adopted by [2] for handling a dynamic node clustering in data readings.
Self-configuration characteristic for a routing protocol of WSNs developed by [3] aimed at dis-
covery the best route for delivering information with minimum energy consumption. Finally,
self-localization is a basic feature in WSN for finding out the location of unknown nodes because
GPS that is usually used to find the location of a device is not suitable for WSNs [4].

Many phenomena exist in the natural system around us, which have inspired many scientists
to solve various problems within the engineering field or the specific problems of WSNs. The
basic requirements of WSNs such as synchronization and synchronicity need a self-organized way.
Both are a mutually complementing requirement of WSNs. The synchronization is an ability to
align the time of node’s internal clock referring on the global time to perform a simultaneously
collective action. On the other hand, the synchronicity is a way to align the phase of the
internal clock of node to conduct a synchronously collaborative action. The application of the
synchronicity in WSNs is very useful as a simple sensor network coordinator in sampling the
high data rates such as seismic analysis of structure [5], and volcanic monitoring [6]. Moreover,
is also used as a scheduling mechanism of the node duty cycles in order to save energy, so that
all nodes in a network can wake up at the same time.

There are some challenges of the robust synchronicity requirements, i.e. simple, fast, low
energy consumption, self-configuration and high scalability. In this study, we propose a new node-
clustering synchronicity method using a firefly-inspired algorithm to address three synchronicity
requirements in simple, fast,and self-configured way.

Clustering in the WSNs is often used in some applications because it is extremely useful
for various purposes. The purposes are divided as primary and secondary [7]. The first purpose
represents the objectives that are the most substantial in the node clustering such as scaling, fault-
tolerance, data aggregation, load balancing, network topology stabilization, network lifetime
extension. Instead, the second purpose points out the objectives that are not highly important,
and they are indirectly achieved by clustering node such as increasing connectivity, reducing
routing delay, avoiding collision, and utilizing sleeping schemes. Therefore, in this research we
propose the node clustering model as a new approach to synchronize the node in the network,
where the node clustering is an extremely important requirement to relieve the load of the
network to reach the synchronicity.

Our NCIPP-RFS approach provides two main contributions that consist of (i) in clustering,
there are some node subsets that perform an intra-cluster synchronicity in parallel, continued
to an inter-cluster synchronicity. The total of periods required to execute both synchronicity
processes is smaller than that of without clustering. This emphasizes that our approach is faster
than the non-clustered synchronicity algorithm. (ii) Self-configuration is an important problem
in the distributed system for executing both its primary duties and basic function as well as
for the synchronicity function. In fact, there are many natural phenomena around us in which
their population can organize themselves toward a synchronicity state, in which one of them is
the firefly. The behavior of firefly flashing has inspired a number of researchers to create the
firefly-inspired synchronicity algorithms [8]-[13]. In this research, we utilize the synchronicity
algorithm developed by [10] for intra-cluster synchronicity.

The remainder of this paper is organized as follows: Section 2 presents literature review
related with the firefly-inspired synchronicity. Section 3 describes the approach used to solve the
synchronicity requirements. Section 4 presents the simulation results to show the performance
evaluation. Finally, Section 5 concludes this paper and ideas for future work.



92 M. Misbahuddin, R.F. Sari

Phase1

1

0

ε
f(φ1)+ε

f(φ1)

∆φ

φ1 φnew

Figure 1: The state function of M&S model

2 Firefly-inspired Synchronicity

In the natural system, there are several synchronicity phenomena that have been observed by
many researchers to understand the mutual interaction of a population toward a self-organized
synchronicity without a notion of time. Examples of the natural synchronicity include circadian
rhythm [14], pacemaker cell of the heart [15], and synchronous flashing of fireflies [16].

Fireflies are one of the species around us, which can interact mutually to fire synchronously.
This phenomenon is one of the most spectacular self-organized synchronicity, which was imitated
as a firefly-inspired synchronicity algorithm. The population of the fireflies can be analogized as
a population of the pulse-coupled biological oscillators (PCO) that was introduced by Mirollow
and Strogatz [8], which is known as the M&S model. However, this model cannot be implemented
directly in a real WSNs because it still uses some ideal assumptions that are not in accordance
with the realistic wireless communication [17]. The assumptions are: (1) the characteristic of
oscillators is identical, (2) the node’s firing event occurs and other nodes respond instantaneously.
(3) Node’s computations are conducted perfectly and immediately.

