Additional Mathematics Project Work Form 5 2012 Task 1 ... · PDF fileAdditional Mathematics...

Additional Mathematics Project WorkForm 5

2012

Task 1:Mobile Telephone

Name: Jeremy Loo Kah YowClass: 5 ClancyI/C No.: 950104-14-5159Teacher: Pn. Yong Lai YenSchool: SMK(L) Methodist, Kuala Lumpur

1/22Jeremy Loo Kah Yow

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Contents

Cover Page 1

Contents 2

Acknowledgment 3

Objectives 4

Introduction 5

Hand Phone Traffic 11

Hand Phone Rate Plan Selection 14

Further Exploration 19

Conclusion 20

Reflection 21

Reference 22


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Acknowledgment

Firstly, I would like to thank God for His much-needed guidance and for granting me the

knowledge, wisdom, intuition and resourcefulness throughout this project. I would also like to

express my thanks to my teacher, Pn. Yong Lai Yen, in cementing the base of my knowledge

in the subject throughout the past one-and-a-half years. Lastly, but most certainly not the

least, I would like to record my appreciation for the support, both emotional and moral, given

to me by my friends and family.

Without them, I would not be able to accomplish what I have and I would definitely not be the

person I am today.


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Objectives

The objectives of conducting this project are as follows:

To apply and adapt a variety of problem-solving strategies to solve problems.

To improve thinking skills.

To promote effective mathematical communication.

To develop mathematical knowledge through problem solving in a way that increases a

student's interest and confidence.

To use the language of mathematics to express mathematical ideas precisely.

To provide learning environment that stimulates and enhances effective learning.

To develop a positive attitude towards mathematics.


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Introduction

History of Hand Phones

The first generation of wireless telephone technology is known as 1G or 1-G were

analog telecommunications standards introduced in the 1980s. Nippon Telegraph and

Telephone (NTT), in Japan, was the first to launch the first commercially automated cellular

network in 1979. It was launched in the metropolitan area of Tokyo, but within five years, it

had expanded to cover the whole of Japan and became the first nationwide 1G network.

This was followed by the launch of the Nordic Mobile Telephone (NMT) system in

Denmark, Finland, Norway and Sweden in 1981. The NMT was the first system to feature

international roaming. In the United States of America, the first 1G network to be launched

was the Chicago-based Ameritech in 1983 using the Motorola DynaTAC mobile phone. In the

early-to-mid 1980s, several countries then followed suit, including the United Kingdom,


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Mexico and Canada.

The 1G system achieved speed between that of a 28k modem (28kbit/s) and a 56k

modem (56kbit/s), with actual download speeds of 2.9 kilobytes per second to 5.6 kilobytes

per second.

In 1991, the GSM standard was commercially launched in Finland by Radiolinja (now

part of Elisa Oyj). This heralded in the 2G system for the mobile phone. While the 1G systems

were analogous systems, the 2G systems were digitally encrypted. This made it much more

efficient on the spectrum allowing for far greater mobile phone penetration levels as well as

introducing data services for the mobile, starting with Short Message Services (SMS) or text

messages.

There are several 2G standards. These standards can be categorized into TDMA-

based and CDMA-based standards. TDMA stands for Time Division Multiple Access and

divides the signal into different time slots. Meanwhile, CDMA stands for Code Division

Multiple Access, and divides the signal into different frequencies.


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Storno 940 by NMT

The GSM, which is TDMA-based, originally came from Europe, as stated above, but is

used in almost all countries today. It accounts for over 80% of all subscribers worldwide. Over

60 GSM operators are also using CDMA2000 in the 450MHz frequency band (CDMA450).

In the Americas and parts of Asia, the IS-95 or cdmaOne is used. It is CDMA-based


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Illustration 1: TDMA Frame Structure

Illustration 2: CDMA Frame Structure

and accounts for about 17% of all subscribers globally. Over a dozen CDMA operators have

migrated to GSM including operators in Mexico, India, Australia and South Korea.

In Japan, the PDC (TDMA-based) is used exclusively, while the iDen, also TDMA-

based, is a proprietary network used by Nextel in the United States of America and by Telus

Mobility in Canada. The IS-136 or D-AMPS, which is TDMA-based, was once prevalent in the

Americas but have mostly migrated to GSM.

2G networks were built mainly for voice services and slow data transmission. However,

as time went on, there were several evolutions to this system. The first was the 2.5G, used to

describe 2G-systems that have implemented a packet-switched domain in addition to the

circuit-switched (HSCSD) domain. It is commonly known as the General Packet Radio

Service (GPRS). The GPRS could provide data rates from 56kbit/s up to 115kbit/s and can be

used for services such as Wireless Application Protocol (WAP) access, Internet access and

Multimedia Messaging Service (MMS).

