wireless queuing system

A

بسم اهلل الرحمن الرحيم

FACULTY OF ENGINEERING

ELECTRICAL ENGINEERING DEPARTMENT

ENEE520

WIRELESS QUEUING SYSTEM

Prepared by

Mousa Al-Shareef

Mohamad Lahaseh

Fadi Karajeh

Under the Guidance of

Mr Nofal Nofal

An Introduction to Graduation Project is submitted to the Electrical Engineering

Department in a partial Fulfillment of the Requirements for the Degree of BSc in

Electrical Engineering

BIRZIET

May - 2010

B

TABLE OF CONTENTS

Page

List of Tables I

List of Figures I

Abstract III

IV المستخلص

Chapter 1 Introduction to Wireless Queuing System 1

11 Queuing System 2

12 Why Wireless Queuing System 2

13

14

Basic Components of Queuing System

Basic Operation of Queuing System

3

3

15 Advantages of Queuing System 4

Chapter 2 Analysis and Performance of Queuing System

6

21 Introduction 7

22 What is the system 7

23

24

Types of Queuing System

Queuing System Characteristics

8

8

25 Birth Death Process 9

26 Queuing Behavior 11

27 System Statistics 11

28 Queuing System Modeling 14

C

29 Queuing System Notations 18

210 little‟s law 20

211 Server Utilization 21

212 Long-Run Measures of Performance 21

213 Steady State behavior of Infinite-Markovian Models 22

Chapter 3 Queuing System Components

25

31 Introduction 26

32 Entrance Numbering Unit 26

33 Teller Units 27

34 Display Units 28

35 Examples and Specifications of Some Practical Queuing

Systems

29

36 Connection of the System

34

Chapter 4 Wireless Technology

37

41 Introduction 38

42 WLANs Characteristics 39

43 Wi-Fi Technology 40

44

45

80211g Performance and Characteristics

Wi-Fi Access Protocol

41

44

46 Security Standards 44

47 Modulation

47

D

Conclusion and

Future Work

55

References

56

Appendix A

57

A1 MATLAB Code of PDF for Exponential Distribution 57

A2

A3

A4

A5

MATLAB Code of CDF for Exponential Distribution

MATLAB Code of PDF for Poisson Distribution

MATLAB Code of CDF for Poisson Distribution

Histogram of Average Waiting Time

57

57

58

58

A6 MATLAB Code to Calculate the Parameter of the

Queuing System From the Entered Lambda and Mu

59

E

List of Tables

I

Chapter 2

Chapter 4

2-1

2-2

2-3

2-4

2-5

4-1

4-2

Service Time Probability

Data Related to 20 Customers

Notations of Queuing System

Formulas for MG1

Formulas for MM1

Comparison between Wi-Fi Standards

Data Rates Parameters in 80211g

List of Figures

Chapter 1

1-1 Queuing System Configuration

Chapter 2

2-1

Flowchart for Departure Process

2-2

2-3

Flowchart for Arrival Process

Bank Queuing System

2-4

2-5

PDF for Poisson Distributions

CDF for Poisson Distributions

2-6 PDF for Exponential Distributions

2-7 CDF for Exponential Distributions

Chapter 3

3-1

Token Dispenser Unit

II

3-2 Terminal Unit

3-3 Main Display Unit

3-4

3-5

3-6

3-7

3-8

3-9

3-10

Counter Display Unit

TRONIX Wireless Queuing System

Automatic Queue Management System (AKIS)

LONBON Wireless Queuing Machine

Servicing the Customer

Practical System Connected Wirily

Practical System Connected Wirelessly

Chapter 4

4-1

Expected 80211a 80211b and 80211g Data Rates at

Varying Distance from Access Point

4-2 80211g Behavior in Different Environments

4-3 OFDM System Transmit Data on Multiple Subcarrier

4-4a Serial to Parallel Conversion

4-4b

4-5

4-6

4-7

4-8

4-9

4-10a

4-10b

OFDM Spectrum

Equivalent generation of OFDM signal

16-QAM constellation diagram

OFDM output with QAM incorporate

80211g OFDM carrier assignments

Simple OFDM Transmitter

OFDM Transmitter

OFDM Receiver

Abstract

III

Queuing systems are one of the most successful organizing techniques which are

used almost in every public place such as hospitals libraries sport centers museums

banks shopping centers and governmental institutions in order to spare peoples time and

effort by controlling and arranging their entrance waiting and servicing In this project

we will introduce all theoretical information and data needed to build a wireless queuing

system

The operation of such systems depend on the teller devices that will transmit

information to display units or LCDs through wireless channels also a server that saves

the readings and calculate every parameter that serves the customer such as number of

customers in the system or the queue waiting time service time and average time spent

in the system

The first part of this project focuses on studying the characteristics of queuing

systems and describing various models that implements them which contributes

significantly to improve the service quality in a customer oriented establishment

Furthermore statistical analysis can be adopted to achieve our goal such as Poisson-

Distribution Exponential Distribution and some measures of random variables

The second part deals with hardware devices which will generally be used to

construct the overall wireless queuing system These parts mainly consist of the Entrance

Numbering Unit the Teller Units and the Display Units A brief research on cost

availability and quality of components is taken into consideration Wireless techniques

are also introduced in order to be able to connect our system wirelessly for moving

purposes

MATLAB language program is used to illustrate some of the above operational and

statistical analysis

المستخلص

IV

ف اذس أ اصف أحذ أوثش ذماخ ارظ ااخحح اسرؼح ذمشثا ف ؼظ األاو االرظاسظا

ح اؼا ج شاوض اشاظح اراحف اثن شاوض ث اسرشفاخ اىرثاخ اؼا ساخ ق اؤطارس

ج ره ى ذفاحى خذر رظاساذشذة دخ اط الد ادذ ػ طشك س ػى ا

ف صف ارظاسظا اءةا حراج ار جي اؼاخ اثااخ اظشين لذط اششعف زا ح

السى

احذاخ ػشضحذاخ اي إى ؼاخ ذشس ار اإلخثاس أداخ ػى األظح ز ث ػ ػرذي

حسةي امشاءاخ فش ازي خاداي أعا االسى لاخ خالي ػذد ث اضت جخذي ا حراخ و

اظا ف اسره لدرسط اي خذحاي لد رظاساال ص اطاتس أ اظا ف اضتائ

طثمح ارج صف صفاي ظا ف الرظاسا خصائص دساسح ػى اششع زا األي ادضء شوض

صتؤسساخ ار ذخ اي اخذح ػح ذحس ف حظ تشى ذسا ز األظح خرفح

تؼط أس ذصغ تض ذصغ ث ذفا إحصائ ذح سم تؼ ره إى تاإلظافح

اؼشائ ارغش ػاخ

صفاي ف رظاساال ظا ثاء سرؼسد ياد األخضج داخاأل غ اششع اثا ادضء رؼا

ع لصش تحث اؼشض حذاخ خثاساإل حذاخ اذخ حذج اؼذ ػى ذش األخضاء ز االسى

اخ ػح ارافش اىفح ى أعا ذمذسف السىاي ذماخ االػرثاس تؼ ذؤخز سف اى

السى يتشه ظاا إصاي ػىساػذا خ

سسرخذ ف زا اششع تشاح ااذالب رحمك افا اظشح اإلحصائح

1

Chapter 1

Introduction to Wireless Queuing System

2

11 Queuing System

Queues build up in the institutes and companies that cater to large number of customers

where the customer service is necessary and the arrival rate to queue is larger than the service

rate Long time of waiting is unpleasant to customer and his service and therefore long queues

damage the company‟s image

Queuing System contributes significantly to improve the service quality in any customer

ndashoriented company Queuing System is ideal for bank university counter hospital and payment

center Queuing System avoid the dissatisfaction customer simply take a site where waiting his

turn to be served or reading advertisements

12 Why Wireless Queuing System

In this project we will build a practical Wireless Queuing System the use of the wireless

in the transfer of data is one of the major purposes of this project

Wireless network is commonly associated with a telecommunications network whose

interconnections between two nodes is implemented without using wires otherwise it is

implemented via some type of remote information transmission system that uses the EM waves

