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International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
90 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
An Analytical Model for Best Effort Traffic in WiMAX
Networks
Swati Sahu, Anjulata Yadav, Shekhar Sharma
Department Of Electronics and Telecommunication Engineering
S.G.S. Institute of Technology and Science, Indore, India
swati03.sahu@gmail.com , yadawanjulata@rediffmail.com , shekhar.sgsits@gmail.com
A B S T R A C T
WiMAX is based on standard IEEE 802.16 and it is a very promising technology for broadband
wireless access due to its middle range access, high data rates, mobile access, high scalability and
convenient deployment. WiMAX designed to support different type of application like voice, video
and data. To support different types of application, there is various service classes defined in
WiMAX. Best Effort is one of the service class which supports web traffic. In this paper, analytical
model has been presented for mono and multi profile web traffic based on Markov chain analysis.
In this model Maximum Sustained Traffic Rate (MSTR) which is one of the QoS (Quality of service)
parameter associated with the BE service class is taken into account. This model provides closed
form expressions giving all the performance parameters such as average instantaneous user
throughput, average number of active users and average resource utilization. This model allows
the WiMAX network operator and manufacturer to find the minimum number of users in a cell
that give 50% average resource utilization and the maximum number of users in the cell can also
be found that guarantee the minimum throughput threshold.
Index Terms: WiMAX, Markov Chain, Scheduling, OFDMA, MSTR, QoS.
I. INTRODUCTION
Due to the increasing demand of internet population, the interest in broadband wireless access has
increased dramatically in recent few years. This encourages manufacturer and academic researcher
towards the development of IEEE802.16 based WiMAX networks. WiMAX operates at a high frequency at
a high frequency of 2-11 GHz and 10-66 GHz for Non Line Of Sight (NLOS) and Line Of Sight (LOS)
transmission respectively [1].Theoretically, WiMAX Base Station (BS) can provide coverage are for
wireless access in the range of 50 km for fixed Subscriber Station (SS) and 5 to 10 km for Mobile Station
(MS) with maximum of data rate up to 70 Mbps [2].
One of the most important features of WiMAX is to support of Quality of Service (QoS) to different type of
traffic such as Voice Over IP (VOIP), File Transfer Protocol (FTP), video streaming, http etc. In order to
facilitate QoS features to different applications, the network traffics are categorized into five different
types of service: Unsolicited Grant Service (UGS), real time Polling Service (rtPS), extended real time
Polling Service (ertPS), non real time polling service (nrtPS) and Best Effort (BE). Most of the web traffic
falls into the BE service class. Each service class has different network characteristics and QoS
requirements. MSTR is one of the QoS parameter associated with BE service. This is not a guaranteed rate
but an upper bound [2].This parameter defines the peak information rate of the service. The rate is
expressed in bits per second. The procedure to implement this rate has been left open in the standard. In
this paper, MSTR is taken into account while deriving the expression for performance parameter. This
implies the implementation of a throttling scheduling policy [3] that regulates the user peak data rate.
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
91 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
IEEE 802.16 defines the specifications for MAC and Physical layers of WiMAX networks. Physical layer
considers two types of transmission techniques Orthogonal Frequency division Multiplexing (OFDM) and
Orthogonal Frequency division Multiple Access (OFDMA). Both of these techniques have frequency band
below 11 GHz and use Time Division Duplexing (TDD) and frequency Division Duplexing (FDD) as its
duplexing technology. OFDM divides the available spectrum into a number of parallel orthogonal
subcarriers then the available subcarriers are grouped into subset of subcarriers called sub-channel.
Different sub-channels can be allocated to different mobile stations depending on their channel
conditions and data requirement. There are several sub-channelization schemes defined in mobile
WiMAX [2]. Distributed subcarrier permutation is most preferable sub-channelization scheme in which
subcarriers are pseudo randomly distributed across the frequency spectrum. Partial Usage of SubCarriers
(PUSC) is a type of Distributed subcarrier scheme.