The M&S model presents a basic concept of the firefly-inspired synchronicity algorithm,
which is described through two pulse-coupled oscillators. Each oscillator is characterized by
a monotonically increasing and concave down function representing a firing function as shown
in Figure 1. When the oscillator’s phase increase monotonically to reach a threshold, it fires
and falls immediately to zero. The mutual interaction occurs between two oscillators when an
oscillator fires and sends a firing message to another oscillator that causes another oscillator
responds by adjusting its own phase toward firing.

As a result, it will jump to a new phase φnew with coupling strength ε. The new phase can
be calculated using the following equation [6]:

φnew = min(1,f
−1(φ) + ε)) (1)

where f(φ)=1
b
.ln(1+[eb-1].φ), and b is a dissipation parameter.

The essential weakness of the M&S model, which violates the practical WSNs, is when re-
sponding immediately a firing message that is sent by its neighbor nodes without considering an
unpredictable delay because of the channel contention prior to message transmission. Therefore,
the Reachback Firefly Synchronicity (RFA) developed by Werner-Allen et al.[10] overcomes the
realistic wireless communication problems of the PCO model. Three problems handled by the
RFA are related the wireless communication and one problem of the load computation. They are



Initial Phase Proximity for Reachback Firefly Synchronicity in WSNs: Node Clustering 93

the timestamping message, the notion of pre-emptive message staggering, reachback response,
and simplified firing function. The amount of time a message that was delayed before being
broadcasted can be estimated using the low-level timestamping. The oscillator of the PCO
model that reacts shortly to each firing event can be overcome utilizing the notion of reachback
response, that is, all firing events as the phase jumps are recorded and are calculated once at the
end of each period that is used to jump at the beginning of the cycle. The wireless contention, in
the worst case, can be avoided employing the notion of pre-emptive message staggering. Finally,
the computation complexity is reduced by simplifying the firing function. The detail description
of four ways to be applied in the real wireless network are as follows:

1. A node experiences a delay between when it reaches a firing and when it starts to transmit
a message. The delay can be estimated using MAC-layer timestamping. The measurement
of the MAC-delay can be started using a trigger to record it in the header of the outgoing
message when the message is transmitted. In the receiver node, the information is used to
determine the proper firing time by calculating the difference between the MAC-delay and
the reception time of the message.

2. In the M&S model, a node responds immediately to each firing message from other nodes.
In contrast, the RFA uses the notion of reachback response to record each received firing
message and calculates them as the phase jumps once at the end of each period, which is
used as a jump at beginning of the next cycle as illustrated in Figure 2. This approach will
be discussed in more detail in subsection 3.2.

3. In the M&S model, perhaps many nodes transmit the firing message together when they
fire simultaneously. This event is the worst case of the CSMA scheme because they can
cause channel collisions. To avoid such a worst case and to control the extent of the message
delay, the RFA model introduced a notion of pre-emptive message staggering by adding a
random transmission delay to the firing message at the application level of the node. The
delay value is assigned to a uniformly random value between 0 up to a constant D before
node fires. Furthermore, a random waiting time W (where D<W<<T) is added for a node
that has fired to receive the delayed messages before processing the firing message in the
queue.

4. The M&S model’s firing function can be simplified to make a faster calculation of firing
response. Therefore, the RFA algorithm reduces the computation complexity by simplifying
the firing function. The new phase obtained after receiving a firing message at phase φ1 is
φ2 = φ1 + εφ1 or φ2 = (1 + ε)φ1.

