Efficient Tree-based Aggregation and Processing Time for Wireless Sensor Networks

David Fotue & Houda Labiod
International Journal of Computer Science and Security (IJCSS), Volume (15) : Issue (3) : 2021 73
ISSN: 1985-1553, https://www.cscjournals.org/journals/IJCSS/description.php
Efficient Tree-based Aggregation and Processing Time for
Wireless Sensor Networks
David Fotue david.fotue@univ-yaounde1.cm
Département d’Informatique
Ecole Normale Supérieure de Yaoundé
BP 47, Yaoundé, Cameroun
Houda Labiod houda.labiod@telecom-paristech.fr
Informatique Réseaux et Sécurité (INFRES)
Télécom ParisTech
46, Rue Barrault, France
Abstract
Tree-based data aggregation suffers from increased data delivery time because the parents must
wait for the data from their leaves. In this paper, we propose an Efficient Tree-based Aggregation
and Processing Time (ETAPT) algorithm using Appropriate Data Aggregation and Processing
Time (ADAPT) metric. A tree structure is built out from the sink, electing sensors having the
highest degree of connectivity as parents; others are considered as leaves. Given the maximum
acceptable latency, ETAPT's algorithm takes into account the position of parents, their number of
leaves and the depth of the tree, in order to compute an optimal ADAPT time to parents with
more leaves, so increasing data aggregation gain and ensuring enough time to process data from
leaves. Simulations were performed in order to validate our ETAPT. The results obtained show
that our ETAPT provides a higher data aggregation gain, with lower energy consumed and end-
to-end delay compared to Aggregation Time Control (ATC) and Data Aggregation Supported by
Dynamic Routing (DASDR).
Keywords: Wireless Sensor Networks, Aggregation Time, Aggregation Gain, Parent, Leaf.
1. INTRODUCTION
Recent innovations in micro-electro-mechanical technologies bring significant advantages to the
development of low-power, low-cost multifunctional sensors equipped with storage, computing
and communication capabilities. Wireless Sensor Networks (WSNs) are ad hoc wireless networks
that consist of a large number of small devices, known as sensors, scattered over a particular
geographical area [1]. In recent years, WSNs are seen as a reality, due to the potential
applications in various domains such as industrial, biological, medical, military, nuclear science,
forest fire detection and so on. The lack of a predefined communication infrastructure increases
the challenges of designing of communication techniques for these networks, especially in hostile
environments, where it is often difficult to replace sensor batteries after deployment and where
communication infrastructures are not accessible or available.
In WSNs, all sensors send their data towards the central sink, which is the final recipient of the
sensed information. Sensors are equipped with a limited amount of storage capacity, and
powered by batteries with a finite life, making power saving an important issue in achieving long-
lived wireless multi-hop networks [2]. In WSNs, each sensor covers a defined area, collecting
local data and sending it towards the main sink. It may happen that some sensors deployed in the
monitored area sense common data. Therefore, much energy will be wasted if all these data are
forwarded towards the sink. Data aggregation schemes exploiting in-network processing have
been proposed as efficient techniques to conserve energy by locally processing the data as much
as possible in order to reduce the amount of data transmitted by each sensor towards the sink [1].