Slot allocation is also another responsibility of the PHY layer. Slot is a minimum time –frequency resource
that can be allocated by a WiMAX to a given link [2].For PUSC, every slot is made over 2 symbol and one
subchannel. In TDD mode the frame is divided into two subframes: a downlink frame followed by a
uplink frame after a small guard interval.
Another important feature of mobile WiMAX is that it supports adaptive modulation and coding schemes
(MCS) enabling it to vary MCS according to the channel conditions. WiMAX MCS can be changed on a
burst by burst basis per link, depending on the channel condition. Most critical part of the MAC layer is
the scheduling. Scheduling mechanism makes decision that how to allocate available resources among
the users to meet the QoS requirements.
The rest of the paper is organized is as follows: section 2 describes the related work of performance
analysis of BE traffic in WiMAX. Section 3 defines the assumptions made for the analytical model. The
proposed Markov Chain model for mono and multi profile traffic are describes in the section 4 .Numerical
results are presented in section 5.Conclusion and area of future research are finally drawn in section 6.
II. RELATED WORK
Many research efforts have been dedicated to performance evaluation of traffic scheduling schemes. Kim
and Yeom in [8] have presented a comprehensive performance analysis of BE traffic in IEEE 802.16
networks. First, they have derived two request-based bandwidth allocation schemes, and then compared
them with a scheme for bandwidth allocation without request. Authors of [9] have presented a fair
resource scheduling scheme for BE traffic and have analyzed the system performance with the help of
simulations. In [10], authors have proposed a Weighted Proportional Fair (WPF) scheduling for BE traffic
of WiMAX. Analytical expressions have been derived for different performance metrics.
While considering the BE traffic, users may generate traffic of different profiles (characterized by the
volume of data generated and reading time) [5]. In [11] the performance of multi-profile internet traffic
for a WiMAX cell using packet level simulations has been studied. They have evaluated the throughput
performance in a cell while considering the number of users, modulation schemes to be used by users
and data rate required by users using System Level Simulation (SLS).
An analytical model for BE traffic without considering MSTR has been proposed in [6]. In the paper [3],
authors have put forward an analytical model for mono and multi profile traffic taking MSTR into
account. The author considered 4 MCS technique QPSK ½, QPSK-3/4, 16QAM-1/2 and 16QAM-3/4. In
this paper, similar analytical model as [3] has been considered with 6 MCS schemes: QPSK-1/2, QPSK-
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
92 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
3/4, 16QAM-1/2, 16QAM-3/4, 64 QAM-2/3, 64QAM-3/4 and also behavior of the model is observed for
higher and lower loads (1 Mb, 3Mb and 6Mb) and for different MSTR requirement.
III. SYSTEM DESCRIPTION
In this section, WiMAX scheduling mechanism is discussed briefly and then throttling scheduling policy
has been introduced. To develop an analytical model, some assumptions have been made. Finally,
assumptions have been discussed.
3.1 WiMAX scheduling mechanism
Scheduling is the main component of the MAC layer that assures QoS to various service classes. The MAC
scheduling Services are adopted to determine which packet will be served first in a specific queue to
guarantee its QoS requirement. Scheduling architecture should ensure good use of bandwidth, maintain
the fairness among users, and satisfy the requirements of QoS. Two types of scheduling schemes are
supported by WiMAX i.e. uplink request/grant scheduling and downlink scheduling. Scheduling
algorithm can be implemented in the BS as well as in the MSs.BS has to deal with the both uplink and
downlink traffics and hence two schedulers are needed at the BS to schedule the packet transmission in
downlink and uplink subframe and one scheduler at the SS for uplink to apportion the assigned BW to its
connections. The scheduling decision for the downlink traffic is relatively simple as only the BS transmits
during the downlink sub frame and the queue information is located in the BS. In this paper, a throttling
scheduling policy has been introduced as BS scheduler.
3.2 Throttling scheduling policy
In this scheduling policy [3], there is a limit on maximum achievable instantaneous user throughput and
in a TDD frame, the user can be allocated only the number of slots required to guarantee its MSTR. If a
mobile is in outage it does not receive any slot and its throughput is degraded temporarily. If at a given
time the total number of available slots is not enough to satisfy the MSTR of all active users, they all see
their throughputs equally degraded. After ensuring that each active user attains his maximum
throughput, if there are still resources available in the frame these resources go unused.
