international journal of pure and applied mathematics ... · modified leach not only improved the...

A DISPERSED GAUSSIAN HIERARCHICAL ENERGY EFFICIENT MULTIPATH

ROUTING FOR DATA AGGREGATION IN WSN

S. Sheeja Rani

Research Scholar, Department of Computer

Science and Engineering

Noorul Islam University

Kanyakumari, India 629180

[email protected]

Dr. K. Siva Sankar,

Noorul Islam University,

Department of Information and Computer

Engineering

Kanyakumari, Tamil Nadu, India

Abstract

The accessibility of low cost and small-scale sensors has created to broad adoption of

Wireless Sensor Networks (WSNs) for several application uses. Sensors have been applied in

several institutions and establishments and one of the eminent concerns in WSN applications is

how to minimize energy and average end-to-end delay in the process of data transfer. Data in

WSN should be aggregated using clustering in order to reduce energy and average end-to-end

delay. However, no single clustering is optimal with different clustering algorithm generating

different partitions. Ensemble-based clustering has attained wide interest due to its most robust

and stable clustering benefits it offers. Many clustering based energy efficient routing were

adopted by several researchers. These techniques were not efficient in reducing the average end-

to-end delay since they considered only residual energy and reducing energy per packet. In this

work an efficient ensemble cluster framework called, Dispersed Gaussian and Hierarchical

Energy-efficient Multipath Routing (DG-HEMR) is proposed. An efficient data aggregation

framework based on a Dispersed Gaussian Expectation Maximization addressing how to reduce

the average end-to-end delay through efficient selection of neighbor nodes based on dispersed

Gaussian factor for longer network lifetime is first designed. Next, resource efficient

Hierarchical Energy Efficient model for multi-path routing in which optimal number of routers

are investigated for efficient data aggregation in WSN and concurrently increase the

communication efficiency. Experiments are conducted to evaluate the performance in terms of

average end-to-end delay, average energy consumption and network lifetime. Simulation results

show that the algorithms extensively optimize the energy consumption amount and decrease the

average end-to-end delay for data aggregation and increases the network lifetime in WSNs.

Keywords: Wireless Sensor Networks, Dispersed Gaussian, Multipath Routing, Gaussian factor,

Data aggregation

1. Introduction

Wireless Sensor Networks (WSNs) comprises of hundreds or thousands of small devices

that are competent of transmitting with each other with confined power. These sensor nodes in

WSNs are positioned in a real-world environment to sense different environmental effects.

Nevertheless, WSN suffers from immense confinements such as restricted memory, insignificant

computational capability, and restricted battery.

International Journal of Pure and Applied MathematicsVolume 119 No. 17 2018, 1321-1336ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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In Modified Low Energy Adaptive Clustering Hierarchy (Modified LEACH) [1], proper

cluster head node was selected at each round. This was performed based on the updated values of

the cluster head election threshold. Followed by the dynamic selection of cluster head based on

the threshold value, Modified LEACH also circumvented the process of certain sensor nodes that

transmitted more data packets than other sensor nodes in the whole network. This was performed

by rescheduling the TDMA schedule. The rescheduling of TDMA scheme for each sensor node

was performed by its cluster head. This in turn balanced all the sensor nodes present in the

network towards balancing all nodes to transmit nearly same amount of data. As a result,

Modified LEACH not only improved the energy consumption of the wireless sensor nodes, but

also the network lifetime.

However with complex and multifaceted operations, delay is said to occur. This is

because the sensor node possessing higher residual energy is only considered without

considering other factors such as the distance between the sensor node and Base Station (BS),.

Chances may also persist where the positioning of sensor node is located far away from Base

Station (BS), therefore increasing the average end to end delay. Potential solution is to identify

the neighboring nodes based on the nearest neighbor factor. So, the distance between the sensor

nodes and neighboring nodes are reduced, therefore between the sensor nodes and Base Station,

reducing the average end to end delay. This is performed in the proposed work using the

Dispersed Gaussian Expectation Maximization model.

Minimizing energy necessarily does not provide an increase in the network lifetime in

WSN. This is because of several factors, to name some few include, network topography,

inappropriate data packet dissemination in the network. Most of the existing works had been

designed on the basis of reducing energy per packet to improve network lifetime, or in certain

other cases, by conserving battery of one sensor node. Distributed Medium Access Control

(Distributed MAC) [2] considered first node death as the criteria for network lifetime

performance. To this an optimization technique was proposed for selecting hop and therefore to

improve the network lifetime.