Such as radio wave

Our selections of the wireless refers to the features of this method of transfer data the

advantages using wireless rather than use another method are listed below

A) The addition of additional wires or drilling a new hole in office could be prohibited

impractical or too expensive

B) Flexibility of locations and data port required

C) Keep the look of the company nice

3

13 Basic Components of Queuing System

Queuing System consists from Server (PC) Entrance Numbering Unit Teller Unit

Display unit or Main LCD and other small LCDs

The components of Queuing System will discussed in chapter 3 but in this chapter let us

understand the basic operation of such a system

14 Basic Operations of Queuing System

There are two processes that affect the queuing system (birth process death process) To

explain the operation of the Queuing system we have to take each process independently and

show how the state of the system changes

To have a clear understanding of the operation of the Queuing System Let us assume that

it is installed in bank

When a customer enter the bank (birth occur) he will press on some key on the

numbering unit board or in some cases touch a sensitive screen then the Numbering unit

transfer the data to the server which make a calculations depend on two things first the number

of teller and customer in wait also on the profile and statistical data provided by the

programmer Then the server send information to the numbering unit contain the number of the

customer and the expected waiting time then it will print these information on a ticket also at

the same time the server communicates with Tellers units and Main LCD

However when a customer is served teller unit transfer data to the server which is

transfer these data to the main LCD so as a result a new customer is forwarding to the teller unit

The Figure [1-1] shows a simple graph for the Wireless Queuing System

4

Figure [1-1] Queuing System Configuration

15 Advantages of Queuing System [1]

Even though Queuing Systems improve the service quality in the company there are

several advantage of the use of such a system which are listed below

A) Reduction the waiting and service time for customers

Since the use of Queuing System avoid the dissatisfaction the service personal will work

in free conditions and he will served the customers efficiently so as a result the reduction of the

service and waiting time is achieved

B) Forward the customer to other operator

The use of such a system make it possible to forward the customer to other teller when

the first one is busy

C) Possibility to give a priority for a certain customer (Gold Customers)

In addition the Queuing system gives the flexibility to give a priority to certain

customers such as VIP person

D) Company manager can get report including statistical data

5

Also as a company use the Queuing System the manger can get statistical data this data

including the number served waiting time service rate and employee work loadhellipetc

This data give the manager indications to increase or decrease the number of employee

change the scenario on which the employee served the customers and other things related to the

company

E) The main display unit can not only show the information to the Queuing System but

also it can use to show the date and time and other advertising

6

Chapter 2

Analysis and Performance of Queuing

System

7

8

21 Introduction

In the previous chapter we introduce the component of the Wireless Queuing System In this

chapter we will show some basic concepts of the Queuing System In this system we have a multiple

server an infinite waiting room exponentially distributed inter-arrival times For which at least the mean

value and the standard deviation is known The service discipline is FIFO

However before starting with the desired system we present some concepts The heart of this

chapter is to derive formulas for the expected waiting time

22 What Is the System [1]

Let us first introduce the required definitions

System A set of objects joined to accomplish some purpose

Events Object of interest in the system

Attribute Property of an entity

Activity Predefined set of actions in a specified time period

State of system Collection of variables that describes the system at any time

Event Instantaneous occurrence that may be associated with change of system state

Delay Duration of time of unspecified length which is not known until it ends

Event notice Record of an event to occur at some present or future time along with the

associated data

Event list List of event notices (Future Event List FEL)

List A collection of associated entities ordered in some logical fashion

More and more understanding of these concepts is obtained by applying these previous

concepts to our system

A) Entities server queue

B) State

9

1- Number of units (customers for the bank example) in the system Q

2- Server status busyidle S = B I

C) Events In the analysis of the Queuing System we interested in two events Arrival

and Departure

D) Simulation Clock tracks simulated time

E) Actions Different actions depending on the type of the event and the current system

state

23 Types of Queuing System[1]

Queuing System is widely classified into one of the following type

1) Open-type System In open-type system customers arrive from outside and depart to

outside

2) Closed-type System There are no customers arrive from outside and depart to

outside All customers operate internally

Remark1 In our case we desired in the first type (Open-type)

24 Queuing System Characteristics[2][4]

In order to get the analysis of the Queuing System Firstly we have to investigate the

characteristics of such a system The characteristics of the Queuing System are discussed below

A) Calling populations calling population may be finite and infinite

Finite Customers in queue have reduced the available size of population and so

as a result causing a reduction in the arrival rate

Infinite Customers already in the queue do not influence the arrival rate process

B) System Capacity There may be a limit on the queue size When a customer arrive and

find the queue full will return to the calling population Other scenario may be found

Since the system capacity may be limited some customer will not be served and they will

go outside let us take the following definition

10

Effective arrival rate number of customers who arrive and enter the system (are served

or are waiting in queue to be served) per unit time

C) Arrival process specified in terms of inter arrival time between successive customers

Arrival may occur at deterministic or at random times The random one is given by

probability density function (PDF) The customers may arrive one a time or in batches

that can be constant size or variable size Usually the Poisson arrival process is used to

implement the arrival process

D) Queue Discipline there are various scenarios for this queue discipline we will take

some of them

I FIFO first-inndashfirstndashout

II LIFO last-in-first-out

III SIRO service in random order

IV SPT shortest processing time first

V PR service according to priority

Remark 1 FIFO and PR are mostly used in queuing system Also we can use both in the same

system as in our desired system

Remark 2 FIFO means that the first in is taken first however the discipline may be not depend

on the order of the customer since the service time is different

25 Birth Death Process[1]

Assume that a Queuing System in state S _n where n is the number of customers in the

system The system can only transition to S_n-1 or S_n+1

Death process Is the process where one customer is departed from a system The system is then

described by S_n-1

Birth process Is the process where one customer is entered to the system The system state is

given by S_n+1

The block diagram shown in the figure below are describe both the Arrival and the

Departure

11

Figure [2-1] Flowchart for Departure Process

Figure [2-2] Flowchart for Arrival Process

12

26 Queuing Behavior[2]

Customer behavior while standing in a queue line is different

Balk Incoming customers may leave when they see that the line is too long

Renege Leave after being in the line when they see that the line is moving

slowly

Jockey Move from one line to another if they think they have chosen a slow line

27 System Statistics[1]

In this section we will introduce some formulas needed to estimate the parameters of the

Queuing System such as waiting time service timehellipetc These parameters required in the

distributions that modeling the arrival and the departure processes

Average time between arrivals = (sum of all inter-arrival times) (number arrivals

-1)

Expected time between arrival E(T) = tp(t)

Average service time = (total service time) (total number of customers)

Average waiting time = (total waiting time in queue) (number of customers who

wait)

Average time spent in the system = (total time that customers spend in the system) (total

number of customers)

Average time in queue+ average time in service = average time spent in the

system

Probability that a customer has to wait in a queue

P (wait) = (number of customers that wait) (total number of customers)

Fraction of idle time for server

P (idle) = (total idle time) (total simulation time)

Let us take a queuing system work in a bank as an example Figure [2-3] shown below

13

The data in this example are collected for 20 customers enter the bank in a period

of time see Table [2-2] then we do some calculations needs to show the customers behaviors

and the servers behaviors

In this system the service policy stat that if both teller are idle Teller 1serves the

next customers otherwise the customer is served by the next available teller

If the service time distribution is specified as in the Table [2-1]

Service time(min) probability Cumulative probability

3 035 035

4 025 060

5 020 080

6 020 100

Table [2-1] Service Time Probability

Figure [2-3][1] Bank Queuing System

14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21

Table [2-2][1] Data Related to 20 Customers

We can use the formulas discussed above to calculate the desired parameters

We have to see other options for the service policy

If both teller flip a coin and randomly choose one to service the next customer

Add a new teller to serve only preferred customers (priority)

Two separate line

Two queuing times one for regular customers the other for the preferred

customers

We can add a more rapid teller with high salary instead if slower tellers

28 Queuing System Modeling[3]

In the previous sections we introduce some concepts needed to analysis the Queuing

System and we take simple example of such a system In this chapter we will introduce

important branch in the studying of the Queuing System which is the Queuing System

Modeling The model of the Queuing System enables us to derive formulas to calculate expected

waiting time which is the heart of this chapter

Arrival process

In section 24 we see that customer may arrive one at a time or in batches

Also in our system the arrival of the customer occur randomly which is described by

Poisson distributions

Poisson process

A Poisson process is a counting process N(t) for t ge 0 where N(t) is the number of

events occurred in the interval [0t] if arrival happens once at a time N(t) has stationary and

independent increments and the probability of K arrivals in [0t] is

P (N(t) = k) = λt k lowast eminus λt

k k=0 1hellip (2-1)

Useful properties of the Poisson process

16

1) Random splitting

The arrival process for two types of arrivals X and Y are Poisson with rates

λX = λ P and λY = λ (1-p) (2-2)

2) Pooling of more than one arrival stream

The arrival process will be Poisson with rate equal to the sum of all rates

arrived

λ = λki=1 i

(2-3)