As the sink has to receive the data from sensors in a timely manner, this data aggregation has a
relationship with the data aggregation time [3]. We need to determine the data aggregation time
that each parent in the tree should spend in aggregating the data sent from its leaves. As the
network topology can vary, some parents might have many leaves, making it very expensive for a
parent to store all incoming data in its buffer. Failing to account for data aggregation time may
lead to a longer waiting time for each parent and increase overall data delivery latency.
We propose an Efficient Tree-based Aggregation and Processing Time (ETAPT) algorithm using
Appropriate Data Aggregation and Processing Time (ADAPT) metric. Given the maximum
acceptable latency, ETAPT's algorithm takes into account the position of parents, their number of
leaves and the depth of the tree, in order to compute an optimal ADAPT time to parents with
more leaves, so increasing data aggregation gain and ensuring enough time to process data from
leaves. Simulations were performed in order to validate ETAPT. The results obtained show that
our ETAPT provides a higher data aggregation gain, with lower energy consumed and end-to-end
delay compared to Aggregation Time Control (ATC) [4] and Data Aggregation Supported by
Dynamic Routing (DASDR) [5].
The remainder of this paper is organized as follows: Section 2 outlines related work. Section 3
formulates the problem and presents our proposition. Section 4 presents our model and
describes notation. Section 5 presents our approach. Section 6 presents performance metrics
and comparative results and Section 7 concludes the paper.
2. RELATED WORK
As our WSN focuses on gathered the data from the environment, it is important to forward the
data in a timely manner towards the sink. Several approaches have been proposed concerning
data aggregation time. Actually, we use tree and cluster structure for data aggregation because
they are useful in environment monitoring where the maximum data values received by the sink
provide the most useful information [2].
[4] proposes dynamic Aggregation Time Control (ATC) based on the number of leaves of the root
node in a tree-structure. ATC adjusts the aggregation time of the sensor.to assign more
aggregation time to sensors having more children in order to give more possibilities to aggregate
the data. Simulations show that ATC has a high aggregation gain. However, ATC cannot be
adopted to the multi hop sensor networks since it requires the global knowledge of the network. In
addition, the broadcast scheme used during the construction of the tree needs a high
communication overhead and decreases network performance. [5] proposes Data Aggregation
Supported by Dynamic Routing (DASDR), which can adapt to different scenarios without incurring
much overhead. Sensor nodes that monitor events are concentrated in space as far as possible
and data packets flow to the sink along different paths. Dynamic routing constructs a depth
potential field, which aims to guarantee that packets will reach the sink eventually and a queue
potential field, which makes packets more spatially convergent, making data aggregation more
efficient. Simulations show that DASDR improves the data aggregation ratio, saves energy, and
scales well with network size. [6] focuses on a real-time data delivery, but do not take the data
aggregation and processing into account. [7] proposes a cascading time-out in which sensors
schedule their time-outs based on their position in the aggregation tree. A sensor's time-out
happens after its leaves' time-outs, so enabling a sensor to aggregate the data from all its
children. [8] computes the data aggregation time-out for clustered WSNs. The time-out is
calculated for each sub-tree in the cluster taking into account packet transmission and cascading
delay, leading to a reduction in aggregation time and energy use. [9] develops an approach which
delivers the data to the sink within the deadline. They estimate the time-out of each sensor in the
tree, so that the data generated by each sensor is delivered to the sink before the deadline. [10]
proposes to construct a centralized and decentralized structure in the network in order to reduce
the transmission delay during the collection of data. [11] proposes a Delay-minimized Energy-
efficient Data Aggregation (DEDA) algorithm to minimize data aggregation latency. The physical

distance between sensors is takes into account in DEDA to save the transmission energy in order
to improve network lifetime.
Our proposal is similar to the one used by [4] and [5]. However we take into account the position
of parents, their number of leaves and the depth of the tree, in such a way those parents with
more leaves will be dynamically allocated an appropriate aggregation time, so maximizing the
data aggregation gain and improving network performance.
3. PROBLEM STATEMENT AND PROPOSITION
In this section, we formulate the problem addressed in this paper and present our proposal.
3.1 Problem Statement
In our context (spatial aggregation), the data gathered by sensors that are close to each other do
not vary much over time. Tree-based data aggregation results in increased data delivery time
because the parents must wait for the data from their leaves. Since the network topology can be
random, as shown in Figure 1, some parents may have many leaves, making it very expensive
for a parent to store all incoming data in its buffer. [4] shows that if a parent waits for the data
from its leaves for a long time, it collects more data and hence Data Aggregation Gain (DAG)
increases. DAG is the ratio of traffic reduction due to aggregation to the total traffic without
aggregation [12]. However, this long waiting time means that the data delivery time to the sink
FIGURE 1: WSN: Tree Construction.
may increase. Thus, it is important to consider the time taken by parents to aggregate and
process the data, because it takes more time to aggregate and process the data than to transmit
the data towards the sink. Lacking of attention to the data aggregation and processing time may
increase the overall data delivery latency or reduce the DAG. [13] shows that neglected the data
aggregation and processing time may increase the overall data delivery latency or reduce the
DAG.
3.2 Proposition : ETAPT Algorithm
We propose an Efficient Tree-based Aggregation and Processing Time (ETAPT) algorithm using
the Appropriate Data Aggregation and Processing Time (ADAPT) metric to calculate the data
aggregation and processing time for parent nodes as shown in Figure 2. After have been built the
tree out from the sink, in order to elect sensors with the highest degree of connectivity as parents
and sensors with the lowest degree of connectivity as leaves as shown in Figure 2. Given the
maximum acceptable latency, ETAPT's calculation takes into account the position of parents,
their number of leaves and the depth of the tree, in order to compute for each parent an optimal
ADAPT before aggregating and processing the data from its leaves. So, allocating an appropriate
aggregation time (AggTime) to parents with more leaves in order to increase the DAG, thus
ensuring enough time to process the data from leaves.