Distributed MAC designed an adaptive priority based hop selection to improve the

network lifetime. It also considered an ideal transceiver optimization strategy that fully

considered the residual energy, while transmission. Despite energy conservation and network

lifetime said to be improved, routing efficiency was not considered. Potential solution is to

design a resource-efficient multi-path routing model for efficient data aggregation in WSN. This

is performed in the proposed work using the Hierarchical Energy Efficient model for Multipath

Routing (HEE-MR).

This paper is organized as follows. Section 2 presents an analysis of existing methods for

data aggregation considering varying factors in the literature. Section 3 describes the system

model and network model and introduces the proposed Dispersed Gaussian and Hierarchical

Energy-efficient Multipath Routing framework. Section 4 shows the performance obtained with

proposed framework and, finally, in Section 5 the paper is summarized, reporting the

conclusions.

International Journal of Pure and Applied Mathematics Special Issue

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2. Related works

One of the most crucial factors in WSN planning and design is the network optimization

plays. A well-designed WSN not only results in the improvement of network efficiency, but also

the data aggregation task. Hence, network optimization has become a vital objective. In [3],

ensemble fuzzy clustering was applied based on random projections resulting in the

improvement of accuracy and space-time complexity. Quality of service through fusion

mechanism using Fuzzy Logic Controller (FLC) was presented in [4]. Another cluster ensemble

based on fuzzy was investigated in [5], resulting in network optimization. An extensive

comparison of several data aggregation techniques was presented in [6].

The applications of sensor networks extend from terrestrial to underwater. However, one

of the major drawbacks in such WSNs is the energy consumption that grows when data

transmission grows. To address this issue, an efficient data transmission protocol was designed

in [7] using redundant measure and distance study. In [8], a survey of broad literature analysis of

data aggregation techniques was provided. Yet another energy efficiency method using Decoding

Delay-based Distributed Source Coding was presented in [9], resulting in the energy efficiency.

An approximate holistic data aggregation technique in WSN was investigated in [10] to

determine the optimal sample size and also proved the efficiency on the aspects of accuracy and

energy consumption.

Recent advancements in micro-electro-mechanical systems (MEMS) and wireless

communications have emphasized the importance of WSNs for information dissemination. In

[11], an energy-efficient routing protocol using A-Star was provided by forwarding data packets

via optimal shortest path, therefore improving the network lifetime. A Qos-aware and

Heterogeneous Clustered Routing (QHCR) [12] protocol was designed that conserved energy

and provided optimal routing. An advanced energy conserving optimal path schedule algorithm

was designed in [13] with the objective of providing higher packet delivery ratio and lower

energy consumption. A homomorphic encryption algorithm was provided in [14] for reducing

energy consumption.

With the evolution of WSNs, one of the most important problems to be addressed is

privacy preservation in several WSN applications. A novel Cluster-based Secured private Data

Aggregation scheme called, (CSDA) was presented in [15] and was proved to be better in terms

of communication efficiency. However, network lifetime was not concentrated. In [16], a generic

deployment-based optimization model was presented resulting in longer optimal network

lifetime. Though data aggregation routing protocols and link cost was considered, a trade-off was

found. To address this issue, Weighted Data Aggregation Routing Strategy (WDARS) [17] was

designed to increase the overlap routers for efficient data aggregation.

Despite energy efficiency and communication efficiency, in case of parent node failures,

overall network gets affected and therefore the network lifetime. To provide solution to this, an

energy-aware fault tolerant mechanism was designed in [18]. A detailed empirical evaluation

was provided in [19]. A greedy algorithm based on LEACH clustering algorithm was

investigated in [20] to improve energy consumption and network lifetime. However, with the

positioning of the neighbor node placed far away and routing efficiency was not addressed.


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This literature review does not introduce a pertinent solution for end-to-end delay and

routing efficiency. In this paper, an effective algorithm based on the Dispersed Gaussian

Successor Node Identification and Hierarchical Multipath Routing is designed to provide an

effective solution to minimize the research gap. The methodology of the proposed framework is

divided into sections. Analyzing the network and determining the neighboring node based on

nearest neighbor factor using Dispersed Gaussian Expectation Maximization and rating each

sensor node according to its prominence or minimum distance. After that a hierarchical multipath

routing model and proposing a Hierarchical Multipath Routing algorithm to evaluate optimal

route for efficient data aggregation is developed. Finally comparing the proposed algorithm, with

the Modified LEACH and Distributed MAC in existence is presented.