Figure [2-4] shows the PDF for the Poisson distributions

Figure [2-4] PDF for Poisson Distributions

And Figure [2-5] shows CDF for Poisson distributions

0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)

PDF for Poisson Distribution

lamda=5

lamda=1

lamda=9

17

Figure [2-5] CDF for Poisson Distributions

For more details see Appendix A

Service process

Service process can be described using probability density function (PDF) which in our

case the exponential distributions with mean E(X) = 1 (μ) and variance Var(X) = 1 μ 2

Let us noting some properties

μ is the average service time

Exponential PDF is given by

F(x) = μ e- μx

xge 0 and 0 other wise (2-4)

Mean E(X) =1 (μ) (2-5)

Variance Var(X) = 1 μ 2

(2-6)

f(x) is strictly decreasing of x

Lack of memory actions are independent of each other The serving of adjacent

customers is independent

Memory-less property P(X gt s+t Xgts) = P(X gt t) (2-7)

Conditional property for two events A B

0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)

CDF for Poisson Distribution

lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)

And we can show that the memory-less property for random of the exponential random

variable

P(X gt s+t X gt s) = P(X gt 119904+119905 119883 gt 119904)

P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)

See Figure [2-6] which shows the sketch of the PDF for different value of μ

Figure [2-6] PDF for Exponential Distributions

Also Figure [2-7] shows the sketch of CDF of the exponential distributions

0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)

PDF for Exponential Distribution

mu=5

mu=1

mu=9

19

Figure [2-7] CDF for Exponential Distributions

29 Queuing System Notation[1]

Usually we use the notation for the simplification purposes Queuing system also can be

described using notations In this section we will introduce these notations and we will take

some systems and describing them using these notations

A B X Y Z

A Describes the inter-arrival time distributions

B Describes the service time distributions

X Number of parallel server

Y System capacity

Z The size of calling population

0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)

CDF for Exponential Distribution

mu=5

mu=1

mu=9

20

Notation for A and B

I M exponential or Poisson distributions

II D deterministic constant

III G general arbitrary

Remark If the system capacity and the size of calling population are infinite then Y Z

can be dropped from the notation

So in our desired system the notation contain A B X

A can be replaced by M since Poisson

B can be replaced by M since exponential

X is the number of servers or tellers in our system

As a result the system is finally described by MMX

Remark Exponential distributions are related to the Poisson distributions

If the interval between generation of events (eg arrival service) is an exponential

random variable with mean 1 λ then the event generation process is a Poisson process with

mean λ

ndash Example If buses arrive at the station at intervals that are exponentially distributed the

arrival process for the buses is Poisson

So we can referred to both exponential and Poisson distributions by M in the notation

There are other notations for the Queuing system and we listed these notations in table [2-3]

21

Table [2-3] Notations of Queuing System

210 Littlersquos Law[1]

Little‟s law or conservation equation stats that the average number of arrivals at a given

time multiplied by the average total time in the system per number of arrivals equals the average

number of customers in the system or in another words average number of customers in the

system at random interval of time equals the arrival rate times average time spent in the system

Pn Steady-state probability of having n customers in the system

Pn(t) Probability of n customers in system at time t

λ Arrival rate

λe Effective arrival rate

μ Service rate of one server

ρ Server utilization

An Inter-arrival time between customer n and n-1

Sn Service time of the nth arriving customer

Wn Total time spent in the system by the nth arriving customer

Wn

Q

Total time spent in the waiting line by the nth arriving customer

L(t) Number of customers in system at time t

LQ(t) The number of customers in queue at time t

L Long-run time-average number of customers in the system

lQ Long-run time-average number of customers in the queue

W Long-run average time spent in system per customer

WQ Long-run average time spent in queue per customer

22

This is a powerful consequence since it is applied almost for every queuing system

regardless of its characteristic

Little‟s law

L = λ W (2-10)

211 Server Utilization[1]

It is a percentage of time measures how much the server is busy and for an infinite

population it must be less than one for the system to be stable

ρ = λ

micro but from stability condition arrival rate ltservice rate

As a result we say that ρlt 1

For a simple queuing system with single server say MM1

ρ = λ

micro (2-11)

And for multi-server like MMX

ρ = λ

xmicro (2-12)

212 Long-run measures of performance[1]

Time average number in system L

Observe the system for period T L (t) = no customers at time t Ti = total time during

[0T] in which the system contained exactly (i) customers

Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23

Lavrarr L as Trarr infin

Time average number in system LQ

For the same reason as above

LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)

LQavrarr LQ as Trarr infin

Average time spent in system by customer

Similarly Wav=(1N) 119882119894infin119900 (2-16)

Wavrarr infinW as Trarr infin

N Number of arrival during [0 T]

Average time spent in queue by customer

Similarly WQav = (1N) 119882119876119894infin119900 (2-17)

WQavrarr infinWQ as Trarr infin


213 Steady-state behavior of infinite-population Markovian

models[1]

In order to have a clear understanding of the system we have to investigate the behavior

of it in the steady-state

In this system we have the following properties

I Infinite population the arrival rate not influenced by the customers already in the

system

II Queuing discipline is FIFO

24

Steady ndashstate system state the number of customer in the system is independent of time

The system in the steady-state is referred as a statistical equilibrium

P (L(t) = n) = Pn(t)= Pn (2-18)

Remark If a system is stable it will approach equilibrium state regardless of the initial

state And once the equilibrium is reached the system will remain in it

Let us list the formulas describe the system behavior in the steady-state (desired state)

A) Average number of customer in the system is given b

L= 119899119875119899infin0 (2-19)

B) Average customer time in the system by using little‟s law

W=L

λ (2-20)

C) Average number of customer in queue is given by

LQ=WQ λ (2-21)

D) Average customer time in queue

WQ=W-1 μ (2-22)

Steady-state formulas for MG1 with mean service time 1micro and service variance σ2 are listed

in table [2-4]

Equation Parameter

λmicro ρ

ρ + ρ2(1+σ2micro2)

2(1minusρ)

L

1micro + λ(σ2+ 1micro2)

2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0

Table [2-4] Formulas for MG1

25

Steady-state formulas for MM1 with arrival rate λ and service mean 1micro are listed in Table [2-

5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn

Table [2-5] Formulas for MM1

26

Chapter 3

Queuing System Components

27

31 Introduction

In this chapter we will introduce some information about the hardware devices used in

building either wirelessly connected or wired queuing systems and these information will help

us later choose the appropriate equipments and sets used to design manufacture and install full

system completely

Banking machines manufactures and companies try always to improve such systems at

the beginning they built very simple systems which were connected using cables and that

affected the range of freedom the customer have then although they are technologically

advanced wireless types were improved for making movement easier and simplifying the

service

Common industrialization through these companies exists when building the system The

Entrance Numbering Unit or known as the Ticker Dispenser is one of the main devices then we

have the Teller Units or known as Terminal devices the Display Units which consists of special

types of LCDs with different implementations the server that has software running on it for

calculation and service issues

Different examples will be given for each part describing the interfaces between them

how they work and the suitable choice we should take

32 Entrance Numbering Unit[5]

Improvement of service quality and speeds it up with getting the customer satisfaction

can be achieved first by using the Entrance Numbering Unit which is a ticket dispenser that

dispense a ticket for the customer immediately after using it and displays information on that

ticket necessary for who people who need service like the expected waiting time average

waiting time number of customers and at which counter one should go to be served after his

number appears on the main display

The unit consists of

A number of bush buttons for selecting the type of service

Thermal printer

28

Two cables one of them used as a power cable the other for transferring data

Wireless connection may be used instead of this data cable but transmitting data will be slower