FIGURE 2: Distribution of Aggregation Time.
4. NETWORK MODEL AND NOTATION
4.1 Network Model
The proposed WSN can be modeled as a connected graph G = (S, E), where S is the set of N
fixed sensors, and E is the set of wireless links. We use the locality model suggested in [14] to
determine network connectivity. The probability of a link between two sensor nodes Si and Sj is
given by:
Where D(Si, Sj) is the Euclidean distance between sensors Si and Sj, and R is the locality radius.
4.2 Notation
Let s € S. Let Path (s1, sk) be the sequence: s1, s2...sk. We define Hop (s1, sk) = k-1 as the number
of hops from sensor s1 to sk. Let d(s) be the degree of sensor s. δ is the minimum transmission
time between two sensors of the same Hop in the tree, and ensures that there is a difference in
the waiting times at consecutive Hop of the tree. We define:
as the set on leaves in the tree,
as the set on parents in the tree and,
as the number of hops of the Path (s, sink). We recall that Hop (sink) = 0. Let the depth of the
tree be:
the number of hops from the sink to the deepest leaf in the tree (the maximum number of hops
towards the sink in the tree). We define the weighted length of the Path (s1, sk) as:
(1)
(2)
(3)
(4)
(5)

the sum of the degrees of the descendant sensors. Let L’EAF be all the leaves in a subtree rooted
at sensor s, s € M. We define the maximum weighted depth of the subtree as:
the maximum degree of all the descendant sensors in L’EAF to root to sensor s in the subtree. For
all (s € LEAF), MaxWP(s) = 0. Finally, Tmax be the maximum acceptable latency.
In the following Section 5, we describe our ETAPT algorithm.
5. EFFICIENT TREE-BASED AGGREGATION AND PROCESSING TIME
(ETAPT) ALGORITHM
5.1 Assumptions
We assume in our approach that:
 Sensors are deployed in an area of size L.
 Sensors are homogeneous (same computing, memory...) and fixed.
 Each sensor maintains a list of identifies (Id) of its neighbors.
 Each sensor keeps track of its own degree of connectivity value d(s).
 Each leaf has one parent that is responsible for forwarding the received data towards the
sink.
 Leaves can only sense and transmit their data to their parents.
 Aggregation of multiple packets results in one packet.
 A single sink is the final recipient of all the sensed data.
 Tmax is the maximum acceptable latency.
As shown in Figure 2, the tree is built out from the sink, taking into account the degree of
connectivity of sensors d(s). The sensors with the highest degree of connectivity are selected as
parents and those with lowest degree of connectivity as leaves. Given Tmax, ETAPT will determine
the ADAPT for each parent based on its position, its number of leaves and the depth of the tree.
We assume that every sensor generates a data packet of the same length periodically, and
multiple packets can be combined into one packet after the data aggregation process. Any
packets arriving after the ADAPT time calculation are discarded. The algorithm consists of two
major procedures: MaxWPath, HopDistance, degree of sensor and average waiting and aggregation
time’s determination.
5.2 MaxWPath, HopDistance and Degree of Sensor Determination
The first step consists in determining by each sensor in the tree: its degree d(s), MaxWPath(s) and
HopDistance(s).The Sink broadcasts a beacon message as a RequestMaxWPath with a HopDistance
field, which is incremented as the beacon travels through the tree as shown in Figure 3(a). Every
sensor, on receiving the RequestMaxWPath, adds its HopDistance value to the beacon, and forwards
it to its neighbours. In order to reply to the RequestMaxWPath message, every sensor, starting
from the deepest leaf, calculates its own degree and the MaxWPath to its parent, generates a
ReplyMaxWPath message and forwards it to its parent as shown in Figure 3(b).
(6)
(7)