The CDMA2000 networks evolved as well through the introduction of 1xRTT. The

1xRTT supports bi-directional peak data rates up to 153.6kbit/s, with an average user data

throughput of 80-100kbit/s. It can also be used for WAP, SMS & MMS services, as well as

Internet access.

The next evolution was the Enhanced Data rates for GSM Evolution (EDGE), also

known as the 2.75G. EDGE, Enhanced GPRS (EGPRS) or IMT Single Carrier (IMT-SC)

which allowed improved data transmission rates, as an extension on top of standard GSM. It

began in 2003, initiated by Cingular (now AT&T) in the United States.

EDGE is standardized by 3GPP as part of the GSM family and it is an upgrade that

provides a potential three-fold increase in capacity of GSM/GPRS networks. The specification


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achieves higher data-rates (up to 236.8kbit/s) by switching to more sophisticated methods of

coding (8PSK), within existing GSM timeslots.

3G or 3rd generation mobile telecommunications is a generation of standards for mobile

phones and mobile telecommunication services fulfilling the International Mobile

Telecommunications-2000 (IMT-2000) specifications by the International Telecommunication

Union.

The first pre-commercial 3G network was launched by NTT DoCoMo in Japan in 1998,

branded as FOMA. It was first available in May 2001 as a pre-release (test) of W-CDMA

technology. The first commercial launch of 3G was also by NTT DoCoMo in Japan on 1

October 2001, although it was initially somewhat limited in scope; broader availability of the

system was delayed by apparent concerns over its reliability.

The first European pre-commercial network was an UMTS network on the Isle of Man

by Manx Telecom, the operator then owned by British Telecom, and the first commercial

network (also UMTS based W-CDMA) in Europe was opened for business by Telenor in

December 2001 with no commercial handsets and thus no paying customers.

The first network to go commercially live was by SK Telecom in South Korea on the

CDMA-based 1xEV-DO technology in January 2002. By May 2002 the second South Korean

3G network was by KT on EV-DO and thus the Koreans were the first to see competition

among 3G operators.

The first commercial United States 3G network was by Monet Mobile Networks, on

CDMA2000 1x EV-DO technology, but this network provider later shut down operations. The

second 3G network operator in the USA was Verizon Wireless in July 2002 also on

CDMA2000 1x EV-DO. AT&T Mobility is also a true 3G UMTS network, having completed its


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upgrade of the 3G network to HSUPA.

The first pre-commercial demonstration network in the southern hemisphere was built

in Adelaide, South Australia by m.Net Corporation in February 2002 using UMTS on 2100

MHz. This was a demonstration network for the 2002 IT World Congress. The first commercial

3G network was launched by Hutchison Telecommunications branded as Three or "3" in J

June 2003.

Emtel Launched the first 3G network in Africa.

By June 2007, the 200 millionth 3G subscriber had been connected. Out of 3 billion

mobile phone subscriptions worldwide this is only 6.7%. In the countries where 3G was

launched first – Japan and South Korea – 3G penetration is over 70%. In Europe the leading

country is Italy with a third of its subscribers migrated to 3G. Other leading countries by 3G

migration include UK, Austria, Australia and Singapore at the 20% migration level. A confusing

statistic is counting CDMA2000 1xRTT customers as if they were 3G customers. If using this

definition, then the total 3G subscriber base would be 475 million at June 2007 and 15.8% of

all subscribers worldwide.


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Hand Phone Traffic

1.

