Analytical Model of Energy Consumption in Clustered ... Sensor Networks Reza Rasouli1, Mahmood...

© 2013, IJARCSSE All Rights Reserved Page | 43

Volume 3, Issue 5, May 2013 ISSN: 2277 128X

International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com

Analytical Model of Energy Consumption in Clustered

Wireless Sensor Networks Reza Rasouli

1, Mahmood Ahmadi

2 , Hadi Tabatabaee Malazi

3 , Behnam Fallah

4

1Department of Information Technology,Science and Research Branch,

Islamic Azad University Kermanshah, Iran 2 Department of Computer Engineering, Faculty of Engineering,

University of Razi, Kermanshah, Iran 3 Department of Computer Engineering,

Power and Water University of Technology, Tehran, Iran 4 Department of Electronic and Computer,

Islamic Azad University, Qazvin Branch, Qazvin, Iran

Abstract— In recent years, energy efficiency and data aggregation is a major concern in many applications of

Wireless Sensor Networks (WSNs).WSNs, consists of a large number of sensor nodes. Each sensor node senses

environmental phenomenon and sends the report to a sink node. Since the sensor nodes are powered by limited power

batteries, so energy efficiency is a major challenge in WSNs applications. For this purpose, many novel innovative

techniques are required to improve the energy efficiency. Data aggregation is one of the most important issues for

achieving energy-efficiency in WSNs. The main goal of data aggregation is decreasing energy consumption by

decreasing need for redundant data transmission. In this paper, we propose an analytical model for evaluating energy

consumption in term of data transmission, reception and aggregation in cluster based WSNs architecture using

M/M/1 queuing model. Analysis support the validity of the proposed approach networks with compare the energy

consumption results for networks with and without data aggregation technique.

Keywords— Wireless Sensor Networks (WSNs), Data Aggregation, M/M/1 Queuing Model, Energy Consumption.

I. INTRODUCTION

Wireless sensor network (WSN) consists of a large number of sensor nodes which are distributed in a given space for

measuring environmental parameters, such as temperature, light, sound, humidity, and so on [1]-[3]. Many applications

have already been envisioned and described for WSNs in a wide range of areas, such as environment monitoring [4], health care applications [5], military surveillance applications [6], positioning and tracking [7], and etc. A critical issue in

WSNs is represented by the limited availability of power within the network and hence optimizing power is very

important [8]. Therefore, energy efficiency is lead to increasing the network lifetime. WSNs have many challenges in use

and deployment including limited power resources and also limited memory and communication capabilities [9].

However, the most important challenges in the WSNs are energy consumption because battery capacities of sensor nodes

are limited and replacing them in many applications are impractical. Sensor nodes use a large amount of energy for data

transmission and aggregation. [10]; therefore reducing amount of transmitted data can increase network lifetime and its

mission ability. In order to reduce data transmission rate, sensor node’s data can be aggregated and then sent to the sink

node. When the nodes are set up in the network, some nodes may have overlaps, and it depends on the distance between

nodes. Whatever the distance between nodes in wireless sensor network is less, nodes have greater overlap with each

other, and nodes that can cover one area, similar data are received from the environment.

This leads to energy waste of in three steps. 1 - Nodes sensing similar data where consume energy.

2 - Sensor nodes send to the data to Cluster-Head (CH) node, where use energy.

3 - CH node combine duplicate data, where use energy.

Data aggregation and hierarchical mechanism are commonly used in many critical applications of WSNs. It reduces the

data redundancy and communication load [11].The goal of data aggregation is the elimination of redundant data

transmission by summarization sensed data. Many data aggregation techniques and protocols are proposed in recent

years. However, the architecture of the WSNs plays a crucial role in the performance of data aggregation protocols and

techniques. In this paper, we propose an analytical model for evaluating energy consumption in term of data

transmission, reception and aggregation in cluster based WSN architecture using M/M/1 queuing model. The proposed

model can help designers to evaluate the energy consumption of clustered wireless sensor network with data aggregation.