3. Methodology

Reducing energy may not assure in increasing the life time of WSN. This is because of

several factors involved like, changes in network topology, irregular dispersal of data packets

between the sensor nodes in WSN and so on. Most of the existing mechanisms have been

designed based on reducing by rescheduling the TDMA schedule to improve the network

lifetime [1], but increasing the average end-to-end delay.

In most other cases improving network lifetime means considering first node death [2].

Here we considered nearest neighbor factor and routing efficiency as the criteria for network

lifetime performance, called, Dispersed Gaussian and Hierarchical Energy-efficient Multipath

Routing (DG-HEMR) for efficient data aggregation in WSN. Figure 1 shows the block diagram

of Dispersed Gaussian and Hierarchical Energy-efficient Multipath Routing (DG-HEMR).

Figure 1 Block diagram of Dispersed Gaussian and Hierarchical Energy-efficient

Multipath Routing

As shown in the figure, two steps are included to perform efficient data aggregation. The

data aggregation starts with the remote nodes ‘𝑅𝑁’ towards the base station ‘𝐵𝑆’. During the

process, initially, a remote node first sent data packets ‘𝐷𝑃’ to its successor nodes ‘𝑆𝑁’through

multi-path routing.

- Remote node - Successor nodes

Neighbor node

identification

Multipath

routing

Data

aggregation

Base station


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The neighbor nodes are identified using Dispersed Gaussian Expectation Maximization

model. Upon successful identification of sensor nodes and upon receiving data packets from

other sensor nodes, base station aggregate them with its own data and forward aggregation

results contained in data packets to their neighboring nodes through multi-path routing. Multi-

path routing is performed in the proposed work using Hierarchical Clustering (to be changed).

The above said iteration is said to be repeated until the base station collects and aggregates the

final results.

3.1 System model

Let us assume a wireless sensor network consisting of sensor nodes ‘ 𝑆 ={𝑆1, 𝑆2, … . . , 𝑆𝑛}’, positioned in two dimensional ‘𝑝’ and ‘𝑞’ direction of area ‘𝐴’, with sensing

range or ‘ 𝑅 ’. Let us further assume that every sensor node 𝑆 = {𝑆1, 𝑆2, … . . , 𝑆𝑛} ’, possess

location ‘(𝑝𝑖, 𝑞𝑖)’ with the position of every sensor node to be represented as graph ‘𝐺 = (𝑉, 𝐴)’.

Here, ‘𝑉’ represents the sensor nodes and base station and ‘𝐴’ representing the directional area.

3.2 Network model

With graph ‘𝐺 = (𝑉, 𝐴)’ as the network model considered, the job of sensor nodes in

WSN is the collection of sensing data packets from all sensor nodes in the network to the Base

Station ‘ 𝐵𝑆 ’. The environment parameters ‘ 𝑃 = {𝑃1, 𝑃2, … . . , 𝑃𝑛} ’ comprising of

‘𝑇𝑒𝑚𝑝, 𝑃𝑟𝑒𝑠𝑠, 𝑊𝑖𝑛𝑑’ are sensed by the sensor nodes and the sensed data packets are aggregated

by the neighboring nodes and finally sent to the Base Station ‘𝐵𝑆’. A channel access of Time

Division Multiple Access (TDMA) is used in the proposed work so that several sensor nodes

share the same frequency channel, by each sensor node using its own time slot.

3.3 Dispersed Gaussian Expectation Maximization model

In this section, successor nodes identification is performed using Dispersed Gaussian

Expectation Maximization model. Successor nodes are identified based on the nearest neighbor

factor, derived through Euclidean distance. The Euclidean distance is measured between the

remote node and the ‘𝑛’ successor nodes. The minimum distance nodes between remote nodes

‘𝑅𝑁’ and the ‘𝑛’ successor nodes are identified as the neighboring nodes ‘𝑁𝑁’.

As the distance between two sensor nodes (between remote nodes and successor nodes)

within the transmission range increases, the sensor nodes in the network requires higher amount

of energy to send/receive data packets. The distance between the remote node to this successor

nodes calculates with (1) that in this formula ‘(𝑝, 𝑞)’ shows the location of remote nodes and

‘(𝑝𝑛, 𝑞𝑛)’ is the location of the base station node.