The figure below shows a ticket dispenser which is a part of the AQMS-16 system

Figure [3-1] Token Dispenser Unit

33 Teller Units[5]

The teller units organize the operation that a customer takes in the institute by calling

him to the counter using a terminal unit connected to the display unit either wirily or wirelessly

and these calling panels usually have a lot of buttons on it for servicing purposes but the most

popular calling method used with this units is by bushing the increment button or the decrement

one to let the customer know that his waiting time in the queue come to an end and he then must

go to the specified counter

The virtual call terminal is an alternative solution of this calling device since a software

program is installed on the employer PC with windows operating system and it can work with

other programs to complete the management

29

So this keypad enables the staff to control the flowing of visitors and customers calling

everyone in specific order and forwarding a customer to another casher box or counter if

needed

Figure [3-2] Terminal unit

34 Display Units[5]

It is the most important part in the management queuing system due to the customer

since it leads everyone to the right position when the number of the customer he took from the

card dispenser displayed on this LCD unit put at every counter box Also a main display LCD

mounted on the ceiling appears for all customers and it is necessary for one who is far from the

counter box and cant see his number so this main display shows the required counter and

customer numbers

These LCDs are directly connected to the terminal units by serial cables and the interface

that connect the overall system together in order to receive data from the server or PC software

in the case of having programs manage the process Or they can wirelessly connected by using

the transceiver module and PIC interfacing

30

Figure [3-3] Main Display Unit Figure [3-4] Counter Display Unit

A sound box also may be connected to the computer server for better service so when a

teller unit chooses the customer voice played on the speaker calling this customer and it must be

interfaced with amplifier to give load voice

35 Examples and specifications of some practical queuing systems

Companies try always to achieve the best specification for their products by making the

advantages of the system more than disadvantages and try to build the lowest cost system which

is economical for both buyer and supplier and the simplicity of the system must exist regardless

of its complex technology used to build it in order to reduce the staff training also the

independency of operation must exist so that it does not affect other new installed systems or

affected by them

A good reliability of the system must be also taken into consideration it must not be

affected by software upgrades or any computer related issues and the setup of the system must

be easy to maintain by the staff and easier to be supported any time Summary reports is given by

the software to document every operation occurred in the system including the calculation of

different parameters

31

We will take examples of queuing systems used all over the world and give some of their

specifications

1) TRONIX WIRELESS QUEUING SYSTEM[6]

This simple system can deal with large number of customers and it is easy to control and

operate with good display It consists of one teller unit one display board and a power adapter

while the display has two 6 high red LED digits set to count from 0099 and the display unit

can be clearly visible up to 100 meter distance

The teller unit uses wireless communication to transmit data to the display unit and has

an INCREMENT-DECREMENT buttons and interfaced with the power adapter in case of low

battery power and has two LED the red one informs us that there is data transmission and the

green one tells us about power

Operation of TRONIX WIRELESS QUEUING SYSTEM

The power adapter is plugged to a 220V power source and then we turn the SWITCH-

ON button on the display unit to display 00 these numbers can be incremented or decremented

by the teller buttons and with every number displayed on the unit there will be a sound indicates

the change of this number

32

Figure [3-5] TRONIX Wireless Queuing System

Technical specifications

o Teller Box has a transmitter that can transmit in the range of 15-20 meter for

indoor applications and 30-45 meter for outdoor application with a transmission time 250

millisecond and can be supplies with 9V battery and 12V adaptor Gross weight is 250 gram

with dimensions 38 cm height x 135 cm length x 76 cm width

o Display Board had a receiver with receiving frequency 315 MHz and two red

LED digits H-6 x L-4 with visibility up to 30 meters and supplies from 110220V AC with

power consumption equals to 7 watt Gross weight is 6 Kilogram with dimensions of 267 cm

height x 318 cm length x 9 cm top width 64 cm bottom width

o Power Adapter the input is 220V-560 Hz AC and it supplies 12V DC with

ratings 1000mA The dimensions are 55 cm height x 55 cm length x 7 cm width

2) AUTOMATIC QUEUE MANAGEMENT SYSTEM (AKIS)[7]

This system can provide advanced service for customers to make them very comfortable

and a very relieving situation in working for the worker staff and providing the data for

managers to develop their companys services

Statistical data can contain the customer distribution in the queue the distribution of

service and the average service and waiting times for customers

33

Operation of AUTOMATIC QUEUE MANAGEMENT SYSTEM (AKIS)

The customer gets to the ticket dispenser and pushes a key service to get his own number

with the time he may wait until service and waits till his number called without needing to wait

in a line and waste his time The employee working in the system knows whether there are

customers waiting for service and then he pushes the calling key to bring the customer to his

window For every ticket taken the system program registers information to make a full report of

what happening in the system in order to improve the quality by making decisions about workers

who works hard or reducing the number of employees and these reports can be made every day

week or month

Figure [3-6] Automatic Queue Management System (AKIS)


o Display Unit it has colored LED digits the electric power is 12 watt per

information line and the interfacing is RS-485 The dimensions of information display line are

600 mm x 140 mm x 30 mm

o Ticket dispenser it has push buttons for various types of servicing and a thermal

printer to print the ticket The Gross weight is almost 40 Kilogram and the dimensions are 408 x

1287 x 185

34

3) LONBON WIRELESS QUEUING MACHINE[8]

This system is applicable at every institute mentioned before easy to be composed and

very convenient in operation It has a wireless ticket master station ticket-caller virtual caller

window display the main display plasma display wireless Main Control Box and sound box

Operation of LONBON WIRELESS QUEUING MACHINE

Wireless master box receive data from the wireless transceiver module which is located

in the touch screen wireless operating system The LCD touch screen has a printer VIP card

reader and a queue communication and statistics software which can control the information

of the calling display and printer also the software can be changes anytime for the purpose of

upgrading and has many options for calling and tickets

Technical specification

o Touch screen wireless ACD it can be supplied from a 220V AC with ripple

factor 5 and consumes 350 watt and the control signal level ranges from 1V to 5V with baud

rate 9600 bps the thermal printer prints with speed reaches 80MMsecond The gross weight is

41 Kilogram and the dimensions are 600 mm length x 500 mm width x 1350 mm height The

wireless working parameters are 433 MHz RF frequency and 192 KHz data rate using half-

duplex FSK with transmission distance up to 50 meter

o Wireless main control box it has six output ports with RJ45 socket and can be

connected to the parts included in the system and it has a speaker output port 24V DC 63A

switch power supply is attached to it and operates with 24V DC 220V AC The dimensions are

253 mm length x 74 mm width x 233 mm height

o Ticket station it is wirelessly connected to the main control box and has three

buttons Next Last and Re-Call The dimensions are 135 mm length x 75 mm width x 40

mm height

o Main LCD display 42 LCD which can display 6 calling numbers

o Other parts like window dot matrix display relay box sound box ceiling

speaker VIP card and paper roll

o

35

Figure [3-7] LONBON Wireless Queuing Machine


To summarize the operation and tell how the system works first the customer comes to

the entrance of the institute and presses a button on the entrance unit to take a ticket and the

counter number required for service appears on the main LCD then the customer goes to the

counter displayed and get served after his number called with a speaker and after he got served

the operator working at the counter presses the increment button on terminal or manipulator unit

to define and the number of the next customer in queue appears on the main LCD again

36

Figure [3-8] Servicing the Customer

The whole practical system is connected as follows

Figure [3-9] Practical System Connected Wirily

37

Figure [3-10] Practical System Connected Wirelessly

38

Chapter 4

Wireless Technology

39

41 Introduction

A wireless local area network (WLAN) is two or more computers joined together using

radio frequency (RF) transmissions unlike the wired LAN which uses cabling to link computers

together

Using wireless technology simplifies the aim of networking it enables multiple computer

users to share resources in a home or business without the need to use wires These resources

might include Internet connection network printers data files and even audio and video files

This kind of sharing has become more practical by making computer users change from using

single stand-alone computers to working on networks with multiple computers

It is very important to notice that WLANs are typically an extension to wired LAN they

might be slower than wired LANs (the nominal data transfer rate in WLANs is between 11 and

54Mbps compared to most wired LANs which operate at 100Mbps or 1000Mbps) But they have

a great advantage of eliminate the need of wires which might cause problems in some situations

Moving data through a wireless network involves three separate elements the radio

signals the data format and the network structure In our project we will focus on the network

structure which includes the wireless network interface adapters and base stations that send and

receive the radio signals The network interface adapters in each computer and base station

convert digital data to radio signals which they transmit to other devices on the same network

and they receive and convert incoming radio signals from other network elements back to digital

data

There are several wireless technologies in existence but most wireless LANs use

wireless Ethernet technologies based on IEEE 80211 standards

40

42 WLANs Characteristics

Advantages

o Fast and Simple Network Set-up there are no cables to install at a user‟s desk or

work area Placing wires or drilling new holes in a home or office could be hard in some

situations such as

- It could be prevented because of rental regulations

- If the work area consists of several buildings

- In historic buildings where placing cables would be difficult

- It could be very expensive

o Flexibility it is typically easier and quicker to add or move devices on the

network (wired LAN is difficult to move and expensive to change)

o Roaming capability a user can stay connected to the network from almost

anywhere inside or outside a home or business depending on the network coverage

o Cost reduction WLANs reduce the cost because there is no need for cables

o Scalability network expansion and reconfiguration is very simple it can be done

by adding more access points

o Small dynamic ad hoc networks can be created very quickly and relatively easily