We compare the energy consumption results for networks with and without data aggregation technique. The paper is organized into sections. The sections provide the information about the parts and modules of the research undertaken by

the current statements. Section I provides the introduction. Section II includes the background of the energy conservation

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Rasouli et al., International Journal of Advanced Research in Computer Science and Software Engineering 3(5),

May - 2013, pp. 43-55


techniques in WSNs, Section III includes the background of Data aggregation in WSNs, Section IV deals with the system model. In Section V, we present energy consumption in clustered WSNs with data aggregation. Section VI we present

energy consumption in clustered WSNs without data aggregation. The proposed work may be extended with the analysis

results to validate the proposed model in section VII. The conclusion is stipulated in Section VIII.

II. Related works

Many recent research works in the area of cluster-based WSNs have extensively focussed on energy efficiency, lifetime,

stability and scalability. We review some related work on energy conservation techniques in wireless sensor networks.

WSNs have many challenges in use and deployment including limited power resources and also limited memory and

communication capabilities [12].

However, the most important challenges in the WSNs are energy consumption because battery capacities of sensor nodes

are limited and replacing them in many applications are impractical. Sensor nodes consume most energy for data transmission and reception [13].

Data aggregation and hierarchical mechanism are commonly used in many critical applications of WSNs.

Low Energy Adaptive Clustering Hierarchy (LEACH) [14] is the first clustering protocol based on single-hop

communication model. It forms clusters based on the received signal strength and uses the CH nodes as routers to the

base-station. All the data processing such as data fusion and aggregation are local to the cluster. In LEACH, during the

setup phase, each node generates a random number between 0 and 1. If this random number is smaller than the threshold

value, T(n), which is given by Equation (1), then the node becomes a CH for the current round. During each round, new

CHs are elected and as a result balanced load energy is distributed among the CHs and other nodes of the network.

(1)

Where P is the desired percentage of CHs, r is the count of current round, G is the set of sensor nodes that have not been

CHs in the last 1/p rounds. In this paper, we refer round, 1/p, as epoch of the heterogeneous WSN. Power-Efficient Gathering in Sensor Information Systems (PEGASIS) [15] is a chain-based power efficient protocol

based on LEACH. It assumes that each node must know the location of all other nodes. It starts with the farthest node

and the chain is constructed by using a greedy algorithm. The chain leader aggregates data and forwards it to the BS.

Energy Efficient Hierarchical Clustering (EEHC): Bandyopadhyay and Coyle [16] proposed EEHC; a distributed,

randomized clustering algorithm for WSNs with the objective of maximizing the network lifetime. CHs collected the

sensors’ readings in their individual clusters and send an aggregated report to the base-station.

In [17], the authors described a heuristic approach to solve the data-gathering problem with aggregation in sensor

networks. In this scheme, the data is collected in an efficient manner from all the sensor nodes and transmitted to the BS

to maximize the lifetime of the network.

In [10], the authors proposed a novel Energy-Efficient Clustering and Data Aggregation (EECDA) protocol for

heterogeneous WSN. In the proposed method, after the CHs election, a path with maximum sum of residual energy would be selected for data communication instead of the path with minimum energy consumption. Therefore, each CH

first aggregates the received data and then transmits the aggregated data to the Base Station (BS). The main contributions

of EECDA protocol is to provide longest stability and improves the network lifetime in comparison to Low-Energy

Adaptive Clustering Hierarchy (LEACH), Energy-Efficient Hierarchical Clustering Algorithm (EEHCA) [18] and

Effective Data Gathering Algorithm (EDGA) [19].

In [20], Chen et al. proposed an algorithm to turn off nodes based on the necessity for neighbor connectivity. They intend

to reduce the consumption of system energy without significantly diminishing the connectivity of network. Approach

[20] used for increased stability in dynamic wireless sensor networks. Self-stabilization is attained by minimizing the

maximum number of nodes that need to change their topology information as a result of node mobility.