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = √(𝑝𝑛 − 𝑝)2 + (𝑞𝑛 − 𝑞)2 (1)

From the above equation (1), the distance between the remote node and all other

successor nodes are identified. The minimum distance possessed between the remote node and

successor node is then considered as the neighbor nodes. With the identified neighbor nodes for

each successor nodes, if more than one identified neighbor nodes possess the same distance, the


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selection of neighbor nodes is made by applying Dispersed Gaussian Expectation Maximization

(DG-EM) model. This DG-EM model is applied to identify global statistics using local

information and neighbor’s local information. Figure 2 shows the block diagram of DG-EM

model.

Figure 2 Block diagram of DG-EM model

As shown in figure 2, each sensor node ‘𝑆𝑖’, ‘𝑆𝑗’, estimates the posterior probability

values. Followed by this, the resultant output is provided as input in order to estimate the

univariate and multivariate Gaussian distribution function. Finally, with these values, the

maximization is said to be arrived at.

Dispersed Gaussian Expectation Maximization (DG-EM) model consists of a probability

model of mixture of Gaussians (i.e. identified neighbor nodes possessing equal distance). The

DG-EM model is equivalent or closer to the natural distribution for having Gaussian function.

The univariate Gaussian distribution (i.e. equivalent distance) is the distribution in which the

resultant identified neighbor nodes is the average of the events (process of neighbor node

identification) that occurs again and again. The univariate Gaussian distribution for identified

neighbor nodes possessing equal distance is mathematically formulated as given below.

𝐺 = (𝑆 | 𝜇, 𝜎) = 1

√(2∗ 𝜋 𝜎2) 𝑒

−((𝑆− 𝜇)2

2 𝜎2 ) (2)

From the above equation (2), ‘𝐺’ represents the Gaussian function, ‘𝜇’ represents the

mean (i.e. maximum likelihood) and ‘ 𝜎 ’ represents the variance (i.e. deviation from the

maximum likelihood). Here, maximum likelihood denotes the capability of the sensor node to

possess similar distance several times, whereas the deviation from the maximum likelihood

represents the capability of sensor node to possess similar distance with slight deviation. As both

maximum likelihood and variance are present in WSN, multivariate Gaussian distribution

(sensor node possessing similar distance) is then formulated as given below.

𝑁(𝑆 | 𝜇, Σ) = 1

√(2∗ 𝜋 Σ) (3)

From the above equation (3), ‘𝜇’ represents the maximum likelihood and ‘Σ’ represents

the covariance between several Gaussian distribution fields (between several sensor nodes).

𝑆𝑖

𝑆𝑗

E step (𝛼𝑖)

E step (𝛼𝑖)

(𝑆 | 𝜇, 𝜎)

(𝑆 | 𝜇, 𝜎)

𝑁(𝑆 | 𝜇, Σ)

𝑁(𝑆 | 𝜇, Σ)

M step

M step


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Multivariate Gaussian distribution is used in the proposed method as the energy of each sensor

and the data packets to be sent are not static and tend to be dynamic at varied time intervals.

Therefore, with more than one identified neighbor nodes possessing same distance, Expectation

Maximization is applied to the Dispersed Gaussian resultant value. To measure the Expectation

Maximization, posterior probability is obtained and mathematically expressed as given below.

𝑃𝑟𝑜𝑏 (𝑆) = 𝑁(𝑆 | 𝜇𝑖 Σ𝑖) (4)

From the above equation (4), the posterior probability of each sensor node ‘𝑃𝑟𝑜𝑏 (𝑆)’ is

measured according to the number of successor nodes ‘𝑖’ with similar distance present in the

network. Followed by which the expected successor nodes (E step) possessing similar distance

are obtained using the mathematical formulates as given below.

𝛼𝑖 (𝑆) = 𝑁(𝑆| 𝜇𝑖Σ𝑖)

𝑁(𝑆| 𝜇𝑗Σ𝑗) (5)

With the expected resultant successor nodes, the maximization (M step) is then used to

solve the optimal node distribution problem. It is mathematically formulated as given below.