3.3 Modeling assumptions
• A single WiMAX cell is considered that handle traffic of BE service class. The number of MS in a
cell is represented by N.
• The overhead in the TDD frame is assumed to be constant and hence number of slots available for
data transmission in TDD frame is constant and it is denoted by Ns.
• The number of MS allowed to be in active transfers is not limited i.e. no blocking can occur and all
connection demand will be accepted.
• Based on the radio link quality, MS can change the MCS very often.It is assumed that MS change
its coding scheme at every frame. At each time step, any MS has probability pk to use MCSk.
• Hanover condition is not taken into consideration.
• Since only Best Effort traffic is taken into account, each mobile station (out of N) is assumed to
generate an infinite length ON/OFF elastic traffic. ON/OFF periods representing web-page
downloads and the intermediate reading times. ON period depend on the system load and
characterized by their size and OFF period (reading time) is characterized by its duration.
• Both ON size and OFF duration are exponentially distributed.
International Journal of Advance Foundation and Research in Computer (IJAFRC)
93 | © 2014, IJAFRC All Rights Reserved
IV. MONO-TRAFFIC ANALYTICAL MODEL
The proposed analytical model for BE traffic of WiMAX is based on a Continuous Time Markov Chain
(CTMC) made of N + 1 states [3]. This CTMC is shown in
Figure 1 General CTMC with state
At any instant state n of this chain (0
(i.e., MS that are in ON period).
• A transition out of a generic state n to a state n + 1 occurs when a mobile in O
into the ON period for data transfer, this transition is called
given by (N −n)λ, where λ is defined as :
• The departure from a state n to a
transfer. If there are n active MS at a given
represented as μ(n).
Departure rate: Firstly some quantities are defined to calculate the departure rate
• In order to compensate losses due to outage
Bit Rate (DBR) is considered
• The number of slots per frame g
given that g0 = 0.
• The average number of slots per frame
MSTR can thus be determined as [
• Once is obtained, the departure rate of
Now the performance parameter will be derived using the departure rate.
Performance Parameters
There are three performance parameters for which formulae could
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014.
© 2014, IJAFRC All Rights Reserved
TRAFFIC ANALYTICAL MODEL
ytical model for BE traffic of WiMAX is based on a Continuous Time Markov Chain
]. This CTMC is shown in Figure. 1.
1 General CTMC with state-dependent departure rates.
state n of this chain (0 ≤ n ≤ N) corresponds to the total number of
A transition out of a generic state n to a state n + 1 occurs when a mobile in O
for data transfer, this transition is called arrival transition and arrival rate is
is defined as : λ= 1/ . Here represents the average OFF period.
departure from a state n to a state n−1 occurs when a mobile in ON period, completes its
er. If there are n active MS at a given time, this departure rate
Firstly some quantities are defined to calculate the departure rate
losses due to outage, an increased instantaneous bit rate called Delive
Bit Rate (DBR) is considered which is given as[3]:
The number of slots per frame gk required by a MS, using MCSk, to attain its DBR is found as [3
The average number of slots per frame required by a MS, using K different MCS, to realize its
MSTR can thus be determined as [3]
is obtained, the departure rate of throttling scheme is given as [3]:
Now the performance parameter will be derived using the departure rate.
There are three performance parameters for which formulae could be derived from the
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
www.ijafrc.org
ytical model for BE traffic of WiMAX is based on a Continuous Time Markov Chain
dependent departure rates.