One of the best techniques for minimizing energy consumption in wireless sensor networks is switching between the

active and sleep state [21]. In this technique, when a sensor node has packet to send, it turns on and switches to active

state and sends packet. When sensor has not any packet to send, it switches to sleep state and turns off. If the number of transitions between the active and sleep state is high, energy consumption is high. Also in idle state, sensor nodes

consume less energy than active state.

By F.C. Jiang and et al [22], an analytical model based on the M/G/1 queuing model to reduce energy consumption by

reducing the average time to access media is competition.

In [23], the overall energy consumption of system can be reduced by turning off some redundant nodes. The objective is

to cover maximum of network with the minimum active sensors. In the proposed method, Sleepy Algorithm is used.

Sleeping method helps to improve network lifetime.

R.Maheswar and R.Jayaparvathy in [24] developed an analytical model of a clustered sensor network using M/G/1

queuing model. The authors have analyzed the system performance in terms of energy consumption and the mean delay.

R. Maheswar and R. Jayaparvathy [24,25] introduce an energy minimization technique using BUSY and IDLE states

where the energy consumed is minimized based on queue threshold using M/M/1 queuing model. The disadvantages of this method is that the amount of energy consumption in idle mode and sleep mode have not been considered.

III. DATA AGGREGATION

A WSN consists of a large number of sensor nodes, which are densely deployed over an unattended area either close to or

inside the targets to be observed. These sensor nodes periodically monitor or sense the conditions of the targets, process

otherwise

Gnif

PrP

P

nT

0

1mod1)(


May - 2013, pp. 43-55


the data, and transmit the sensed data back to a sink node. All of the sensor nodes collaborate together to form a communication network for providing reliable networking service. These networks are constraint with energy, memory

and computing power enhance efficient techniques are needed for data aggregation, data collection, query processing,

decision making and routing in sensor networks. The problem encountered in the recent past was of the more battery

power consumption as activity increases, need more efficient data aggregation and collection techniques with right

decision making capabilities. Sensor network lifetime due to limited power considerably depending on the battery power

of the sensor nodes and if the energy consumption of nodes is reduced, thus increasing the network lifetime. Wireless

Sensor Network [26, 27, 28, 29] generates a large amount of data that has to be aggregated at various levels. In the WSNs

usually sensor nodes that densely deployed. This means close sensor nodes could sense the same event as other nodes and

we have similar and redundant data. Therefore transmitting all the data is unnecessary. In order to save resources and

reduce consuming energy for the data transmission, sensor nodes data can be processed, eliminate the redundant data and

send the result to the sink node. So sensors data in each domain can be aggregated and the result would be send to the sink node. Using this technique will minimize the transmission rate and also save energy and increase network lifetime

[30]. The type of data aggregation technique and protocol that needs to be performed depends on the application, user

requirements and network architecture. There has been extensive work on data aggregation technique in WSNs. Selection

of proper data aggregation technique depends on How data is gathered at the sensor nodes and also how packets are routed

through the network [31, 32].

The performance of different data aggregation protocols and technique depend on architecture of the WSNs. WSNs

architecture can divide in two category; Flat and Hierarchical networks. In a flat network, data aggregation is

accomplished by data-centric routing where the sink node usually transmits a query message to the sensor nodes via

flooding, and the sensor nodes that have data matching the query will send response messages back to the sink node. In a

hierarchical network, sensor nodes are organized into clusters where the cluster heads serve as simple relays for

transmitting the data. Since the cluster heads have the same transmission capacity as the sensor nodes, the minimum

requirement on the number of clusters can be derived from the upper bound of the throughput. Higher throughput can be achieved by using clustering at the cost of having extra nodes functioned as cluster heads. Data aggregation in a

hierarchical network involves data fusion at cluster heads, which reduces the number of messages transmitted to the base

station, and hence improves the energy efficiency of the network. We can divide hierarchical network in four categories;