Disadvantages

o Limited data rate (maximum of 54Mbps)

o Increasing the number of users will decrease the data transfer rate for each device

o Some devices could not be compatible with each other due to the different

wireless standards which mean that we might need to replace some equipments

o Security is more difficult to guarantee

o Coverage of the network is limited due to existence of walls This will force us to

use more access points which mean higher cost

o In practice a wireless LAN is not a complete solution and will still need a wired

LAN to provide a network backbone

o Data speeds drop as the user moves further away from the access point

41

43 Wi-Fi Technology [9]

Wi-Fi stands for Wireless Fidelity Wi-Fi is based on the IEEE 80211 family of

standards and is primarily a local area networking (LAN) technology designed to provide in-

building broadband coverage

The 80211 standard is defined through several specifications of WLANs It defines an

over-the-air interface between a wireless client and a base station or between two wireless

clients There are several specifications in the 80211 family

o 80211 This standard defines the basic wireless LANs and provides 1- or 2-Mbps

transmission in the 24-GHz band using either frequency-hopping spread spectrum (FHSS) or

direct-sequence spread spectrum (DSSS)

o 80211a This is an extension to 80211 that pertains to wireless LANs and goes

as fast as 54 Mbps in the 5-GHz band 80211a employs the orthogonal frequency division

multiplexing (OFDM) encoding scheme

o 80211b This standard gives a data rate up to 11Mbps (with a fallback to 55 2

and 1 Mbps depending on strength of signal) in the 24-GHz band The 80211b specification

uses only DSSS

o 80211g This standard gives the same data rate as 80211a (54Mbps) while

working in the same frequency range as 80211b (24GHz) for backwards compatibility (the best

of the two standards)

Choosing a Service

Our choice of which standard to apply in our project must subject to many factors such

as equipments we are using the size of area to be covered by the network the number of users

to support the applications to be used on the network environmental conditions speed (data

rate) security reliability ease of use and cost

42

This is a technical comparison between Wi-Fi standards

WiFi (a) WiFi (b) WiFi (g)

Standard 80211a 80211b 80211g

Frequency (GHz) 5 24 24

Speed (Mbps) 54 11 54

Range (m) 50 100 100

Table (4-1) Comparison between WiFi standards

In our project we are building a wireless network for a bank we choose the standard of

80211g because

o Its coverage area is perfect for our purpose

o The most important factor we are interested in is the speed (data rate) and this

standard offers the best data rate possible for a WLAN

o It is backwards compatible with 80211b equipments since they are operating at

the same frequency band

44 80211g Performance and Characteristics[11]

80211g Data Rates

The 80211 standard technologies support different data rates to allow clients to

communicate at the best possible speed When a client selects a data rate it considers obtaining

the highest possible speed and trying to minimize the number of communication errors When an

error occurs in data the system must spend time in retransmission of data until it is error free

Each 80211 client performs a procedure to select the best data rate The 80211g clients can

select from the widest possible range of both OFDM data rates of 54 48 36 24 18 12 9 and 6

Mbps and the CCK rates of 11 55 2 and 1 Mbps

43

80211g Range

As distance from the access point increases 80211 based products reduce data rates to

maintain connectivity The 80211g standard has the same propagation characteristic as 80211b

because they both act on the same 24 GHZ frequency band Because 80211b and 80211g

products share the same propagation characteristics we can get the same maximum range at the

same data rate Because 5-GHz radio signals do not propagate as well as 24-GHz radio signals

the 80211a product range is limited compared to the 80211b or 80211g product range

The following figure shows the expected data rate of the different 80211 standards at

different ranges

Figure (4-1) Expected 80211a 80211b and 80211g Data Rates at Varying Distance from

Access Point

NETWORK ENVIRONMENT CONSIDERATIONS

One of the major benefits of the 80211g standard is the ability of 80211g and 80211b

devices to communicate with each other At all 80211b low data rates 80211b devices

communicate with 80211g products as if they were 80211b products However 80211g

44

products behave differently when using OFDM high data rates if there are 80211b devices in the

network environment This is a short discussion of this behavior

80211g-ONLY

When the access point and all clients are 80211g communication occurs at the highest

possible data rate The 80211g AP detects that all of the clients are 80211g and inform the

network not to use any protection method

80211g AP MIXED CLIENTS

When the AP is 80211g and there is a mixture of 80211g and 80211b clients the AP

detects both technologies on the network The 80211g AP instructs 80211g clients to use a

protection mechanism That‟s yields 80211g clients to act at reduced 80211g data rate (up to 15

Mbps) which is faster than the 80211b client that communicates at a maximum rate of up to 58

Mbps

80211b AP 80211g CLIENT

When the AP is 80211b and the client is 80211g the 80211g client is able to

successfully communicate with the 80211b AP Communication between the AP and the

80211g client uses CCK modulation and gives the 80211b speeds An 80211g client can

always act as an 80211b client

Figure (4-2) 80211g Behaviour in Different Environments

45

Protection Mechanism Air Traffic Control

The protection mechanism is provided by the 80211g standard to manage

communication in a mixed 80211bg environment The 80211b radios do not hear when the

airspace is busy with 80211g OFDM signals Protection mechanisms prevent 80211b clients

from transmitting if the wireless channel is busy with the 80211g OFDM signals The 80211g

products have the priority and still communicate at the same 80211g OFDM data rates when

protection is in use

45 Wi-Fi Access Protocol

IEEE 80211 wireless LANs use a media access control protocol called Carrier Sense

Multiple Access with Collision Avoidance (CSMACA)

Wi-Fi systems have a fundamental problem that is all stations share the same media

(transmit and receive on the same radio channel) This problem yields that a station

cannot hear while it is sending and hence it impossible to detect a collision Because of this the

developers of the 80211 specifications came up with a collision avoidance mechanism called the

Distributed Control Function (DCF)

According to DCF A Wi-Fi station will transmit only if it thinks the channel is clear All

transmissions are acknowledged so if a station does not receive an acknowledgement it assumes

a collision occurred and retries after a random waiting interval

46 Security standards

Security of the network we are building needs very large amount of interest because our

project (Queuing System) is dealing with people privacy such as finance (in the bank case) or

private information (in service centers case)

Wireless LAN came with a default security mechanism called Wireless Equivalent

Privacy (WEP) WEP uses data encryption to provide a basic level of security for WLAN users

WEP allows the administrator to define an encryption key which is used to encrypt data before

46

it is transmitted through the airwaves When WEP is enabled all stations (clients and Access

Points) are required to have the same WEP key Network access is denied to anyone who does

not have the correct key However WEP is very weak mechanism WEP mechanism had been

attacked very much by hackers and they success in beating this mechanism so WEP should be

used if other solutions are not available

80211 developers introduced more efficient mechanisms than WEP such as WPA and

WPA2

WPA (Wi-Fi Protected Access)

WPA incorporates features of the IEEE 80211i standard WPA runs in either enterprise

mode or pre-shared key (PSK) mode

o Enterprise Mode requires an authentication server for authentication and dynamic

key distribution

o Personal Mode (pre-shared key) does not require an authentication server A

shared key is entered once on the access point and the wireless client to act as a starting point for

the dynamic encryption process

WPA includes three main elements

o Authentication using the 8021x protocol (only in enterprise mode)

o Data encryption through Temporal Key Integrity Protocol (TKIP)

o Data validation with Message Integrity Check (MIC)

8021x is a protocol for secure mutual authentication of users and networks 8021x uses

Extensible Authentication Protocols (EAPs) to provide a secure link between the client AP and

Authentication server There are three parts to an 8021x solution

o The supplicant (software on the client device incorporating 8021x and at least

one EAP)

o An authenticator (usually the AP which communicates between the client and

authentication server)

o An authentication server (typically a RADIUS server to validate the client)

WPA allows for several different EAPs to be used EAP-TLS is one of the major versions

that have been tested by the Wi-Fi Alliance but it requires Public Key Infrastructure (PKI)

47

certificates on the server and clients 8021x is currently not widely implemented in networks

Organizations may wish to consider a plan to move the whole network (wired and wireless) to

8021x authentication

TKIP enhances WEP and securely alters the key with every data packet sent using Per

Packet Keying (PPK) It uses 128 bit encryption although it still employs the same encryption

algorithm used by WEP

MIC provides data validity to prevent accidental changes to data sent across the network

It should be noted though that WPA offers no support for devices in ad hoc mode For

encryption to take place in this mode WEP will still need to be used

WPA280211i

The 80211i security standard provides a very secure mechanism for wireless networks

WPA2 adds a stronger encryption algorithm based on the Advanced Encryption Standard (AES)

It also reduces the number of data packets involved in key management

It is advisable to ensure that all future purchases are WPA2 compliant Due to the

processing demands of AES many older APs will have to be replaced in order to handle