N) corresponds to the total number of concurrent active MS
A transition out of a generic state n to a state n + 1 occurs when a mobile in OFF period enters
arrival transition and arrival rate is
represents the average OFF period.
in ON period, completes its
when m mobiles are is
Firstly some quantities are defined to calculate the departure rate:
tantaneous bit rate called Delivered
(1)
to attain its DBR is found as [3]
(2)
required by a MS, using K different MCS, to realize its
(3)
]:
(4)
be derived from the model. These
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
94 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
parameters are: average instantaneous resource utilization of TDD frame �� , average number of an active
user �� and average instantaneous user throughput during ON period �� .In order to find the expressions
for these parameters, stationary state probabilities π(n) can be obtained from the birth and death
structure of Markov chain shown in Figure. 1 .Steady state probability of the Figure.1 can be written as
[12]
��� ���� 1� … . �� � � 1��� �� … . � ��0��1��2 … … . ���
��� �! ��
�� �! ∏ ���������0
Putting the value of ��� from eq. (4)
��� �! ��
�� �! ��
�! ∏ ��� !��"#, ��������0
(5)
Where � %#&'(#&)) *+,-
Since
. ��� 1�/0
��0 11 � ∑ �!
�� �! �! ∏ ��� !��"#, ������
2���
(6)
The average number of active users can now be written as:
�� . ����2
���
(7)
Average Numbers of departures per unit of time is given by [3]:
3� . ������2
���
(8)
From little’s law, average duration 4#5� of an ON period-
4�5� ��3�
(9)
And average throughput �� obtained by each mobile in active transfers
�� !#5�4#5�
(10)
The average instantaneous resource utilization (of TDD frame) is given as [3]:
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
95 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
�� . �"#max��"#, �� ���
2
���
(11)
V. MULTI-PROFILE TRAFFIC ANALYTICAL MODEL
For analytical modelling Multi profile BE traffic is considered. Multi profile traffic contain different class
of users and each class is characterised by a specific traffic profile. Now some assumptions have been
made for the multi profile modelling [3].
The users are divided into R classes of traffic, each one having a specific profile
(MSTRr, !#95� , 4#95::), r=1,2…R For a given class r , the average size of ON data volumes (in bits) , required
MSTR and the average duration of OFF periods are denoted by !#95�,MSTRr and 4#95:: respectively. Hence,
a traffic profile of a generic class r will be denoted by:
�9 !#95�4#95::;<=>9
Firstly, the profile of each class (!#95�, MSTRr , 4#95:: ) is transformed into an equivalent profile such that
[3]:
!#5�4#5::9 ;<=> !#5�9
4?�5::9 ;<=>9
After this transformation, the mobile of the equivalent system have the same average ON size !#5� but
different OFF period 4?�5::9 .With this transformation, the equivalent system can be modelled as multiclass
closed queuing network with two station (Figure .2).
• The station 1 is the Infinite Server (IS) station; this station has as many servers as required. This
station models mobiles in OFF periods and has class dependent service rate λ9 4?�5::9 .
• The active MS are modelled by station 2 called Processor Sharing (PS) .This station has class
independent service rate or departure rate μ (n) with n as the number of active MS. Unlike for
conventional schemes, the expression of mono-profile traffic to calculate μ (n) (Eq. 4) cannot be
directly used here. The equation to find μ (n) for station PS is written below [3]
��� ��� !�"#��, �� � ;<=>
!#5�
(12)
where MSTR and !#5� are related to equivalent multi-class after profiles and "# �� is average number of
slots per frame needed by n active mobiles to obtain their MSTR requirement. To estimate "# �� , firstly
"� 9 the average number of slots needed by mobile of class r is defined
"� 9 . @A93B>9=C
�A
D
A��
(13)
Where @A9 is the stationary probability for MS of class r using MCSk and
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
96 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
3B>9 ;<=>91 @09
(14)
Second, the probability E9�� that an active MS belongs to class r, when there are n active MS, has to be
estimated. E9�� can be calculated by considering a multi-dimensional Markov chain which states
corresponds to the detailed distribution of the current active mobiles of each class in the system. Author
of [3] presented a linear approximate solution to estimate E9�� and it is described as follows:
Now if it is known that n = N, where � �� � �F � G … �9 then E9�� can be written as:
E9�� �9/�
And for n = 1, the probabilityE9�1 can be approximated as:
E9�1 �9�9∑ ����-���
After calculating the above two limiting values, let E9�� is a linear function of n such that:
E9�� � � I
Where JK�2LJK��2L� and I 2JK��LJK�2
2L�
The equation for "� ��, can now be expressed as:
"#�� ∑ �E9��-9�� "#9
After transformation of parameters, the closed queuing network shown in Figure. 2 can now be handled
using extension of the BCMP theorem for stations with state-dependent rates [13].