𝜇𝑗 = 𝛼𝑗 (𝑆𝑛)(𝑆𝑛)

𝛼𝑗 (𝑆𝑛) (6)

Σ𝑗 = 𝛼𝑗 (𝑆𝑛)(𝑆𝑛−𝜇𝑗) (𝑆𝑛−𝜇𝑗)

𝑇

𝛼𝑗 (𝑆𝑛) (7)

The pseudo code representation of Dispersed Gaussian Successor Node Identification

algorithm is as given below.

Input: sensor nodes ‘𝑆 = {𝑆1, 𝑆2, … . . , 𝑆𝑛}’, location ‘(𝑝𝑖, 𝑞𝑖)’, environment parameters ‘𝑃 ={𝑃1, 𝑃2, … . . , 𝑃𝑛}’, Base Station ‘𝐵𝑆’, remote nodes ‘𝑅𝑁’, successor nodes ‘𝑆𝑁’,

Output: Neighbor node identification

1: Begin

2: For each sensor nodes ‘𝑆’ possessing location ‘(𝑝𝑖, 𝑞𝑖)’

3: Measure distance between the remote node ‘𝑅𝑁’ to successor nodes ‘𝑆𝑁’ using

equation (1)

4: Obtain identified neighbor nodes ‘𝑁𝑁’

5: End for

6: For identified neighbor nodes ‘𝑁𝑁’

7: Measure univariate Gaussian distribution possessing equal distance using equation

(2)

8: Measure multivariate Gaussian distribution using equation (3)

9: Measure posterior probability using equation (4)

10: Measure expected successor nodes possessing similar distance using equation (5)

11: Subject to maximization using equation (6) and equation (7)

12: End for

13: End

Algorithm 1 Dispersed Gaussian Successor Node Identification algorithm

As provided in the above Dispersed Gaussian Successor Node Identification algorithm,

given a network of sensor nodes with remote nodes ready for sending data packets to the


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successor nodes, the goal is to maximize the likelihood function (successor nodes with minimum

distance) with respect to sensor node that possess similar distance several times and sensor node

that possess similar distance with slight deviation.

To this, both univariate and multivariate Gaussian distribution is obtained to measure the

varying probabilities due to the dynamic nature of the network. In this way, with the maximum

likelihood based on expectation maximization, efficient neighboring nodes for each remote node

are identified. With the neighboring nodes multipath routing is established that is discussed in

the forthcoming sections.

3.4 Hierarchical Energy Efficient model for Multipath Routing

The neighbor sensor nodes, upon receiving data packets from other sensors, will

aggregate them with its’ own data packet and forward aggregation results contained in data

packets to their successor nodes. With the identified successor nodes, Hierarchical Energy

Efficient model for Multipath Routing (HEE-MR) is performed. This distributed and iterative

process continues until the base station receives and aggregates the final results.

To address energy efficient multipath routing, the following assumptions are made, with

‘𝐸𝑟 ’ representing the energy consumed during data packet reception. Then, the total energy

required to send a data packet over single hop is mathematically expressed as given below.

𝐸𝑆𝑖 = 𝐸𝑆𝑖𝑗 + 𝐸𝑟 (8)

From the above equation (8), the energy efficiency ‘𝐸𝑆𝑖 ’, is measured based on the

energy of sensor node ‘𝑆𝑖’ after sending data packet ‘𝐷𝑃𝑖’ to sensor node ‘𝑆𝑗’. Let us assume that

the optimal number of routes in each level ‘𝑖’ is ‘𝐸𝑆𝑖 (𝑖 = 1, 2, … , 𝑛)’ as calculated above in

equation (8). The model selects an expected ‘𝐸𝑆𝑖’sensors as the level ‘𝑖’ routes. The HEE-MR

model is executed for ‘𝑛’ iterations. In the first phase, during iteration ‘𝑖’, a level ‘𝑖 − 1’, router

chooses to become a level ‘𝑖’ router with probability expressed as given below.

𝑃𝑟𝑜𝑏𝑖 ∈ [0,𝐸𝑆𝑖

𝑛] (9)

From the above equation (9), the probability ‘𝑃𝑟𝑜𝑏𝑖’, is measured based on the total

energy ‘𝐸𝑆𝑖’ required for ‘𝑛’ sensor nodes. With the measured probability, each chosen router

has a coverage radius expressed as given below.