Cluster-Based Network, Chain-Based network, Tree-Based and Grid-Based network. In this paper we focus on Cluster-

Based Network architecture. For this manner we can divide WSNs nodes in three categories based on that’s operation and

responsibility. Simple regular sensor nodes that known as (SN), cluster-head (CH) node and sink node. SN sense

environment properties periodically or only sense event and send related data to the CH node that basically collect data

from multiple SN in its cluster, using some aggregation function like sum, count, average, max or min aggregates collected

data packet and then sends aggregated result to sink node. Figure 1 shows this process.

Figure1: cluster-based data aggregation

IV. SYSTEM MODEL

We consider a WSN that consists of a large number of sensors that are uniformly distributed and a sink node at the centre

of the field collects data from nodes.

In our WSN model, the following assumptions are made.

All SN nodes in network are identical.

SN

SN

SN

SN

SN

SN

SN SN

SN

SN

CH SN

SN SN

SN

SN

SN SN

SN

SN

SN

SN

CH

SN

SN

SN

SN

SN

SN

SN

SN

SN

SN

SN CH

SN Sink node

End User


May - 2013, pp. 43-55


The arrival of data packets to SN’s transmitter queue is assumed to follow a Poisson process with mean arrival rate λSN.

All CH nodes in network are identical.

The number of ordinary sensor nodes (SNs) in each cluster are the same.

Each SN nodes sends packets to CH independently and identically and the service rates following exponential

distribution with parameter µ𝐒𝐍

for transceiver queue and µ𝐩 for CH processor queue.

No channel contention.

Here, a SN, during its scheduled period of active time, remains in idle state, switches to active state when the number of

jobs (n) equal to k and the node switches back from active state to sleep state when there are no packets in the buffer. Such

switching actions between idle state to active state and active state to sleep state and sleep state to idle state are referred to

as transitions. Since the focus of this work is to minimize the power consumption of individual sensor nodes in WSN by

reducing the number of transitions during its scheduled period of active time, we analyze the behavior of a single sensor

node.

Figure 2 shows the situation between the three states of transmission.

Figure 2: Three-state transition diagram of a sensor in idle state and active state and sleep state.

V. Energy Consumption Analytical Model With Data Aggregation

In this section, we propose an analytical model based on M/M/1 queue for energy consumption. To compute energy

consumed for transmitting data to sink nod, we model each node based on simple M/M/1 queue. In our model, we

assume that SN nodes periodically sense environment and send sensed data to the CH node. CH node after reception of data will aggregate data and transmits the result to the sink node.

Figure 3 shows system as a network of queue.

In our analytical model, we define following notations:

For each queue λ<μ.

R: the number of job classes in the network.

R={ r1 , r2 , r3 , r4 }

µi,r

: The service rate of the 𝐢𝐭𝐡station of the 𝐫𝐭𝐡class.

Pi,r;j,s :Probability that a job of the 𝐫𝐭𝐡class at the 𝐢𝐭𝐡 station is transferred to the 𝐬𝐭𝐡class and the 𝐣𝐭𝐡station

(routing probability).

Pi.r;0: In an open network the probability that a job of the 𝐫𝐭𝐡 class leaves the network after having been served

at the 𝐢𝐭𝐡 station.

P0;i,r: In an open network the probability that a job from outside the network enters to the𝐢𝐭𝐡 station of the𝐫𝐭𝐡 class.

Ui,r : Utilization of the 𝐢𝐭𝐡 station of the 𝐫𝐭𝐡class.

Pi (0): Probability that the 𝐢𝐭𝐡station be empty.

Eidle :Energy consumption in idle state.

Esleep :Energy consumption in sleep state.

ETransmi t : The amount of energy required to send each packet in SNs node.