3 The Proposed Method of Node Clustering Based on Phase
Proximity for Firefly-inspired Synchronicity

The challenges of synchronicity in the wireless sensor network are how to increase the con-
vergence rate, and to handle the latency delay in wireless communication. Both challenges aim
to reduce the power consumption. The model proposed by Sun Yi et al. [18] is a centralized
node clustering mechanism through sorting the phase value of nodes. This model is difficult
to be implemented in WSNs because they require a node as coordinator to gather the phase
value of all nodes. Furthermore, the coordinator has to be able to organize the phase order of
all nodes in order to construct the node clustering. This research proposes a new decentralized
node clustering mechanism based on original phase proximity of nodes where the nodes in the



94 M. Misbahuddin, R.F. Sari

t1 t2 time

1

∆φ1

∆φ2

φ1

φ2

φm−1

φm

Phase

T

t1 t2 time

1

φ1

φm−1

Phase

t3

∆φtot

(a)

(b)

Figure 2: Phase jump in (a) M&S model, and (b) RFA model

φC1
φC2

φC3

Cluster 1
Cluster 2

Cluster 3

Figure 3: Illustration of the phase cluster for three clusters

network construct the clusters through a self-configuration way. This approach is called Node
Clustering based on Initial Phase Proximity for Reachback Firefly Synchronicity (NCIPP-RFS).

Generally, synchronicity steps of the NCIPP-RFS are similar to the CFSA method: cluster-
construction, intra-cluster synchronicity, and inter-cluster synchronicity. However, unlike CFSA
method, NCIPP-RFS uses a new approach in the cluster construction. The clusters are con-
structed based on the original phase value proximity of nodes that are organized in a self-
configuration way without assistance a node coordinator. Moreover, the inter-cluster synchronic-
ity is added with a Late Sensitive Window (LSW) factor to avoid the overshoot of jump in a
group or cluster.

3.1 Construction of the Clusters Based on Phase Proximity

Node Clustering Based on Initial Phase Proximity (NCIPP) is a simple algorithm used for
clustering in WSNs. This algorithm partitions the nodes into k clusters. The node clustering is
constructed using the following steps:

1. Arbitrarily assign k points as the center clusters, k being the number of clusters desired.
The assignment of the center point of the cluster is intended to ensure that each node only



Initial Phase Proximity for Reachback Firefly Synchronicity in WSNs: Node Clustering 95

exists in a cluster. Next, each node will internally assign its own cluster by calculating a
nearest distance to every center point of the cluster (φc1, φc2, φcj, ...,φck). The distance
can be computed by the following Euclidean equation:

dφij =
√
φ2i −φc

2
j (2)

where dφij is the distance between the ith node’s phase φi and the jth center point of
the cluster φcj, and the node’s phase is φi∈[0 1]. Each node in the network executes the
cluster-initialization function internally to determine its own cluster. The pseudo code is
shown in Algorithm 1 in which the cluster number can be obtained through the minimum
value of the clusterArray. The center points are determined based on the number of clusters
k that is desired, where they are assigned through a balanced division of the distribution
of phase values (between 0 and 1) in k groups. For illustration, let’s assume that there are
three clusters (k = 3) where the center point of the clusters are denoted by φc1 = 0.167,
φc2 = 0.5, and φc3 = 0.833 respectively. When the uniformly distributed phase values are
mapped in a circle window in which the zero and one phase coincide in a point, the nodes
will form three clusters as shown in Figure 3.

2. Each node provides an internal data structure called neighborNodes to store the source
address (srcAddr) of its neighbor nodes in the same cluster and has a cluster number
variable (noCluster).

3. The node clustering is executed by two main functions, i.e., the BroadcastIDCluster and
the RecieveIDCluster. The pseudo codes of the both functions are shown in Algorithm
2. The BroadcastIDCluster is a function to broadcast the source address, and the cluster
number of the transmitter node to other nodes in the same cluster. To avoid simultaneous
transmission in the periodic broadcast, it is added with a random interval delay and a
beacon expire timer in the BroadcastIDCluster. On the contrary, the ReceiveIDCluster is
a function to receive the broadcasting messages. If the sender’s cluster number is equal
to the receiver’s cluster number, the receiver node stores the sender’s address and cluster
number into its data structure, the neighborNodes. This means that they are in the same
cluster.