Let population vector denoted by �MMN ���, �F … … �-, here NR represents the number of MS of
class R.The steady state probabilities are written as:
���MN ���MN�, �MNF 1O P���MN�PFQPNFR
Here �MN� ���� … … . ��- , niR represents the number of class-R MS presents in station i .
P���MN� 1���! … . . ��-!
1λ�
�SS … … . . λ-�ST
PF��MNF ��F� � G � �F-!�F�! … . . �F-!
1∏ ��U�V
A��
and G is a normalization constant presented as:
O . P���MN�PF��MNF�MNSW�MNV�2MMN
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
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Figure 2 Closed-Queuing Network
Performance parameter:
Now, the expressions for performance parameters are derived using steady-state probabilities. The
average number of active MS of class r active mobiles is given by:
�� 9 . �F9���MN�, �MNF�MNSW�MNV�2MMN
(15)
The average number of class r mobiles completing their download per unit time, can be written as:
39 . �9�MNSW�MNV�2MMN
��MNF���MN�, �MNF
(16)
where ���MNF is the departure rate [3]of class r MS when there are �MNF active MS and is given as:
�9��MNF ��� !�"#��MNF, �� �F9
;<=>9!#5�9
(17)
"#��MNF is given by "#��MNF ∑ �F9"#9-9��
The average instantaneous throughput [3] for class-r MS is written as:
��9 !#5�9
4#5�9
(18)
where 4#5�9 on is obtained through Little’s law i.e. 4�5�9 X�KY�K
At the end, parameter �� [3] is given by following equation:
�� . "#��MNF� !�"#��MNF, �� ���MN�, �MNF
�MNSW�MNV�2MMN
(19)
VI. NUMERICAL RESULT
This section examines the proposed analytical model. The results of average active number of users,
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
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average throughput and average utilization of TDD frame are evaluated under different number of
mobile stations. All the system related parameters are listed in table1.A single WiMAX cell. The number
of slots depends on the system bandwidth, the frame duration, the downlink/uplink ratio, the subcarrier
permutation (PUSC, FUSC, AMC), and the protocol overhead (preamble, FCH, maps).The subcarrier
permutation PUSC is considered and it is assumed that protocol overhead is of fixed length (2 symbols)
although in reality it is a function of the number of scheduled users.
Table 1. System Parameters
Parameter Value
Number of cell is system 1
System Bandwidth 10MHz
Downlink/uplink ratio in a TDD frame 2/3
Duration of a TDD frame =C 5ms
Number of data slots per TDD frame 450
In table 2 traffic parameters for mono and multi profile traffic are listed. In this analytical model, it is
assumed that ON data volume and OFF duration are exponentially distributed. For mono-profile traffic,
the behaviour of the model is observed for high data volume and low data volume (6Mbits and 1
Mbits).For multi-profile traffic, the total number of users N is divided equally among two classes.
Table 2. Traffic parameters
Parameter Mono-traffic Multi traffic
Class1 Class 2
MSTR 512,1024,2048 1024 2048
12!#5�Z;I�4[\ Q 3 3
4#5::Z<]^\ 3 3 6
Wireless channel parameters are summarized in table 3.The table lists different MCS with their
respective number of bits transmitted per slot and stationary probabilities [4].
Table 3. Channel Parameters
Channel state
[0,1…K]
MCS and Outage Bits per slot
Stationary
probability
0 Outage �0 = 0 0.04
1 QPSK-1/2 ��= 48 0.26
2 QPSK-3/4 �F= 72 0.18
3 16QAM-1/2 �_= 96 0.24
4 16QAM-3/4 �`=144 0.14
5 64QAM-2/3 �a= 192 0.02
6 64QAM-3/4 �b= 216 0.165
Figure.3-9 respectively show the plot for average number of active users, average instantaneous
throughput and the average channel utilization for mono profile traffic and multi traffic profile .