N: Number of nodes in each cluster

A. Energy consumption in sensor nodes (SNs) The steady state balance equations obtained for the analytical model according to the M/M/1 queuing model which are

given by equations (2) to (7).

Utilization of the sensor nodes (SNs) is determined as:

Idle

state

Active

state

Sleep

state

1<= n <= K-1

n = K

n >= 1

n = 0 n = 1


May - 2013, pp. 43-55


USN = λSN µSN

(2)

Where

µ𝐒𝐍

= BandWidth Packet Size (3)

Where λSN is the mean arrival rate of SN’s transmitter queue and µ𝐒𝐍

is the mean service rate in SN transmitter queue.

PSN n be probability that there are n packet in queue SNs node in the steady-state:

PSN n = 1 − USN UnSN (4)

PSN 0 be probability that there are 0 packet in queue SNs node in the steady-state:

PSN 0 = 1 − USN (5)

So PSN n of equations (3) and (4), is obtained, which is equivalent to:

PSN n = PSN 0 UnSN (6)

So total energy consumption in each SN nodes for transmitting data to CH is:

ESN = PSN 0 ∗ Esleep + USN (Eidle + ETransmit ) (7)

Finally, the total energy consumption for N sensor nodes in the per cluster is:

ESN−Total = N − 1 ∗ ESN (8)

B. Energy consumption in CH nodes A queuing network may be open (Jackson model), closed (Gordon/Newell model), or mixed that just consist of single

classes of job. Jackson and Gordon/Newell model were extended by Baskett, Chandy, Muntz, and Palacios that consider

multiple classes of job in the network [33, 34].

For modeling energy consumption in CH nodes, we consider CH nodes as an open BCMP queuing network model that

consists of 5 service stations and 4 job classes. Our queuing network consists of 5 service stations that each service

station contains a single-server with first-come-first-served (FCFS) policy and equal service rate for all classes of jobs.

In this type of station, the service times must be exponentially distributed and class independent. Therefore for 𝐢𝐭𝐡

service station, µ𝐢,𝟏

= µ𝐢,𝟐

=µ𝐢,𝟑

=…=µ𝐢,𝐑

= µ𝐢 .

We assume that the number of jobs (data packet) in each class at each service station (processor and transmitter/receiver)

is always non negative. We assume that jobs change their classes while transferred through the processor station and

transceiver station after data aggregation.

In our BCMP model, there are 5 stations and 4 job classes. For each class, we specify routing probabilities. Jobs are transferred between any two stations and may be changed its classes according to given routing probabilities.