𝐴 = 2𝑎

√𝐸𝑆𝑖 (10)

During the second phase, a level ‘𝑖 − 1’ router that is not covered by any level ‘𝑖’ router

selects to become a level ‘𝑖’ router with probability ‘𝑃𝑟𝑜𝑏2’, where ‘𝑃𝑟𝑜𝑏1’ and ‘𝑃𝑟𝑜𝑏2’ satisfy

the condition as given below, for ‘𝑆 = 𝑆𝑖’.

𝑆𝑖

𝑛= 𝑃𝑟𝑜𝑏1 + 𝑃𝑟𝑜𝑏2 (1 − 𝑃𝑟𝑜𝑏1) (1 −

𝑃𝑟𝑜𝑏1 𝑅2

𝐴2 )𝑛−1

(11)


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After the routers of all levels are selected, each levels ‘𝑖’ router of all levels is chosen,

each level ‘𝑖’ router ‘(𝑖 = 1, 2, … , 𝑛)’ joins the group of the nearest level ‘𝑖 + 1’ router. The

pseudo code representation of Hierarchical Multipath Routing algorithm is as given below.

Input: sensor nodes ‘𝑆 = {𝑆1, 𝑆2, … . . , 𝑆𝑛}’, location ‘(𝑝𝑖, 𝑞𝑖)’, environment parameters ‘𝑃 ={𝑃1, 𝑃2, … . . , 𝑃𝑛}’, Base Station ‘𝐵𝑆 ’, remote nodes ‘𝑅𝑁 ’, successor nodes ‘𝑆𝑁 ’, identified

neighbor nodes ‘𝑁𝑁’

Output: energy-efficient multipath routing

1: Begin

2: For each sensor nodes ‘𝑆’

3: For each identified neighbor nodes ‘𝑁𝑁’

4: Compute the total energy required over single hop using equation (8)

5: Compute first phase probability using equation (9) (i.e. router chooses to become

level ‘𝑖’ router)

6: Compute second phase probability using equation (11) (i.e. level ‘𝑖 − 1’ router

not covered by level ‘𝑖’ router selects to become a level ‘𝑖’ router)

7: End for

8: End for

9: End

Algorithm 2 Hierarchical Multipath Routing algorithm

As given in the above Hierarchical Multipath Routing algorithm, during topology

identification, neighbor nodes (i.e. identified using Dispersed Gaussian Successor Node

Identification algorithm) sends out a route request data packet, which is flooded to the base

station ‘𝐵𝑆’. Each neighbor node along a path also embeds its transmitting power and the time of

the path from the neighbor node into data packet sent to its next hop or next neighbor node.

Upon receiving multiple copies of route reply message, the neighbor node identifies a

few routes to reach the ‘𝐵𝑆’ based on energy efficiency. Once the route is established, the

neighbor node start to send the data packet to base station ‘𝐵𝑆’ by using the coverage radius. As

a result, the designated routes are more uniformly dispersed over the entire network. This in turn

results in the improvement in the network lifetime.

4. Simulation settings

The performance of Dispersed Gaussian Successor Node Identification algorithm and

Hierarchical Multipath Routing algorithm is evaluated by network simulator 2 (NS2) and is

implemented in two scenarios. This is because NS2 is one of the most famous and most widely

used network simulators. In this simulation, a network with 50, 100, 150, 200, 250, 300, 350,

400, 450 and 500 nodes that are randomly placed in a dimension of 1500m * 1500m are

considered. Each simulation is running for 180 seconds of the simulation time.

As provided above, two scenarios are implemented. The two scenarios are implemented

based on the node transmission range. For scenario 1, 200m transmission range is considered.

For scenario 2, 400m transmission range is considered. Simulations are said to be repeated for

different number of nodes in each scenario. Table 1 given below lists the simulation parameters.

All nodes were taken in a random manner by only regulating the simulation time.


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Table 1 Simulation parameters

Simulation environment

Area 5000 𝑚2

Simulation time 180 seconds

Mobility model Random Way Point

Node density 50, 100, 150, 200, 250, 300, 350, 400, 450, 500

Nodes placement Random

Transmission range 100 m and 200 m

5. Discussion

In this section the result analysis of Dispersed Gaussian and Hierarchical Energy-efficient

Multipath Routing (DG-HEMR) framework is made and compared with two existing methods,

Modified Low Energy Adaptive Clustering Hierarchy (Modified LEACH) [1] and Distributed

Medium Access Control (Distributed MAC) [2] for data aggregation in WSN. The sensor nodes

in EPFMR framework are positioned in uniform topology. To evaluate the efficiency of DG-

HEMR framework, the following metrics like average energy consumption, average end-to-end

delay during data aggregation and network lifetime is measured.