TimeUsers

0 to 700

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

B1 0 0 0.6 0.5 0.6 0.2 0.1 0.2 0.1 0.3 0.4 0.2 0.5 0.2 0.1 0.1 0.1 0

B2 0 0 0.4 0.5 0.6 0.3 0.2 0.3 0.4 0.4 0.5 0.2 0.1 0.1 0.2 0.1 0 0

B3 0 0 0.5 0.6 0.7 0.3 0.2 0.3 0.5 0.4 0.5 0.2 0.1 0.2 0.1 0 0 0.1

B4 0 0 0.1 0.4 0.5 0.2 0.1 0.3 0.4 0.6 0.7 0.3 0.2 0.1 0.3 0.1 0 0

B5 0 0 0.5 0.5 0.6 0.3 0.2 0.1 0.3 0.3 0.4 0.2 0.1 0 0 0 0.1 0

H1 0.1 0 0.1 0 0.1 0 0.1 0.2 0 0.1 0 0.1 0 0.1 0 0.1 0 0

H2 0 0.1 0 0.1 0.1 0 0.1 0 0.1 0 0 0.1 0 0.1 0.3 0 0 0

H3 0 0.1 0.1 0 0.1 0 0 0 0.1 0.1 0.1 0 0 0 0.1 0 0 0

H4 0.1 0 0 0.1 0.1 0 0.1 0 0 0.1 0 0.1 0 0 0 0.1 0 0

H5 0.1 0.1 0.1 0 0 0 0 0 0.1 0 0.1 0.1 0.1 0 0 0 0 0

S1 0 0 0 0 0 0 0 0.1 0.1 0.1 0.05 0.1 0 0.1 0.1 0.1 0 0

S2 0 0 0 0 0 0 0 0.1 0.1 0.1 0.05 0 0 0 0.1 0.2 0 0

S3 0 0 0 0 0 0 0 0.05 0.1 0.05 0.05 0 0 0.1 0.1 0.1 0.1 0

S4 0 0 0 0 0 0 0 0.05 0.2 0 0.05 0.1 0 0 0.2 0 0 0

S5 0 0 0 0 0 0 0 0.1 0.1 0.05 0.1 0.1 0 0.1 0 0 0 0

Traffic Volume(Erlang)

0.3 0.3 2.4 2.7 3.4 1.3 1.1 1.8 2.6 2.6 3 1.8 1.1 1.1 1.6 0.9 0.3 0.1

Table 1

2. In Table 1, there is a total traffic volume of 28.4 erlang. Therefore, the average traffic

volume is 1.183 erlang. The maximum traffic volume for the above 15 users is 360

erlang, assuming they speak for 24 hours a day.


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3. The traffic volume peaks thrice throughout the day, once at 1100 hours, the second

time at 1700 hours, and the third time at 2100 hours. The traffic volume also

experiences troughs at 0000 hours, 1300 hours, 1900 to 2000 hours, and 2400 hours.

Therefore, the peak calling hour is at 1100 hours with 3.4 erlangs.


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4. The method to reduce the traffic volume during the peak hour is to introduce a call

promotion during off-peak hours. Supposing that there are m+n customers, where m

customers subject their communicative activities to call rates, and n customers do not subject

their communicative activities to call rates, introducing a call promotion during off-peak hours

would incentivize m customers to call during off-peak hours instead of during peak hours,

thereby reducing the traffic volume during the peak hour.


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Hand Phone Rate Plan Selection1. (i)

Post paid service plans

Commitment fee (RM) Call rate within the same network (RM

per minute)

Call rate outside the network (RM per

minute)A 23 0.16 0.26B 63 0.13 0.23C 93 0.11 0.21

Table 2

Subscribers Total phone calls per day (minutes)

Calls within the same network (minutes)

Calls outside the network (minutes)

Businessman 253.2 63.3 189.9Housewife 246 136.6 109.4

Student 192 149.3 42.7Table 3

(ii) Assuming that there are 30 days in a month and the phone usage pattern is the same

every day, the Businessman would have made 379.8 minutes worth of calls within the

same network and 1139.4 minutes worth of calls out the network throughout the month.

If the Businessman uses Plan A, the Businessman would pay a total of RM380.00 after

rounding up. If the Businessman uses Plan B, the Businessman would pay a total of

RM374.45 after rounding up. If the Businessman uses Plan C, the Businessman would

pay a total of RM374.05 after rounding up. Therefore, Plan C is the most economical

plan for the Businessman.

Assuming that there are 30 days in a month and the phone usage pattern is the

same every day, the Housewife would have made 819.6 minutes worth of calls within

the same network and 656.4 minutes worth of calls out the network throughout the

month. If the Housewife uses Plan A, the Housewife would pay a total of RM324.80

after rounding up. If the Housewife uses Plan B, the Housewife would pay a total of


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RM320.50 after rounding up. If the Housewife uses Plan C, the Housewife would pay a

total of RM321 after rounding up. Therefore, Plan B is the most economical plan for

the Housewife.

Assuming that there are 30 days in a month and the phone usage pattern is the

same every day, the Student would have made 895.8 minutes worth of calls within the

same network and 256.2 minutes worth of calls out the network throughout the month.

If the Student uses Plan A, the Student would pay a total of RM232.95 after rounding

up. If the Student uses Plan B, the Student would pay a total of RM327.95 after

rounding up. If the Student uses Plan C, the Student would pay a total of RM245.35

after rounding up. Therefore, Plan A is the most economical plan for the Student.

