an analytical model for best effort traffic in wimaxnetworks

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

[email protected] , [email protected] , [email protected]

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.




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-




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.


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


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



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




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]:




�� . �"#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




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




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,




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.




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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Xon=3Mb

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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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Number of usersN= N1+N2 (N1 = N1)




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.

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an analytical model for best effort traffic in wimaxnetworks

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