5.1 Scenario 1: Impact of average energy consumption

The amount of average energy consumption in the WSN depends on the amount of

energy involved to broadcast a data packet from a source node to the base station. With the

optimal energy consumption achieved using the proposed framework, the network lifetime is

also said to be increased. The numerical values that were used for both scenarios (i.e. 200m

transmission range and 400m transmission range) are illustrated in Table 1.

Several parameters persists on energy consumption in the network such as time taken for

network setup, routing time, processing time for CPU, transmitting and receiving data packets

and so on. In this work, the final average energy consumption for the network at the end of

simulation time is measured. The results of average energy consumption for both scenarios are

shown in Figure 4. The graphical representation for average energy consumption is shown for

DG-HEMR and comparison made with the existing Modified LEACH [1] and Distributed MAC

[2] for data aggregation in WSN.


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Figure 3 Results of average energy consumption for two different scenarios (200m

transmission range and 400m transmission range)

As shown in the figure, with larger transmission range (i.e. 400m transmission range), the

level of connectivity increases and as a result energy consumption is said to be optimal and

therefore, the network lifetime is said to increase. The average energy consumption was

measured for 10 simulation runs for each method in two different scenarios. Also, the result

shows that with the increase in the node density for higher transmission range (i.e. 400m

transmission range), the energy saving is found to be better in the network using the proposed

DG-HEMR framework, due to increased level of connectivity.

Here, the proposed DG-HEMR framework has been compared with the existing Modified

LEACH [1] and Distributed MAC [2]. As figure 2 demonstrates, our Dispersed Gaussian

Successor Node Identification algorithm has optimal performance compared to the Modified

LEACH [1] and Distributed MAC [2] and, approximately, they operate the same way when the

node density is lower than 300. As this figure shows, the Dispersed Gaussian Successor Node

Identification algorithm for 300 nodes consumed about 0.025J energy, but Modified LEACH [1]

and Distributed MAC consumed about 0.038J and 0.049J respectively, with the assumption of

200m transmission range. This is because the Dispersed Gaussian Successor Node Identification

algorithm not only considers the nearest neighbor factor based on minimum distance but also the

successor nodes possessing the same minimum distance considers the maximum likelihood

function using EM to arrive at the nearest neighbor. As a result, the average energy consumption

using DG-HEMR framework is said to be reduced by 34% when compared to Modified LEACH

[1] and 46% when compared to Distributed MAC [2] for 200m transmission range and reduced

by 37% when compared to Modified LEACH [1] and 46% when compared to Distributed MAC

[2] for 400m transmission range respectively.

5.2 Scenario 2: Impact of average end-to-end delay

Average end-to-end delay measures the average time taken by a data packet to travel

from the source to the base station. It will be a different value with the routing setup time,

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

50 100 150 200 250 300 350 400 450 500

En

erg

y c

on

sum

pti

on

(J

)

Node density

DG-HEMR (200m)

Modified LEACH

(200m)

Distributed MAC

(200m)

DG-HEMR (400m)

Modified LEACH

(400m)

Distributed MAC

(400m)


1331

because the best neighboring nodes that carries the data packet has been determined before and,

by this field, we will only measure the time from the moment that a packet has been sent by

neighboring node until the moment that data packet will be received by the base station. The

average end-to-end delay is mathematically formulated as given below.

𝐷𝑎𝑣𝑔 = 𝑁 ∗ [𝐷𝑇 + 𝐷𝑃 + 𝐷𝑃𝑟𝑜𝑐 + 𝐷𝑞𝑢𝑒𝑢𝑒] (12)

From the above equation (12), the average end-to-end delay ‘𝐷𝑎𝑣𝑔’ is measured based on

the transmission delay ‘𝐷𝑇’, propagation delay ‘𝐷𝑃’, processing delay ‘𝐷𝑃𝑟𝑜𝑐’ and the queuing

delay ‘𝐷𝑞𝑢𝑒𝑢𝑒’ with respect to the ‘𝑁’ number of routes. It is measured in terms of milliseconds

(ms). The graphical representation of average end-to-end delay is shown for DG-HEMR

framework and compared with Modified LEACH [1] and Distributed MAC [2] in Figure 4. With

the optimal route identified, lower is the average end-to-end delay and therefore improvement is

said to be found in the network lifetime.