FIGURE 3: Beacon Structure.
Suppose that s € M is a parent. It calculates and saves its own d(s) and MaxWPath (s) based on
the ReplyMaxWPath it receives, generates a new ReplyMaxWPath including its own MaxWPath and
forwards it to its parent. The ReplyMaxWPath messages are propagated in a cascading manner
along the tree towards the sink. When the sink has received all the ReplyMaxWPath messages, it
chooses the largest MaxWPath value from among them and sets:
5.3 Determination of average waiting and aggregation times
The second phase of ETAPT consists in determining the average waiting time Avg per sensor in
order to determine the aggregation Time AggTime in the tree. The Avg for each sensor (s) is based
on Tmax, MaxWP(s) and Hop (s). When the sink receives a request from an external user
specifying Tmax, the sink, based on the information it received in the first step, calculates the Avg
per sensor and AggTime in the tree as follows:
We assume that Tmax > (Depth x δ). After the sink has calculated the Avg, it broadcasts a new
beacon message through the network including Tmax and Avg. Every sensor, on receiving the new
beacon message, calculates its AggTime as follows:
δ is the minimum transmission time between two sensors of the same HopDistance in the tree.
(8)
(9)
(10)

FIGURE 4: ETAPT Algorithm.
5.4 Illustration
Consider a simple topology consisting of 15 sensors as shown in Figure 1. We want to calculate
d(s), Hop (s), MaxWP (s) and AggTime (s) for each sensor in the tree. We suppose that Tmax = 5s
and δ = 0.2s. Taking into account equation (9), the Avg = 0.64s and the Depth = 3. The ADAPT
time calculation is summarized in Table 1.
TABLE 1: ADAPT Calculation.

In the following Section 6, we define the performance metrics and present comparative results.
6. PERFORMANCE METRICS AND COMPARATIVE RESULTS
6.1 Performance Metrics
The following metrics are used to evaluate our approach:
 Data Aggregation Gain (DAG)
DAG is defined as the ratio of the benefit of traffic reduction due to aggregation to the total traffic
generated without aggregation.
PAggregated is the total number of data packets aggregated by parents.
 Aggregation Time (AggTime)
AggTime is defined as the appropriate time need by a parent to aggregate the data from its leaves.
 End-to-End Delay (E2EDelay)
DelayE2E is the average of the time difference between sensed data leaving a sensor and it being
received by the sink.
PReceived is the total number of data packets received by the sink. TReceived is the reception time at
the sink, TTransmission is the transmission time from each sensor. The lower the value, the more
promptly is data delivered to the sink.
 Energy Consumed (EC)
Often, sensors are deployed in a hostile environment where replacing the batteries is not always
possible. A good choice of energy model is essential to optimize sensor network lifetime. Our
approach assumes that sensors are usually in the active mode. The energy model used is the
same as in [15]. For each pair of sensors (si, sj), the energy consumed when sending a packet of
m bits over a distance D can be calculated as:
Sending sensor energy consumption:
Receiving sensor energy consumption:
The total energy consumed by each pair (si, sj) is:
ETi is the energy consumed for the transmission of a packet by the source Si, ERj is the energy
consumed to receive a packet sj, Eelec is the energy consumed to run the transmitter and receiver,
Eamp is the energy used by the amplifier and D is the Euclidean distance between si and sj.
(12)
(11)
(13)
(14)
(15)

6.2 Simulation Set-up
We implemented a simulation of our network topology using QualNet 5.0. A topology is totally
described by the number of stationary sensors N belonging to the network and their locations.
Throughout our analysis, we deploy 100 fixed sensor nodes inside a square area L. The sink is
placed at the top left corner of L. During the execution of our simulations, a given source and
destination pair remains in the evaluated set until communication between them fails due to
energy depletion. We repeated the experiments 20 times for the same topology, with the 95%
confidence interval of each data. We took the average value of these 20 runs. Initially, each
sensor was charged with an energy of 10
4
Joules. In the analysis, we set Tmax = 3s, 4s, 5s, 6s.
The parameters are described in Table 2.
TABLE 2: Simulation Parameters
6.3 Comparative Results
We ran simulation to compare our ETAPT strategy vith ATC [4] and DASDR [5] described in
Section 2. Figure 5 depicts the evolution of DAG as a function of Tmax. We can see that as Tmax
increases, the DAG increases for all the three methods. This shows that as Tmax increases, each
parent has enough time to aggregate its data efficiently. ETAPT, with an average DAG of 90%,
outperforms DASDR and ATC, which give 84% and 73.5% respectively. This is because, in
ETAPT, the AggTime of a leaf is proportional to MaxWP (leaf). A leaf with a small MaxWP should
transmit the data quickly to its parent; only leaves having the same MaxWP value have the same
AggTime. However, DASDR and ATC use a cascading time-out. This means that sensors at the
same Hop in the tree have the same AggTime, consequently increasing the amount of data loss due
to congestion at intermediate parents.
We now evaluate the evolution of DAG as a function of the number of sensors, as shown in
Figure 6. In the analysis, we set Tmax = 3s and we observe the evolution. We see a decreasing of
DAG from [60-80] sensors, that is due to the fact that some leaves are disconnected to their
parents resulting in a tree with disconnected sub-trees. We can see that for all algorithms, as the
number of sensors increases, DAG also increases in each algorithm. That means that the three
algorithms continue to deliver data accurately towards the sink as the number of sensors
increases. ETAPT achieves the best DAG with an average of 86.4%, compared to 78.4% for
DASDR and 71.4% for ATC.
After a packet has been sent along a path Pi (i=1....,k), we must perform an energy reduction
operation on each sensor along the path except for the sink. Thus, after a packet is sent by a
sensor, the energy level of that sensor is decremented by the amount of energy required to send
the data packet. A sensor is considered non-functional if its energy level reaches zero. Figure 7
shows the evolution of the total EC for different techniques with a varying value of Tmax.