80211iWPA2 However some APs will only need a software upgrade Users will need to check

with the manufacturer to determine whether this is possible

Both WPA and WPA2 can be used in a bdquomixed mode‟ which allows a WPA device to be

backwards compatible with another device using a previous wireless security protocol

Unfortunately this means that if a WPA device interacts with one using WEP this greatly

reduces the security so is not recommended

48

47 Modulation[10]

80211g is the latest standard in wireless networking It results from the development

80211a and 80211b combining the speed of 80211a with the low cost and the coverage area of

80211b

80211g will have a high data transfer rate by using the orthogonal frequency division

multiplexing (OFDM) modulation technique that is used in 80211a while maintaining the

timing and frequency arrangements from 80211b

80211g is best understood as the combination of 80211a and 80211b wireless

networking standards 80211g will use the two different modulation techniques of the a and b

systems at 24 GHz which is the operating frequency of 80211b to allow compatibility with

80211b systems and get the same coverage area while keeping the data rate of the 80211a

standard

OFDM is a multi-carrier modulation scheme The data is divided to multiple closely

spaced subcarriers By doing so OFDM systems are able to provide very reliable operation and

high data rates

Figure (4-3) OFDM System Transmit Data on Multiple Subcarrier

Let‟s consider transmitting binary digits at a rate of R bps The bandwidth B required to

transmit these bits is R(1 + r) with r the Nyquist rolloff factor Now consider we have a

sequence of N of these bits stored for an interval TS = NR (the OFDM symbol interval) Then the

system carry out the Serial-to-parallel conversion and each of the N bits stored is used to

modulate a separate carrier signal All N modulated-carrier signals are then transmitted

49

simultaneously over the Ts interval Figure (4-4a) shows the operation of OFDM the parameters

ak represent the successive bits stored while the frequencies fk represent the N carrier frequencies

transmitted in parallel Figure (4-4b) shows the resultant OFDM spectrum To make the carrier

frequencies orthogonal to each other it must have the spacing Δf between carriers equal to 1TS

Thus we have B = NΔf where B is the transmission bandwidth as shown in Figure (4-4b) Δf

also represents the bandwidth of each of the N parallel frequency channels

(a)

(b)

Figure (4-4) (a) serial to parallel conversion (b)OFDM spectrum

From the above analysis we conclude that this process has reduced the transmission

bandwidth of each of the transmitted signals by the factor of N Using the previous process of

50

transmitting multiple carriers in parallel can yield a problem in implementation of OFDM To

solve this problem we use the discrete Fourier Transform technique

Back to the N parallel output signals of Figure (4-4a) transmitted over a TS interval We

define the total signal transmitted v(t) as the sum of these signals And the kth carrier frequency

fk as [fc +kΔf] 0lekleNminus1 Consider the kth carrier signal to be cos 2π(fc + kΔf)t then v(t) may be

written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

Now we sample a(t) at intervals TSN apart (at the rate of R samples per second) After

sampling we got the sampled function a(n) with t replaced by nTSN And we can substitute Δf

with 1TS Finally we can write a(n) as

119886 119899 = 1198861198961198901198952120587119896119899

119873 119899 = 0 helliphellip119873 minus 1119873minus1119896=0 (4-2)

We note that the previous equation is exactly in the form of the inverse Discrete Fourier

Transform and it may be evaluated using Fast Fourier Transform (FFT) techniques In place of

the transmitting N orthogonal carriers in parallel we can transmit them at the single carrier

frequency using FFT calculation This process is shown in figure (4-5)

Figure (4-5) Equivalent generation of OFDM signal

51

This is the procedure that followed in high-speed WLANs At the receiver the process is

reversed for each symbol interval TS the receiver demodulate the received modulated carrier

signal the discrete Fourier Transform is calculated from which the N coefficients ak k = 0 N

minus 1 are recovered and parallel-to-serial conversion used to generate the desired output bit stream

Note that N is chosen as multiple of 2 to help carrying out the FFT calculations

In order to get higher bit rate data signals to be transmitted over a specific bandwidth the

previously discussed process of generating the OFDM signal from binary input samples using

FFT may be generalized to an input of QAM signal samples First QAM is used to reduce the

bandwidth required to transmit a given input bit stream Let K lt N successive binary digits be

stored generating one of 2K possible QAM signals Figure (4-6) show an example of 16-QAM

signals each point in the group represents one of the 2K signals to be transmitted the signals may

be represented as a complex number

Figure (4-6) 16-QAM constellation diagram

Let the kth complex number be ak We carry out QAM generation using each successive

group of K binary digits and then store the resultant N successive complex numbers ak k = 0

N minus 1 over the TS OFDM symbol interval and then use serial-to-parallel conversion to transmit

these N complex numbers over different subcarrier for each We have thus obtained a more

general form of OFDM But in this process we have to notice that we deal with complex

numbers ak in place of the binary coefficient used in equation (4-2)The inverse discrete Fourier

52

Transform is again obtained to perform the OFDM operation by sampling the resultant equation

but this time sampling at the QAM intervals( KR units of time apart) Finally we got the more

general case of considering complex coefficients ak in place of the ak coefficients below

119886 119899 = 1199381198961198901198952120587119896119899


Inverse Fast Fourier techniques may be carried out to perform the equation (4-3) The

OFDM more general system (working with QAM) operations before carrying out serial-to -

parallel conversion is shown in figure (4-7)The I and Q signals represent the inphase and

quadrature components of the complex IFFT operation (real part imaginary part ak coefficients)

Figure (4-7) OFDM output with QAM incorporate

Physical layer specifications 80211g and 80211a

The IEEE 80211g standard specifies an OFDM physical layer (PHY) that splits an

information signal across 52 separate subcarrier signals to provide transmission of data at a rate

of 6 9 12 18 24 36 48 or 54 Mbps Operation is done over 20-MHz wide bands within the

overall frequency band used In order to provide the desired OFDM operation subcarriers must

be spaced 3125 kHz apart with the equivalent inverse Fourier Transform technique used to

perform the OFDM operation through IFFT techniques

The carrier spacing of 3125 kHz over the 20-MHz band allows 64 subcarriers to be

transmitted over this band But a bandwidth of 166 MHz within the center of the 20-MHz band

is actually used to carry out the OFDM operation 52 subcarriers with equivalent spacing from

53

each side of the band center as shown in figure (4-8) are used to cover the 166 MHz band 48

carriers of these 52 are used to carry data and the other four are used to carry pilot information

Figure (4-8) 80211g OFDM carrier assignments

OFDM symbols are defined as 48 complex numbers each representing one of the data

subcarriers The OFDM data rates supported by these standards are 6 9 12 18 24 36 48 and

54 Mbps These eight data rates are obtained by using different combinations of QAM with

OFDM as shown in table (4-2) As we mentioned previously for orthogonal frequency

operation the sub-carrier spacing must be 1TS where TS is the OFDM symbol interval With a

sub-carrier spacing here of 3125 kHz we have TS = 32 microsec

Data Rate

(Mbps)

Modulation Coding Rate Coded bits per

subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216

Table (4-2) Data rates parameters in 80211g

Figure (4-9) shows a simple 80211g OFDM transmitter using the IFFT calculation The

bit rate R is one of the eight bit rates mentioned above Forward-error correction and

convolutional encoder is then carried out Some bits of the output bit stream of this encoder is

deleted (the number depends on the input bit rate) to get the desired output bit rate

Figure (4-9) Simple OFDM transmitter

An interleaver is then used to spread out the modified output stream and the resultant bit

stream stored the appropriate number of bits to provide a QAM symbol Each QAM-

constellation complex number referring to a set of input bits received in the QAM interval is

stored until 48 complex numbers are accumulated for input to the IFFT calculator These

complex numbers are represented by a sequence of I (inphase) and Q (quadrature) numbers in a

32 microsec interval and represented by I and Q in figure (4-9)

These 48 complex numbers which represent the data to be transmitted are augmented by

four numbers corresponding to the four pilot signals A 64-point IFFT is used with 16 of the

IFFT input coefficients set equal to zero The IFFT output is then used to modulate the system

carrier

55

The whole operation of transmission and receiving the OFDM signals is represented in

figure (4-10)

(a)

(b)

Figure (4-10) OFDM transmitter (a) and receiver (b)

56

Conclusion and Future work

In this project we understand the basic concepts that related to Wireless Queuing System

and how this system provide an efficient organizing for the companies and institutes