Table 1: routing probabilities

𝐩𝐢,𝐫 ;𝐣,𝐬 0 R,r1 P,r1 T,r1 R,r2 P,r2 T,r2 R,r3 P,r3 T,r3 R,r4 P,r4 T,r4

0 0 1 0 0 0 0 0 0 0 0 0 0 0

R,r1 0 0 1 0 0 0 0 0 0 0 0 0 0

P,r1 1-P 0 0 0 0 0 P 0 0 0 0 0 0

T,r1 0 0 0 0 0 0 0 0 0 0 0 0 0

R,r2 0 0 0 0 0 0 0 0 0 0 0 0 0

P,r2 0 0 0 0 0 0 0 0 0 0 0 0 0

T,r2 0 0 0 0 0 0 0 1 0 0 0 0 0

R,r3 0 0 0 0 0 0 0 0 0 0 0 0 1

P,r3 0 0 0 0 0 0 0 0 0 0 0 0 0

T,r3 0 0 0 0 0 0 0 0 0 0 0 0 0

R,r4 0 0 0 0 0 0 0 0 0 0 0 0 0

P,r4 0 0 0 0 0 0 0 0 0 0 0 0 0

T,r4 0 0 0 0 0 0 0 0 0 0 0 0 0

Figure 3: System as a queuing network

Receiver

r4

Receiver 𝛌𝑐ℎ

µ𝑟 1-P

Processor

r1 µ𝐩

µ𝐫

Transmiter

µ𝐭

𝐒𝐍1 𝛌𝑠𝑛

𝐒𝐍2 𝛌𝑠𝑛

𝐒𝐍𝑛 𝛌𝑠𝑛

Transmiter 𝐏𝛌𝑐ℎ

µ𝐭 r2

𝝀𝑺𝒊𝒏𝒌

r3

SN Queue CH Queue Sink Queue

Transmitter

Transmitter

r1 r1


May - 2013, pp. 43-55


For example (see Table 1), a class r1 job entering from outside goes to the receiver queue (R) with probability P0 ;R ,r1 =1. In the routing probabilities table, because of the large number of zero entries, consequently only non-zero entries obtains

it. Our queuing network consists of service stations that is (R= Receiver, P= Processor, T=Transmitter).

The non-zero entries as follows:

P0 ;R ,r1 = 1

PP ,r1 ; 0 = 1 − p

PR ,r1 ; P ,r1 = 1

PT ,r2 ; R ,r3 = 1

PR ,r3 ; T ,r4 = 1

PP ,r1 ; T ,r2 = P

With that assumption and routing probabilities table, we can set the arrival rate of each class to each node using the

following formula:

ei,r = λ0 ;i ,r + ej ,s S∈Rj=1..N Pj ,s ;i ,r (9)

Where λ0;i,r is the arrival rate from outside to the 𝐢𝐭𝐡 station of the 𝐫𝐭𝐡class and 𝐞𝐢,𝐫 is the visit rate of jobs of the

𝐫𝐭𝐡class at the 𝐢𝐭𝐡station. The visit rate of jobs for 5 service stations from equation 8 is obtained that is equal to:

eR,r1 = λ0 ;i,r1 + 0 = 1 (10)

eP,r1 = λ0 ;P,r1 + eR,r1PR,r1;P,r1 = 1 (11)

eT,r2 = λ0 ;T,r2 + eP,r1PP,r1;T,r2 = eP,r1 ∗ P = P (12)

eR,r3 = λ0 ;R,r3 + eT,r2PT,r2;R,r3 = P (13)

eT,r4 = λ0 ;T,r4 + eR,r3PR,r3;T,r4 = P (14)

Also, the arrival of data packets to CH’s receiver queue is assumed to follow:

λCH = N − 1 λSN (15)

So utilization of each class equals to:

Ui ,r = λr ei ,r

µi

(16)

Thus, utilization for 5 service stations in our model:

UR,r1 = λCH ∗eR ,r1

µR

=λCH

µR

(17)

UP,r1 = λCH ∗eR,r1

µP

=λCH

µP

(18)

UT,r2 = λCH ∗eT,r2

µT

=P λCH

µT

(19)

UR,r3 = λsink ∗eR ,r3

µRsink

=P λCH

µRsink

(20)

UT,r4 = λsink ∗eT,r4

µTsink

=P λCH

µTsink

(21)

For our analytical model, the following notations are used include:

ETCH : is the total energy consumed in each CH for transmitting data in given time interval.

ERCH : is the total energy consumed in each CH for receiving data in given time interval.

EPCH : is the total energy consumed in each CH for processing data in given time interval.

Eidle : Energy consumption in idle state.

Esleep : Energy consumption in sleep state.