(iii) The equation of the monthly payment is as below:

Monthly Payment =

(Calls within the same network(minutes) x RM0.11) +

(Calls outside the network(minutes) x RM0.21)

+ RM93


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Graph of Monthly Phone Bill (RM) against the Total Duration of Calls (Min)

a) The maximum total duration of calls, if the telephone bill allocation is RM1000

per month, is approximately 4903 minutes. Therefore, the maximum total duration of calls, in

hours, is 81.717 hours. Hence, the maximum total duration of calls is 2.724 hours a day. This

is true when the RM93 is taken into account, making the telephone bill allocation for call rates

into RM907 instead of RM1000. The ratio of calls within the same network and calls outside

the network is also taken into consideration.

b) The monthly hand phone bill, if the businessman limits his calls to 5000 minutes

per month, is RM1018. Once again, the commitment fee of RM93 and the ratio of calls within

the same network and calls outside the network is taken into consideration.


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2.

Time 0 to 700

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

0 0 0 0 0 0 0 0 0.1 0.05 0 0.05 0 0 0.1 0 0 0

Total phone calls per day (minutes)

Calls within the same network (minutes)

Calls outside the network (minutes)

18 13.5 4.5

Starter Pack Call rate within the same network (RM per minute)

Call rate outside the network (RM per minute)

RM8.50/packPre-loaded with RM5 talktime.

RM0.36 before hitting RM1, RM0.12 after RM1 total

usage.

RM0.36 before hitting RM1, RM0.12 after RM1 total

usage.

Assuming that there are 30 days in a month and the phone usage pattern is the same every

day, I would have made 540 minutes of phone calls in a month, with 405 minutes of calls

within the same network and 135 minutes of calls outside the network. If I use Plan A, I would

pay a total of RM122.90 after rounding up. If I use Plan B, I would pay a total of RM146.70

after rounding up. If I use Plan C, I would pay a total of RM165.90 after rounding up. If I use

the Pre-paid Plan, I would pay a total of RM93.60 after rounding up, but ignoring the starter

pack price. Therefore, the Pre-paid Plan is the most economical plan for me.


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Further Exploration

Pr (received power)= Pt (transmitted power)4π dλ2

Coverage distance for carrier frequency of 900MHz:

10−11W = 5W4 πdλ

2

10−11W = 5W4 πd0.333

2

3.33x10−12= 5W4π d 2

1.502x1012m=4πd 2

3.755x1011m=π d 2

1.195x1011m=d 2

d =√1.195x1011m

d =345687.720m

Coverage distance for carrier frequency of 1800MHz:

10−11W = 5W4 πdλ

2

10−11W = 5W4 πd0.166

2

1.66x10−12= 5W4π d 2

3.012x1012m=4πd 2

7.53x1011m=πd 2

2.397x1011m=d 2

d =√2.397x1011m

d =489591.667m

Due to the higher coverage distance, I, as the service provider, I would choose the carrier

frequency of 1800MHz.


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Conclusion

Handphones are taken for granted in today's world, especially with the advent of the newest

electronic gadgets, for example, the Samsung Galaxy S III, the HTC Droid Incredible 4G LTE,

the LG A340, the Lumigon T2, the Motorola RAZR V XT889, the Sony Xperia Miro, the Nokia

110, the BlackBerry 9320, the iPad 3, the iPod touch and the iPhone.

However, after extensive research, question answering and problem solving, I have come to

realize that handphones have an enriching history coupled with a near-mystical way of

functioning (to the average untrained person).

Handphones have the central aim of providing a mobile means of communication and has

empowered the commoner to experience the novelty of distant communication. The usage of

handphones have ensured that everyone may now have a functioning system to speak over

long distances.

In conclusion, handphones have evolved to be an integral and important part of our lives.

Many are of the opinion that most youths are unable to survive without their handphones.

Although this may be obviously untrue, it shows how handphones have become so vital to our

daily lives that we seem to be attached to it at all times. Therefore, we should be thankful to

those who have contributed throughout the years to the development and perfection of the

handphone.


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Reflection

While conducting this project, I have examined and disseminated much information, all of

which came from the Internet. Over the course of a few weeks, during which I completed this

project, I learnt many things, including the history of the handphone as well as the system by

which the telecommunicative portion of the system works.

In another aspect, however, I feel that this project have also taught me to manage my time

better. It has been an enjoyable and educational experience.


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Reference

Wikipedia

en.wikipedia.org/wiki/1G



Scribd

www.scribd.com

Flickr

www.flickr.com

Connexions

cnx.org

The RadioPics Database

www.radiopics.com


5 Clancy 2012

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