Algorithm 1 Cluster initialization
ClusterInitilization()
Assign the number of cluster k
Assign the center point of the clusters (φc1, φc2, ...,φck )
for j:k do

clusterArray[j] ←dφij
noCluster ← index of min(clusterArray)

3.2 Intra-cluster Synchronicity

After all logical clusters based on the initial phase are constructed. Every logical cluster can
start to perform a synchronicity concurrently. There are two firefly-inspired algorithms that can
be used to perform the synchronicity, i.e., M&S and RFA model. The M&S model still uses a
simple algorithm without considering the delay effect of real communication in WSNs. A firing



96 M. Misbahuddin, R.F. Sari

Algorithm 2 Node Clustering
BroadcastIDCluster(srcAddr, noCluster)
Send(srcAddr, noCluster)
Delay(interval+rand())
BeaconExpireTimer ()

ReceiveIDCluster(srcAddr, noCluster)
if (noClusterOfSender=noCluster) then

neighborNodes.srcAddr ← srcAddr
numCluster ← numCluster+1

message that is sent by a node is responded instantaneously by its adjacent nodes regardless of
its unpredictable delay because of the delay latencies [8]. For illustration, let’s assume that in a
cluster, node x receives a firing message from another node y at time t1 or phase φ1. In response,
the node x adjusts its oscillator’s phase by increasing slightly to a new phase φ2 that can be
computed through the following firing function:

φ2 = min(1, (1 + ε)φ1) (3)

Every time node x receives a firing message from any node in same cluster; it calculates its
phase jump using the following equation:

∆φi = min(1, (φ2 −φ1)) = min(1,εφ1) (4)

To address the delay latency in a real network, a reachback response mechanism of the RFA
model is a proper choice. In this model, the node x does not jump every time it receives a firing
message, but it always stores its entire phase jumps until the period end. Furthermore, the sum
of phase jumps in the previous period will be used to jump at the beginning of next period.
Figure 2a illustrates the M&S model where the node x receives two firing messages at time t1
and t2 respectively. In contrast, in the RFA model node x will jump at time t3 in the beginning
of the next period as shown in Figure 2b. The sum of phase jumps can be calculated through
the following equation:

∆φtot =
n∑
i=1

∆φi (5)

where n is the number of firing events received in a period.

3.3 Inter-cluster Synchronicity

After all clusters achieve the synchronicity condition, every cluster can be considered as a
converging node group. It can be assumed as a firing node if its phase comes near to one. In this
case, the RFA mechanism can still be used to reach the synchronicity condition for all nodes in
the network. The synchronicity condition can be completed through sending the firing message
among the node groups. The number of node groups will decrease, which are caused by the
merging of a few of the node groups into one group and finally there is only one group as the
synchronicity condition of the network.

In a period the group Gx will receive the firing messages from the firing group Gy equal to
the number of the Gy’s members. The sum of phase jumps of group Gx is as follows:

∆φ(tot),Gx =

ny∑
i=1

∆φi,Gx (6)



Initial Phase Proximity for Reachback Firefly Synchronicity in WSNs: Node Clustering 97

where ny is the number of Gy’s members. This enlarged the sum of phase jumps of group
Gx, so that it can cause an overshooting jump in the nodes of the groups Gx. To avoid this
event, the RFA model is added a Late Sensitive Window (LSW) introduced by [11], where the
window inhibits the response of node against the firing messages falling outside of the window.
When group Gx achieves phase φ = 1 (or t = T), it fires and adjusts its phase based on the
sum of phase jump in the previous period and jumps in the beginning of next period. The phase
jump of the group Gx is calculated by the following equation:

∆φGx =




0 φ ≤ LSW and �φ ≥ 1
εφ φ ≥ LSW and �φ ≤ 1
1 otherwise.