Now we can model the energy consumption in CH node:

ECH = PCH 0 ∗ Esleep + ERCH + EPCH + ETCH + USN ∗ Eidle (22)

Where

PCH 0 = 1 − λCH UR 1 − λCH UT 1 − λCH UP (23)

Where according to the equation (22):

Ui = Ui,r (24)

Consequently:

UR = UR,r1 + UR,r3 =λCH

µR

+P λCH

µRsink

(25)


May - 2013, pp. 43-55


UT = UT,r2 + UT,r4 =P λCH

µT

+P λCH

µTsink

(26)

UP = UP,r1 (27)

Also if ET ,CH is the transmission energy in CH nodes, ER ,CH is the receiving energy in CH nodes and EP,CH is the

processing energy in CH nodes, so:

ERCH = UR,r1 ∗ ER ,CH (28)

EPCH =UP,r1 ∗ EP,CH (29)

ETCH =UT,r2 ∗ ET ,CH (30)

So total energy consumed in each cluster equals to the following equation:

ECluster = ESN −Total + ECH (31)

Also total energy consumed in K cluster equals to the following equation:

EClusters = K ∗ ECluster (32)

C. Energy consumption in sink node The steady state balance equations obtained for the analytical model according to the M/M/1 queuing model which are

given by equations (33) to (38). The probability that the sink node is in idle state is determined as:

PSink 0 = 1 − λSink URsink 1 − λSink UTsink (33)

Also, the arrival of data packets to sink receiver queue is assumed to follow:

λSink = p λCH (34)

Now we can model the energy consumption in sink node:

ESink = PSink 0 ∗ Esleep + ERSink + ETSink + UCH ∗ Eidle (35)

where ESink is the total energy consumed in sink node for receiving and transmitting data in given time interval, ETSink

is the total energy consumed in sink node for transmitting data in given time interval, ERSink is the total energy consumed in sink node for receiving data in given time interval.

Where in (34):

UCH = 1 − PCH 0 (36)

Also if ET ,Sink is the transmission energy in sink node, ER ,Sink is the receiving energy in sink node, so:

ERSink =UR,r3 ∗ ER ,Sink (37)

ETSink =UT,r4 ∗ ET,Sink (38)

Finally, the total energy consumption in the network of equations (31) and (35), is obtained, which is equivalent to:

ENetwork = EClusters + ESink (39)

VI. Energy consumption analytical model without data aggregation

For achieving result of energy consumption in WSNs without data aggregation, we use equation (7) for total energy

consumption in each SN nodes for transmitting data to CH nodes.

Also total energy consumption in each CH nodes for transmitting data to sink node is assumed to follow:

E1CH = P1CH 0 ∗ Esleep + ERCH + ETCH + USN ∗ Eidle (40)

That:

P1CH 0 = 1 − λCH UR 1 − λCH UT (41)

Also, we use equations (28), (29) for the total energy consumed in each CH for transmitting data (ETCH ) and the total

energy consumed in each CH for receiving data (ERCH ) in given time interval. Also,

UR,r1 =λCH

µR

(42)

UT,r2 =λCH

µT

(43)

So total energy consumed in each cluster equals to the following equation:

E1Cluster = ESN −Total + E1CH (44)

Also total energy consumed in K cluster equals to the following equation:

E1Clusters = K ∗ E1Cluster (45)

Now we can model the energy consumption in sink node:

E1Sink = P1Sink 0 ∗ Esleep + ERSink + ETSink + U1CH ∗ Eidle (46)

where E1Sink is the total energy consumed in sink node for receiving and transmitting data in given time interval, ETSink

is the total energy consumed in sink node for transmitting data in given time interval, ERSink is the total energy

consumed in sink node for receiving data in given time interval.


May - 2013, pp. 43-55


Where in (45):

U1CH = 1 − P1CH 0 (47)

Finally, the total energy consumption in the network of equations (45),(46) which is equivalent to:

E1Network = E1Clusters + ESink (48)

VII. MODEL Analysis Now, we compare the result of proposed model with result of model that created for WSNs without data aggregation

technique. We use simulator MATLAB for wireless sensor networks. We consider Mica2 mote sensors for a wireless

sensor network. We perform the simulation for a WSN using the parameters as in [35]. The various network parameters

and the power consumption parameters of Mica2 mote sensors used for the simulation model are shown in Table 2.