Mono-Traffic analysis: Figure 3 shows the variation of active number in accordance with the number of
users present in the cell. It can be seen that the number of active users in the cell increase linearly as with
the number of MS present in the cell i.e. the rate of increment of the number of active users is linear.
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
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Figure. 4 Show the graph between average instantaneous user throughputs for mono-traffic different
values of MSTR. The graph shows that as the number of MS in the cell is less, throughput is higher for MS
which has high MSTR requirement but as the number of MS increases in the cell, throughput degraded for
all MS irrespective of their MSTR. Figure. 5 shows the variation of average resource utilization for mono
traffic with the number of users. Utilization of resources increases with increase in number of users.
Form Figure.6 one more important thing can be observed that the analytical model performs well under
low (1MB), medium (3Mb) and high (6Mb) load traffic condition. It can be also observed that throughput
is high for low load.
Figure 3 Average number of active users, mono Figure 4 Average instantaneous user throughput -
traffic(MSTR=512kbps, c� de fgh, i#djj fklm) mono-traffic different values of MSTR( c� de 3Mb, i#djj f klm
Figure 5 Average resource utilization, mono Figure 6 Average instantaneous user throughput
traffic, (MSTR=512 kbps, n� op fgh,) mono-traffic different loads ( n� op qgh, 3Mb
r#oss fklm ) and 6 Mb, MSTR=2048 Kbps, r#oss fklm)
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International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
100 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
Figure 7 Average number of active users, multi- Figure 8 Average instantaneous user throughput,
profile, (n�opq n�opt fgh, r#ussq fklm, multi-Profile ( n�opq n�opt fgh, r#ussq fklm, r#osst vklm, gwxyq zqt {h|k, i#djjt v klm , gwxyq zqt{h|k and
gwxyt=1024 Kbps) gwxyt=1024 Kbps)
Figure 9 Average resource utilization, multi-profile, (c�deq c�det fgh, i#ujjq fklm, i#djjt vklm,
gwxyq zqt{h|k , gwxyt=1024 Kbps)
Multi-traffic Analysis- Figure 7 Shows the variation of active users with the total number of users
present in cell. With the same number of MS present in the cell, class 1 has more active number of MS
than class 2.The reason is that the MSTR requirement of the class 1 MS is less than the class 2 and also,
hence departure rate of class 1 MS will be higher than the class 2 and therefore the steady state
probability for 2 different class of MS. Therefore the active number of MS is different for different class of
MS. From Figure.8, it can be observed that ���and ��F are not equal. From equation (19) it is clear that
when a mobile belonging to class 1 enters the PS queue ,its probability to find a given number of mobiles
already present in the queue ( n21) is different from the one of a mobile of class 2(n22). As such, the
mobiles of each class don’t get the exact same amount of resource and hence result into different
throughputs.
Figure.9 shows the variation of average resource utilization with the number of users. It can be observed
that as number of user increases frame utilization increases and when the users are more than 25,
utilization is nearly 100%.
VII. CONCLUSION AND FUTURE WORKS
In this paper, an analytical model using Continuous Time Markov Chain (CTMC) has been developed to
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tio
n
Number of usersN= N1+N2 (N1 = N1)
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
101 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
evaluate the performance parameter for BE traffic in WiMAX networks. This model takes into account the
QoS parameter MSTR and multi profile web traffic and provide closed-form expressions giving all the
required parameters such as average throughput, average resource utilization and average number of
active users. It can be concluded from the papers that as number of users increases, utilization of
resources increases but throughput decreases. From the paper, minimum number of users in the cell can
be found that gives more than 50% average resource utilization. WiMAX developer or manufacturer
decides certain minimum throughput threshold in the cell. The maximum number of users in the cell can
also be found that guarantee the minimum throughput threshold.
There are several aspects possible for future study. One extension would be validate the model through
simulation. In this model MSTR is taken into consideration, another extension would be considering
other QoS parameter to obtain the performance parameter. Analytical model has been developed only for
BE service class, another area of future wok will be integrating other service classes into the model.