FIGURE 5: Evolution of DAG vs Tmax.
FIGURE 6: Evolution of DAG vs Number of sensors.
We observe that ATC and DASDR have a higher energy consumption than ETAPT. That is due
to the fact that in the construction of the tree, we elect sensors having the highest degree of
connectivity as parents instead of these with the highest identifier, as in ATC and DASDR. Thus,
each sensor has exactly one parent that forwards its data, considerably reducing concurrent
transmissions in the network. Our proposal reduces the total EC compared to DASDR and ATC
by around 35% and 67% respectively. We evaluated the evolution of the total EC with increasing
number of sensors, as shown in Figure 8. We observe a decreasing of EC with increasing
number of sensors. That is due to the fact that in dense network, parent nodes might have many
leaves which helps by reducing the number of parents necessary to transmit the data in the tree,
and hence reduces the EC. The average maximum energy is obtained by ATC with around 45J.
An improvement is obtained by DASDR, which uses only around 25J. ETAPT outperforms both,
with an average EC of just 16J.

FIGURE 7: Evolution of EC vs Tmax.
FIGURE 8: Evolution of EC vs Number of sensors.
Figure 9 shows AggTime vs. the locality radius. In this analysis, we set Tmax = 6s, and vary the
locality radius of sensors among [20, 30, 40, 50, 60] m. We can see that as locality radius
increases, the AggTime decreases in all methods. That is because increasing the locality radius
creates a disjoint network in which some sensors are not connected. This decreases the degree
of connectivity of parents, and considerably reduces the AggTime of each parent. ETAPT reduces
the AggTime compared to DASDR and ATC by around 31% and 60% respectively.
Figure 10 depicts the evolution of AggTime vs. the depth of the network. We set Tmax = 6s, and vary
the depth of the network among [3, 4, 5, 6]. As we have seen in Section 5, AggTime is a function of
the depth of the network. We observe that as the depth of the network increases, AggTime also

FIGURE 9: Evolution of Aggtime vs Locality radius.
FIGURE 10: Evolution of Aggtime vs Depth.
increases because, the deeper the tree, the more time parents in the tree will need to aggregate
the data from leaves. In all three methods, while increasing the Depth, ETAPT reduces the
AggTime compared to DASDR and ATC by around 17% and 40% respectively.
Figure 11 depicts the evolution of DelayE2E vs. the degree of connectivity. We set Tmax = 6s, and
vary the degree of connectivity of the network among [5, 10, 15, 20] with a network consisting of
200 sensors. ETAPT has a smaller DelayE2E compared to DASDR and ATC. This is because
there is no need for each parent to synchronize with other parents in the tree before sending
data.

FIGURE 11: Evolution of of DelayE2E vs Degree of connectivity.
7. CONCLUSION
In this paper, we have proposed an efficient ETAPT algorithm using the ADAPT metric. Given the
maximum acceptable latency, ETAPT's calculation takes into account the position of each parent,
its number of leaves and the depth of the tree, allocating an ADAPT time to parents with more
leaves, so increasing the data aggregation gain and ensuring enough time to process data from
leaves. The results obtained show that our ETAPT provides a higher data aggregation gain with
lower energy consumed, AggTime and DelayE2E compared to the alternative DASDR and ATC
methods. Our suggested ETAPT algorithm is particularly useful in resource-constrained networks,
since it does not need synchronization among sensors in the network.
In the future, we will take into account the cost of maintaining the tree in dynamic networks,
evaluate the overhead as proposed in [16]. Later, we will study the relationship between waiting
time and data aggregation gain in order to make it scalable in more complex WSNs.
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