Figure 4 Results of average end-to-end delay (400m transmission range)

This Figure depicts our Hierarchical Multipath Routing algorithm, although it has a

bigger routing setup time for identifying optimal route, and when the route was decided, the

optimal route of the average end-to-end delay or the data packet delivery time using DG-HEMR

framework was found to be better than the Modified LEACH [1] and Distributed MAC [2]. As

figure 4 shows, the average end-to-end delay time is approximately reduced when the data

packet size was below 48 and started increasing with higher data packet size. In this figure also,

100 nodes in a 400m transmission range was assumed. However, average end-to-end delay while

applied with DG-HEMR framework was found to be comparatively lesser than the Modified

LEACH [1] and Distributed MAC [2]. This is because of the efficient selection of ‘𝑖’ router,

followed by the level ‘𝑖 − 1’ router not covered by level ‘𝑖’ router in an hierarchical manner

results in the minimization of average end-to-end delay using DG-HEMR framework by 36%

when compared to Modified LEACH [1] and 45% when compared to Distributed MAC [2].

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

8 16 24 32 40 48 56 64 72 80

Av

era

ge

end

-to

-en

d d

ela

y (

ms)

Data packet size

DG-HEMR

Modified LEACH

Distributed MAC


1332

5.3 Scenario 2: Impact of network lifetime

The network lifetime represents the time consumed by a protocol to identify routes from

source node to base station. It involves the time taken to identify the successor nodes, time taken

to identify the neighboring nodes and the time taken to identify optimal routes. Therefore, it is

the time since the first discovery data packet is sent till the source nodes has an optimal route to

the base station. By this field, we will measure the time from the moment that the route

discovery phase starts until the moment that the optimal hierarchical router updates all

intermediate (i.e. remote node, successor nodes, neighboring node) nodes in its route to base

station. Figure 5 given below illustrates the network lifetime for DG-HEMR framework and

comparison made with the existing Modified LEACH [1] and Distributed MAC [2] with a

transmission range of 200m for 500 nodes.

Figure 4 Results of network lifetime (200m transmission range)

In this figure, comparison of the network lifetime for two algorithms in different hop

counts between the source and the base station is provided. Again as expected, the network

lifetime increases with increase in the node density. However, for the existing Modified LEACH

[1] and Distributed MAC [2], the increase is smaller. As this figure shows, our proposed DG-

HEMR framework is suitable for higher node density, to find the optimal route between

successful neighbor nodes and base station, because of waiting time for identifying different

levels of router will take bigger time for hierarchical routing. Of course, this parameter is highly

influenced based on the successful identification of neighbor nodes because sooner the

identification of neighbor nodes, faster is the time taken for optimal routing and whenever the

neighboring nodes are identified in a swift manner, the routing setup time is faster and so the

improvement in terms of network lifetime. As a result, the network lifetime using DG-HEMR

framework is found to be improved by 25% when compared to Modified LEACH [1] and

improved by 54% when compared to Distributed MAC [2].

0

20

40

60

80

100

120

50 100 150 200 250 300 350 400 450 500

Net

wo

rk l

ifeti

me

Node density

DG-HEMR

Modified LEACH

Distributed MAC


1333

6. Conclusion

In this paper, we propose a novel ensemble-based clustering framework for data

aggregation in WSN with Dispersed Gaussian and Hierarchical Multipath routing called, DG-

HEMR. Our proposed Dispersed Gaussian Successor Node Identification algorithm based on

maximum likelihood function for identifying minimum distance between sensor nodes select the

shortest distance between the remote nodes and successor nodes. This in turn optimizes the

energy consumption and therefore the average end-to-end delay for data aggregation is said to be

reduced. Next, the Hierarchical Multipath Routing algorithm based on Gaussian factor arrives at

the optimal route based on energy efficiency and therefore improving the network lifetime. The

performance of this proposal has been compared with the state-of-the-art data aggregation

methods. In this work, the average energy consumption, end-to-end delay and network lifetime

are measured. The proposed algorithm increases the network lifetime by reducing the nodes

energy consumption and average end-to-end delay. Also DG-HEMR framework has proven its

efficiency by achieving better average results than the state-of-the-art methods.

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