(7)

4 Simulation Results

The performance of both RFA and NCIPP-RFS method is evaluated using a network simu-
lator NS-3 to obtain the convergence rate. A total of 40 simulations were run for each coupling
strength in all scenarios. Hence, results presented in Figure 4, 5 and 6 for each coupling strength
show the average values and the corresponding 95% confidence interval. The network topology
uses a mesh type in a variety of sizes of 25, 50, 75, and 100 nodes spread uniformly in a con-
stricted rectangular area sized 1000 x 1000 m2. Furthermore, the network is designed to represent
a realistic environment to evaluate the convergence rate of the synchronicity. Several simulation
parameters used to evaluate the convergence rate of the synchronicity are varied in the simulation
both RFA and NCIPP-RFS model as shown in Table 1. The coupling strengths (ε) are varied in
the range of 0.01 through 0.1 for cluster 2, 3, 4, and 5. The metric evaluation used to measure
the convergence rate is the number of periods required to reach the synchronicity condition.

Table 1: Simulation parameters

Parameter Value
Oscillating period T (milliseconds) 100
Phase of oscillator φ φ ∈ [0,1]
Phase rate dφ

dt
= 1
T

0.01
Coupling strength � � ∈ [0.01, 0.1]
The number of nodes 25, 50, 75, 100
The number of clusters 2, 3, 4, 5

Figure 4 shows a set of charts that evaluates the influence of the coupling strength parameter
on the number of periods in both the RFA and the NCIPP-RFS. It presents some comparison
of the convergence rate between the RFA and the NCIPP-RFS with various number of clusters.
It can be seen that the convergence rate of the RFA is comparable to the NCIPP-RFS in 25
nodes. However, at the number of nodes, 50, 75 and 100, the convergence rate of the RFA is much
slower than the NCIPP-RFS, especially in the lower coupling strength of 0.01 through 0.05. This
happens because of the influence of the clustering way in the less the number of nodes to increase
the convergence rate does not contribute significantly. Actually, the such way is to synchronize
some groups of nodes in a network concurrently to reduce the load of the network. If node has
not been synchronized in the network, all other nodes must keep the effort to synchronize it.
Therefore, the clustering method of 25 nodes in the RFA results in the convergence rate similar
to the NCIPP-RFS. Otherwise, in the larger the number of nodes (50, 75, and 100 nodes), the



98 M. Misbahuddin, R.F. Sari

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

25 Nodes

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

10

20

30

40

50
RFA
NCIPP−RFS, 2 Clusters
NCIPP−RFS, 3 Clusters
NCIPP−RFS, 4 Clusters
NCIPP−RFS, 5 Clusters

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

50 Nodes

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

10

20

30

40

50

60

RFA
NCIPP−RFS, 2 Clusters
NCIPP−RFS, 3 Clusters
NCIPP−RFS, 4 Clusters
NCIPP−RFS, 5 Clusters

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

75 Nodes

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

20

40

60

80
RFA
NCIPP−RFS, 2 Clusters
NCIPP−RFS, 3 Clusters
NCIPP−RFS, 4 Clusters
NCIPP−RFS, 5 Clusters

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

100 Nodes

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

20

40

60

80

100 RFA
NCIPP−RFS, 2 Clusters
NCIPP−RFS, 3 Clusters
NCIPP−RFS, 4 Clusters
NCIPP−RFS, 5 Clusters

Figure 4: The comparison of the convergence rate between the RFA and the NCIPP-RFS model
when the number of clusters is varied for 25, 50, 75, and 100 Nodes.



Initial Phase Proximity for Reachback Firefly Synchronicity in WSNs: Node Clustering 99

convergence rate of the NCIPP-RFS declines along with the increasing number of nodes. The
influence of the clustering method in synchronicity that contributes significantly to the increase
in the convergence rate is in the larger the number of nodes. Finally, the number of nodes which
are greater than or equal to 50 nodes generates the best performance of the NCIPP-RFS among
all scenarios when the number of node is varied.