In the first part of this project we studied all the theoretical and statistical analysis of the

system also we studied all the parameters associated with the system MATLAB codes were

used to implement these parameters

In the second part we learn how the system operates and how it will be interfaced

wirelessly Also we introduce some examples of such a system Wireless technology was

introduced and focused on the Wi-Fi technology in order to help us in the Wireless connection

As a future work we look forward to implement the system practically and making all the

interfacing and the code program that will be used in the server (PC) This is our plan for the

first semester of the Final Graduation Project (EE530) but our plane can be modulated or

changed according to discussion committee

57

References

[1] Gross and Harris ldquoFundamentals of Queueing Theoryrdquo 3rd Ed Wiley 1998 (Required)

[2] Banks Carson Nelson amp Nicol ldquoDiscrete Event System Simulation Prentice Hall 2001

[3] Kleinrock ldquoQueueing Systems vol 2 Computer Applicationsrdquo Wiley 1976 (Reference)

[4] httpwwwecestevens-techedu~ccomaniccpe345_05html

[5] httpwwwwikipediaorg

[6] httpwwwinnovatronixcom

[7] httpwwwqms-akiscom

[8] httpwwwlonboncom

[9] Institute of Electrical Engineer (IEEE) wwwieeeorg][wwwwikipediaorg]

[10] Mobile Wireless Communication Mischa Schwartz Department of Electrical Engineering

Columbia University

58

Appendix A

A1 MATLAB Code for Exponential Distributions

PDF for exponential x = 0520 y = exppdf(x5) z=exppdf(x1) a=exppdf(x9) plot(xy-r) hold plot(xz-or) plot(xa-r) grid on legend(mu=5mu=1mu=9) title(PDF for Exponential Distribution) xlabel(K) ylabel(P(X=K))

A2 MATLAB Code of CDF for Exponential Distributions

CDF for exponential gtgt x = 0520 y = expcdf(x5) z=expcdf(x1) a=expcdf(x9) plot(xy-r) gtgt hold plot(xz-or) plot(xa-r) grid on legend(mu=5mu=1mu=9) title(CDF for Exponential Distribution) xlabel(K) ylabel(P(X=K))

A3 MATLAB Code of PDF for Poisson Distributions

PDF for poisson gtgt x = 015 y = poisspdf(x5) z=poisspdf(x1) a=poisspdf(x9) plot(xy-r) gtgt hold

59

plot(xz-or) plot(xa-r) grid on legend(lamda=5lamda=1lamda=9) title(PDF for Poisson Distribution) xlabel(K) ylabel(P(X=K))

A4 MATLAB Code of CDF for Poisson Distributions

CDF for poisson gtgt x = 015 y = poisscdf(x5) z=poisscdf(x1) a=poisscdf(x9) plot(xy-r) gtgt hold plot(xz-or) plot(xa-r) grid on legend(lamda=5lamda=1lamda=9) title(CDF for Poisson Distribution) xlabel(K) ylabel(P(X=K))

A5 Histogram of Average Waiting Time

MM1 queue

a = 15 average number of arrivals per minute b = 2 average number of people served per minute ncust = 1000

at = zeros(ncust1) arrival time of a person joining the queue ft = zeros(ncust1) finish time after waiting and being served

Generate random arrival times assuming Poisson process r = rand(ncust1) iat = -1a log(r) Generate inter-arrival times exponential

distribution at(1) = iat(1) Arrival time of first customer for i=2ncust at(i) = at(i-1) + iat(i) arrival times of other customers end

Generate random service times for each customer r = rand(ncust1) st = -1b log(r) service times for each

60

Compute time each customer finishes ft(1) = at(1)+st(1) finish time for first customer for i=2ncust compute finish time for each customer as the larger of arrival time plus service time (if no wait) finish time of previous customer plus service time (if wait) ft(i) = max(at(i)+st(i) ft(i-1)+st(i)) end

total_time = ft - at total time spent by each customer wait_time = total_time - st time spent waiting before being served ave_service_time = sum(st)ncust ave_wait_time = sum(wait_time)ncust ave_total_time = sum(total_time)ncust

Plot histogram of waiting times hist(total_time0520)

A6 MATLAB Code to Calculate the Parameter of the Queuing System from

the Entered Lambda and Mu

MM3 (poisson inter-arrival exponential service three servers) queuing

system model with FCFS

lambda = input(Enter lambda ) entering arrival rate

-5 0 5 10 15 20 250

50

100

150

200

250

61

mu = input(Enter mu ) entering service rate

x = [ lambda mu] y = [lambda mu] disp(x) disp(y)

rho = lambda(3mu) rho which is the

utilization factor or how busy the servers are Lq = (27rho^4)(6(1 - rho)(1+2rho+15rho^2)) the number of customers

in a queue (waiting) or the average length of a queue L = Lq + 3rho the number of customers

in the system (waiting and served) Wq = Lqlambda the average or mean

waiting time ( customer spend in a queue) W = Llambda the average or mean

time spend in the system (waiting in queue and being served) P0 = (1-rho)(1+2rho+15rho^2) probability that the

system is empty Pn2 = (((lambdamu)^2)P0)2 probability of having n

customers (lets say n=2 lt= servers) in the system (in queue and being

served) Pn6 = (((lambdamu)^6)P0)162 probability of having n

customers (lets say n=6 gt servers) in the system (in queue and being served) Pw = ((lambdamu)^3)(1(1-rho))(P06) probability of an

arriving customer to wait in the queue before being served

A = [ rho L Lq Wq W P0 Pn2 Pn6 Pw] B = [rho L Lq Wq W P0 Pn2 Pn6 Pw] disp(A) disp(B)

k = input(Enter row matrix of values k ) c = 3muWq(1 - rho) probability that P(Wq gt 0) PW3 = exp(-muk)(1 + (c(1 - exp(-2muk + lambdak))(2-3rho)))

calculate P(W gt k) for lambda not equal 2mu PW3eq = exp(-muk)(1 + (cmuk))

calculate P(W gt k) for lambda equal 2mu

F = [ k P(Wgtk)for lambda not equal 2mu] f = [k PW3] disp(F) disp(f)

S = [ k P(WgtK)for lambda equal 2mu] s = [k PW3eq] disp(S) disp(s)