Model results are obtained in various scenarios by varying the mean arrival rate from 0.1 to 1 per SN and varying the

elimination probability from 0.1 to 1 after data aggregation in CH to determine the average energy consumption.

Table 2: Model and simulation parameter

Value Parameter

to1 0. 1 Mean arrival rate per to SNs transmitter

queue

10 Number of sensor nodes per each cluster (N)

10 Number of Cluster (K)

250 B Packet size

350 Kbps Band width

0.1 to 1 Elimination probability(P)

30mj ETransmit

65µj Esleep

8mj Eidle

15mj ER ,CH

15mj EP,CH

35mj ET ,CH

15mj ER ,Sink

40mj ET,Sink

1000 sec Time simulation

Also analysis results are obtained for sink node by changing the mean arrival rate and various elimination probability. We

measure the average energy consumption of N sensor nodes and the average energy consumption of K cluster in network.

Finally, the total energy consumption in the network is obtained.

In Figure 4–a, X-axis is equal to the mean arrival rate (Lambda) and Y-axis is equal to the average energy consumption

in the CH node. From Figure 4-a, it is results that the average energy consumption for per CH node by using analytical

model with data aggregation and analytical model without data aggregation. As we can see, increasing the mean arrival

rate would result in increasing energy consumption. We consider elimination probability P=0.4.

Figure 4-a: energy consumption per CH node for P=0.4


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Figure 4-b: energy consumption per cluster for P=0.4

In Figure 4–b, X-axis is equal to the mean arrival rate (Lambda) and Y-axis is equal to the average energy consumption

in per cluster. We can see the total energy consumption in one cluster by using analytical model with data aggregation

and analytical model without data aggregation. We consider elimination probability P=0.4.

In Figure 5, we can see the total energy consumption in per CH node by using analytical model with data aggregation and

analytical model without data aggregation for elimination probability P=0.5.

Figure 5: energy consumption per CH node for P=0.

In Figure 6, we can see the total energy consumption in one cluster by using analytical model with data aggregation and

analytical model without data aggregation. In each figure, we compute energy consumption with different mean arrival

rate to SN’s transmitter queue. As we can see, increasing the mean arrival rate would result in increasing energy

consumption. We consider different elimination probability. We can see that for elimination probability less than 0.7, energy consumption for one cluster with data aggregation is less than network without data aggregation.

6-a


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6-b

6-c

Figure 6: energy consumption per cluster for a:P=0.4, b:P=0.5, c:P=0.7

In Figure 7, we can see the total energy consumption in sink node by using analytical model with data aggregation and

analytical model without data aggregation for elimination probability P=0.4.

Figure7: energy consumption in sink node for P=0.4 in sink node


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In Figure 8, we can see the total energy consumption in the network by using analytical model with data aggregation and analytical model without data aggregation. In each figure, we compute energy consumption with different mean arrival

rate to SN’s transmitter and CHs queues and sink queues. As we can see, increasing the mean arrival rate would result in

increasing energy consumption. We consider different elimination probability. We can see that for elimination

probability less than 0.8, energy consumption for one cluster with data aggregation is less than network without data

aggregation. However this result depends on the value of WSN parameters that illustrated in table 2.

8-a

b

8-c


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.8-d

Figure8: total energy consumption in network for a:P=0.3, b:P=0.4, c:P=0.5,d=p=0.8

VIII. Conclusion

In this paper we have proposed the new simple energy consumption estimation scheme in cluster based WSN with data

aggregation using queuing network model. The main goal of data aggregation is decreasing energy consumption by

decreasing need for redundant data transmission. For comparison of network with data aggregation and network without

it, we proposed another analytical model. After comparison result of two models in various scenarios, we can see that

energy consumption in the best state 25% decreased, also for elimination probability less than 0.8, energy consumption for network with data aggregation is greater than network without data aggregation. However those values are based on

ours case study and may be different in other case study with various WSNs parameters

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