A set of charts presented in Figure 5 is to discover the best performance among all scenarios
when number of clusters is varied in the NCIPP-RFS model. The chart on the top left shows
the convergence rate of the NCIPP-RFS in the two-clusters scenario. It shows that the number
of periods declining rapidly along with the gradual increase of the coupling strength value in all
scenarios of the number of nodes. This means that the NCIPP-RFS of two clusters will show
a better performance. This is in line with the aim of the adjustment of the coupling strength
parameter to increase the convergence rate gradually. Next, in the chart for the experiment with
three clusters, the convergence rate slows down along with the rising number of nodes to 75 nodes,
but it can increase the convergence rate in 100 nodes. Similarly, the larger the number of clusters
(4 and 5) the NCIPP-RFS is slower than in the scenario for two clusters. This happens because
the increase of the number of clusters causes the increase of the number of periods to reach a
convergence in the inter-cluster synchronicity, so that they will slow down the convergence rate
of the synchronicity process in the network. Therefore, the best performance of the NCIPP-RFS
among all scenarios of the number of clusters is the scenario of two clusters.

An important problem that needs to be understood is the caution of the highly different
convergence rate to the others as shown in Figure 5. They are 50 nodes with coupling strength
of 0.01 in two clusters, 75 nodes with coupling strength of 0.01 in three clusters, 25 nodes with
coupling strength of 0.04 in four clusters, and 25 nodes with coupling strength of 0.01 in five
clusters. These problems are caused by the process of inter-cluster synchronicity that is hard to
reach a synchronicity percentage of 100 percent as shown in Figure 6. It can be seen that the
graphs express the movement of the synchronicity percentage that is constant in some periods
causing a difficulty to rise forward to 100 percent. This problem will slow down the convergence
rate of the synchronicity.

0 5 10 15 20 25 30

30

40

50

60

70

80

90

100

Periods

P
e
rc

e
n
ta

g
e
 o

f 
S

y
n
c
h
ro

n
ic

it
y
 (

%
)

2 clusters, 25 nodes
3 clusters, 75 nodes
4 clusters, 50 nodes
5 clusters, 25 nodes

Inter−cluster synchronicity

Figure 6: Inter-cluster synchronicity that is difficult to reach a synchronicity convergence



100 M. Misbahuddin, R.F. Sari

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

NCIPP−RFS, 2 Clusters

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

5

10

15

20

25

30

35
25 Nodes
50 Nodes
75 Nodes
100 Nodes

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

NCIPP−RFS, 3 Clusters

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

10

20

30

40
25 Nodes
50 Nodes
75 Nodes
100 Nodes

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

NCIPP−RFS, 4 Clusters

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

10

20

30

40
25 Nodes
50 Nodes
75 Nodes
100 Nodes

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

NCIPP−RFS, 5 Clusters

Coupling Strength

N
u
m

b
e
r 

o
f 
P

e
ri

o
d
s

0

10

20

30

40

50
25 Nodes
50 Nodes
75 Nodes
100 Nodes

Figure 5: The comparison of the convergence rate among the number of nodes in the varied
number of clusters.



Initial Phase Proximity for Reachback Firefly Synchronicity in WSNs: Node Clustering 101

Conclusions

The clustering scheme approach based on the initial phase proximity is a way to synchronize
all nodes in a network executed concurrently. The clusters are constructed through a self-
configured way. The intra-cluster synchronicity uses the Reachback Firefly Algorithm (RFA)
simplifying the firing function and considering the realistic transmission effects. The inter-cluster
synchronicity utilizes the RFA with the Late Sensitive Windows (RFA with LSW) model to avoid
the overshooting jumps due to the flood of the firing messages from a node group to others.

We compare the RFA and the NCIPP-RFS clustering scheme using the Network Simulator
(NS-3). The simulation results show that the convergence rate of the NCIPP-RFS can reach a
synchronicity faster than the RFA. Moreover, the NCIPP-RFS can contribute significantly to
the increase of the convergence rate if the number of nodes is greater than or equal to 50 nodes.

The NCIPP-RFS was also evaluated and compared in the various number of clusters. The
best performance of the NCIPP-RFS among all scenarios of the number of clusters is the scenario
of the least number of clusters. However, the movement of the synchronicity percentage that is
constant in some periods is difficult to rise toward the 100 percent.

As future work, we will implement our approach to test it in a data-gathering application
referring a temporal and spatial relationships.

Acknowledgement

The authors gratefully acknowledge the Ministry of Research, Technology and Higher Edu-
cation of Indonesia for supporting this work through DIKTI’s research grant under grant No.
1173/UN2.R12/HKP.05.00/2016

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