VIII. REFERENCES
[1] IEEE, IEEE standard for local and metropolitan area networks Part 16: Air interface for fixed and
mobile broadband wireless access systems (amendment and corrigendum to IEEE Std 802.16-
2004), 2005, URL reference <http://standards.ieee.org/getieee802/download/802.16e-
2005.pdf>.
[2] Jeffrey G. Andrews, (2007) “Fundamentals of WiMAX Understanding Broadband Wireless
Networking”, ISBN 0-13-222552-2,478 pages, Prentice Hall Communications Engineering and
Emerging Technologies Series, text printed in the United States in Westford, Massachusetts. First
printing, February 2007.
[3] B. Baynat, S. Doirieux, G. Nogueira, M. Maqbool, and M. Coupechoux, “An Analytical Model for
WiMAX Networks with Multiple Traffic Profiles and Throttling Policy,” in Proc. of WiOpt, June
2009. [Online]. Available: http://perso.telecom-paristech.fr/∼coupecho/publis/WiOpt09.pdf.
[4] M. Maqbool, M. Coupechoux and P. Godlewski, “Comparison of Various Frequency Reuse Patterns
for WiMAX Networks with Adaptive Beamforming,” in Proc. of IEEE VTC Spring, May 2008.
[Online]. Available: http://perso.telecom-paristech.fr/�coupecho/publis/vtc08spring1.pdf
[5] B. Baynat, S. Doirieux, G. Nogueira, M. Maqbool and M. Coupechoux,“An Efficient Analytical Model
for WiMAX Networks with Multiple Traffic Profiles,” in Proc. of ACM/IET/ICST IWPAWN, October
2008. [Online]. Available: http://perso.telecom-paristech.fr/�coupecho/publis/iwpawn08.pdf
[6] B. Baynat, G. Nogueira, M. Maqbool, and M. Coupechoux, “An Efficient Analytical Model for the
Dimensioning of WiMAX Networks,” in Proc. of 8th IFIP-TC6 Networking Conference, May 2009.
[Online]. Available:http://perso.telecom-paristech.fr/�coupecho/publis/networking09.pdf.
[7] K. Ramadas and R. Jain, “WiMAX System Evaluation Methodology,”WiMAX Forum, Tech. Rep.,
January 2007.
[8] S. Kim and I. Yeom, “Performance Analysis of Best Effort Traffic in IEEE 802.16 Networks,” IEEE
Transactions on Mobile Computing, 2008.
International Journal of Advance Foundation and Research in Computer (IJAFRC)
Volume 1, Issue 4, April 2014. ISSN 2348 - 4853
102 | © 2014, IJAFRC All Rights Reserved www.ijafrc.org
[9] G. Leonardi, A. Bazzi, G. Pasolini, and O. Andrisano, “IEEE802.16e Best Effort Performance
Investigation,” in Proc. of IEEE ICC, June 2007.
[10] F. Hou, J. She, P.-H. Ho, and X. Shen, “Performance Analysis of Weighted Proportional Fairness
Scheduling in IEEE 802.16 Networks,” in Proc. Of IEEE ICC, May 2008.
[11] D. Sivchenko, N. Bayer, B. Xu, V. Rakocevic, and J. Habermann, “Internet Traffic Performance in
IEEE 802.16 Networks,” in Proc. of 12th European Wireless Conference, April 2006
[12] K.S.Trivedi,”Probability and Statistics with Reliability, Queuing, and Computer science
Applications”ISBN81-203-0508-6 Prentice-Hall of India private limited,Delhi Publication-2006
[13] F. Baskett, K. Chandy, R. Muntz, and F. Palacios, “Open Closed and Mixed Networks of Queues with
Different Classes of Customers,” Journal of the Association of Computing Machinery, April 1975.
[14] IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed
Broadband Wireless Access Systems, (2004). <
http://pubs.cs.uct.ac.za/archive/00000511/01/802-16AirInterface.pdf>
[15] http://pastel.archives-ouvertes.fr/docs/00/50/14/05/PDF/Thesis_Maqbool_2009.pdf
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