B

TABLE OF CONTENTS

Page

List of Tables I

List of Figures I

Abstract III

IV المستخلص

Chapter 1 Introduction to Wireless Queuing System 1

11 Queuing System 2

12 Why Wireless Queuing System 2

13

14

Basic Components of Queuing System

Basic Operation of Queuing System

3

3

15 Advantages of Queuing System 4

Chapter 2 Analysis and Performance of Queuing System

6

21 Introduction 7

22 What is the system 7

23

24

Types of Queuing System

Queuing System Characteristics

8

8

25 Birth Death Process 9

26 Queuing Behavior 11

27 System Statistics 11

28 Queuing System Modeling 14

C







25

31 Introduction 26


33 Teller Units 27

34 Display Units 28


Systems

29


34


37

41 Introduction 38



44

45



41

44


47 Modulation

47

D

Conclusion and

Future Work

55

References

56

Appendix A

57


A2

A3

A4

A5





57

57

58

58



59

E

List of Tables

I

Chapter 2

Chapter 4

2-1

2-2

2-3

2-4

2-5

4-1

4-2




Formulas for MG1

Formulas for MM1



List of Figures

Chapter 1


Chapter 2

2-1


2-2

2-3


Bank Queuing System

2-4

2-5





Chapter 3

3-1


II

3-2 Terminal Unit


3-4

3-5

3-6

3-7

3-8

3-9

3-10








Chapter 4

4-1






4-4b

4-5

4-6

4-7

4-8

4-9

4-10a

4-10b

OFDM Spectrum






OFDM Transmitter

OFDM Receiver

Abstract

III






system





in the system











purposes



المستخلص

IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















C







25

31 Introduction 26


33 Teller Units 27

34 Display Units 28


Systems

29


34


37

41 Introduction 38



44

45



41

44


47 Modulation

47

D

Conclusion and

Future Work

55

References

56

Appendix A

57


A2

A3

A4

A5





57

57

58

58



59

E

List of Tables

I

Chapter 2

Chapter 4

2-1

2-2

2-3

2-4

2-5

4-1

4-2




Formulas for MG1

Formulas for MM1



List of Figures

Chapter 1


Chapter 2

2-1


2-2

2-3


Bank Queuing System

2-4

2-5





Chapter 3

3-1


II

3-2 Terminal Unit


3-4

3-5

3-6

3-7

3-8

3-9

3-10








Chapter 4

4-1






4-4b

4-5

4-6

4-7

4-8

4-9

4-10a

4-10b

OFDM Spectrum






OFDM Transmitter

OFDM Receiver

Abstract

III






system





in the system











purposes



المستخلص

IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















D

Conclusion and

Future Work

55

References

56

Appendix A

57


A2

A3

A4

A5





57

57

58

58



59

E

List of Tables

I

Chapter 2

Chapter 4

2-1

2-2

2-3

2-4

2-5

4-1

4-2




Formulas for MG1

Formulas for MM1



List of Figures

Chapter 1


Chapter 2

2-1


2-2

2-3


Bank Queuing System

2-4

2-5





Chapter 3

3-1


II

3-2 Terminal Unit


3-4

3-5

3-6

3-7

3-8

3-9

3-10








Chapter 4

4-1






4-4b

4-5

4-6

4-7

4-8

4-9

4-10a

4-10b

OFDM Spectrum






OFDM Transmitter

OFDM Receiver

Abstract

III






system





in the system











purposes



المستخلص

IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















E

List of Tables

I

Chapter 2

Chapter 4

2-1

2-2

2-3

2-4

2-5

4-1

4-2




Formulas for MG1

Formulas for MM1



List of Figures

Chapter 1


Chapter 2

2-1


2-2

2-3


Bank Queuing System

2-4

2-5





Chapter 3

3-1


II

3-2 Terminal Unit


3-4

3-5

3-6

3-7

3-8

3-9

3-10








Chapter 4

4-1






4-4b

4-5

4-6

4-7

4-8

4-9

4-10a

4-10b

OFDM Spectrum






OFDM Transmitter

OFDM Receiver

Abstract

III






system





in the system











purposes



المستخلص

IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















I

Chapter 2

Chapter 4

2-1

2-2

2-3

2-4

2-5

4-1

4-2




Formulas for MG1

Formulas for MM1



List of Figures

Chapter 1


Chapter 2

2-1


2-2

2-3


Bank Queuing System

2-4

2-5





Chapter 3

3-1


II

3-2 Terminal Unit


3-4

3-5

3-6

3-7

3-8

3-9

3-10








Chapter 4

4-1






4-4b

4-5

4-6

4-7

4-8

4-9

4-10a

4-10b

OFDM Spectrum






OFDM Transmitter

OFDM Receiver

Abstract

III






system





in the system











purposes



المستخلص

IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















II

3-2 Terminal Unit


3-4

3-5

3-6

3-7

3-8

3-9

3-10








Chapter 4

4-1






4-4b

4-5

4-6

4-7

4-8

4-9

4-10a

4-10b

OFDM Spectrum






OFDM Transmitter

OFDM Receiver

Abstract

III






system





in the system











purposes



المستخلص

IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















III






system





in the system











purposes



المستخلص

IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















IV





السى













1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















1

Chapter 1


2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















2

11 Queuing System















Such as radio wave







3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















3






















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















4
















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















5





company



6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















6

Chapter 2


System

7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















7

8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















8

21 Introduction

















associated data






B) State

9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















9




and Departure



state




outside















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















10









some of them














described by S_n-1


given by S_n+1


Departure

11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















11



12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















12





slowly







-1)




wait)




system






13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















13








3 035 035

4 025 060

5 020 080

6 020 100



14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















14

Customer

Arrival

time

Service

time

Time

service

begins

T1

Time

service

ends

T1

Time

service

begins

T2

Time

service

ends

T2

Time

in

Queue

Idle

time

T1

Active

time

T2

1 0 4 0 4 0 0 0

2 8 1 8 9 0 4 0

3 14 4 14 18 0 5 0

4 15 3 15 18 0 0 3

5 23 2 23 25 0 5 0

6 26 4 26 30 0 1 0

7 34 5 34 39 0 4 0

8 41 4 41 45 0 2 0

9 43 6 43 49 0 0 6

10 46 5 46 51 0 1 0

11 47 4 49 53 2 0 4

12 48 3 51 54 3 0 0

13 53 4 53 57 0 0 4

14 59 3 59 62 0 5 0

15 62 5 62 67 0 0 0

16 70 4 70 74 0 3 0

17 71 4 71 75 0 0 4

18 73 1 74 75 1 0 0

19 77 5 77 82 0 2 0

15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















15

20 82 4 82 86 0 0 0

Total 6 32 21






Two separate line


customers








Arrival process




Poisson process





k k=0 1hellip (2-1)


16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















16

1) Random splitting


λX = λ P and λY = λ (1-p) (2-2)



arrived

λ = λki=1 i

(2-3)




0 5 10 150

005

01

015

02

025

03

035

04

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















17



Service process






F(x) = μ e- μx


Mean E(X) =1 (μ) (2-5)


(2-6)






0 5 10 150

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


lamda=5

lamda=1

lamda=9

18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















18

P(AB)=P(A B)P(B)=P(B A)P(A) (2-8)


variable


P(Xgt119904)

= eminus λ t+s

eminus λ s

= e- λt

(2-9)




0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















19






A B X Y Z




Y System capacity


0 2 4 6 8 10 12 14 16 18 200

01

02

03

04

05

06

07

08

09

1

K

P(X

=K

)


mu=5

mu=1

mu=9

20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















20















mean λ





21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















21









λ Arrival rate







Wn

Q








22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















22



Little‟s law

L = λ W (2-10)




ρ = λ




ρ = λ

micro (2-11)


ρ = λ

xmicro (2-12)





Lav = 1

119879 119894 lowast 119879119894infin

0 = 119894 lowast (119879119894infin0 119879) (2-13)

But 119894 lowast 119879119894infin0 = 119871 119905 119889119905

119879

0

So Lav=1

119879 119871 119905 119889119905

119879

0 (2-14)

23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















23




LQav = 1

119879 119871119876 119905 119889119905

119879

0 (2-15)











models[1]





system


24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















24



P (L(t) = n) = Pn(t)= Pn (2-18)





L= 119899119875119899infin0 (2-19)


W=L

λ (2-20)


LQ=WQ λ (2-21)


WQ=W-1 μ (2-22)


in table [2-4]

Equation Parameter

λmicro ρ


2(1minusρ)

L


2(1minusρ)

W

W ndash 1micro Wq

ρ2(1 + σ2micro2)

2(1 minus ρ)

Lq

(1-ρ) P0


25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















25


5]

Equation Parameter

λmicro ρ

ρ

(1minusρ)

L

1 (micro - λ) W

W ρ Wq

λ Wq Lq

(1-ρ) ρn Pn


26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















26

Chapter 3


27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















27

31 Introduction




system completely





service

















Thermal printer

28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















28





33 Teller Units[5]










29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















29



needed


34 Display Units[5]






customer numbers





30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















30











affected by them






31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















31


specifications















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















32



















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















33









week or month





600 mm x 140 mm x 30 mm



1287 x 185

34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















34
























mm height




o

35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















35









36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















36




37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















37


38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















38

Chapter 4

Wireless Technology

39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















39

41 Introduction



together
















data



40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















40


Advantages



situations such as













Disadvantages











41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















41
















uses only DSSS




Choosing a Service





42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















42



Standard 80211a 80211b 80211g



Range (m) 50 100 100



80211g because







80211g Data Rates








43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















43

80211g Range








different ranges


Access Point





44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















44



80211g-ONLY









Mbps







45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















45


























46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















46







WPA2





key distribution












one EAP)






47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















47










WPA280211i












48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















48

47 Modulation[10]



80211b








standard



high data rates







49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















49







(a)

(b)




50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















50






written as

119907 119905 = 119877119890 119886119896 119873minus1119896=0 1198901198952120587 119891119888+119896∆119891 119905

= 119877119890 1198901198952120587119891119888119905 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905

= 119877119890 1198901198952120587119891119888119905 119886(119905) (4-1)

With a(t)= 119886119896 119873minus1119896=0 1198901198952120587119896 ∆119891119905




119886 119899 = 1198861198961198901198952120587119896119899







51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















51




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















52




119886 119899 = 1199381198961198901198952120587119896119899

















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















53










Data Rate

(Mbps)


subcarrier

Coded bits per

OFDM

symbol

Data bits per

OFDM

symbol

6 BPSK 12 1 48 24

9 BPSK 34 1 48 36

12 QPSK 12 2 96 48

18 16-QAM 34 2 96 72

24 16-QAM 12 4 192 96

36 16-QAM 34 4 192 144

48 64-QAM 23 6 288 192

54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















54

54 64-QAM 34 6 288 216
















carrier

55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















55


figure (4-10)

(a)

(b)


56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















56














57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















57

References











Columbia University

58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















58

Appendix A







59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















59





MM1 queue






60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















60









-5 0 5 10 15 20 250

50

100

150

200

250

61




















61




















wireless queuing system

Documents