Lab 10

I've Got Your Number

Mathematics
for
Telecommunications

Prof Mary Kay Abbey
AMATYC – Writing Team Members
Montgomery Community College
Takoma Park, Maryland
Prof Ellena Reda
AMATYC – Writing Team Members
Dutchess Community College
Poughkeepsie, New York
MWP Logo

Project Grant Team

John S. Pazdar
Capital Community College
Hartford, Connecticut
Karen B. Gaines
St Louis Community College – Meremac
St Louis, Missouri
This project was supported, in part,
by the National Science Foundation.

Peter A. Wursthorn
Capital Community College
Hartford, Connecticut

Opinions expressed are those of the authors
and not necessarily those of the Foundation.
Patricia L. Hirschy
Asnuntuck Community College
Enfield, Connecticut

#Introduction

Communication is the oil for all relationships whether at work or at home. The growth of the cell phone industry has been exponential in nature. Cell phones have made it possible to keep in touch almost everywhere at any time. The key word in the preceding statement is "ALMOST". More and more people have come to view their cell phone as a necessity and not as a luxury. In the business world a missed call could mean the difference between making a deal or losing a customer. To a parent whose teenager is out driving late at night or the person concerned about an elderly parent who lives alone, the cell phone brings piece of mind. For those who live in areas that regularly lose telephone service due to severe summer or treacherous winter storms, the cell phone provides a means of maintaining contact with others.

#Technology Problem

In this lab you will be exploring different aspects of the cellular phone industry. You will have specific tasks to do or problems to solve. Oftentimes, when we are asked to solve a problem or perform a task, we become too focused on the task at hand and forget about the big picture. Your first activity as a class, therefore, will be to examine the cellular phone industry as a whole. You will then focus on one or more of the following specific areas:

Section I: Cellular Tower Placement — this focuses on the business, engineering, environmental, and artistic aspects of tower placement. This activity will primarily use geometry and statistics.

Section II: Health and Safety Issues — this deals with the effects of cellular phone use on our health and also the safety issues involved with driving while using a cell phone. This activity will primarily focus on statistics.

Section III: Consumer Education — this addresses different cellular plan options available to the consumer. This activity will primarily focus on creating functions that model the plans.

The Big Picture

A cellular network is composed of cellular towers. A call is placed from your cell phone and travels by radio waves to a cellular tower that picks up the signal from your phone. The signal is then sent to a Mobile Telephone Switching Office (MTSO) which handles calls from several towers called a cluster. The MTSO transfers the signal to a local phone line that sends the signal to the final destination via landline, microwave signals or satellite. If you are driving while making your call, the MTSO links your call to neighboring cells. It senses when the signal is becoming weak and hands your call off to the next tower or the MTSO in the next cluster. It controls the quality of your radio link by keeping you connected to the best possible signal as you move from cell to cell. The process is seamless as far as the cell phone user is concerned. When you have traveled beyond the range of the towers, the signal is lost and you cannot make or receive calls. It is difficult for the towers to track you if you are traveling more than 50 mph, so this may also contribute to service problems.

As you continue to investigate the technology problem, use the scientific method (problem, question, hypothesis, test, decision) to support and guide your thinking process. The first two steps refer to developing a better understanding of the problem by asking and answering questions. This leads to research.

#Bibliotechnology Research

The foregoing description of a cellular phone network only scratches the surface of how the whole system works. It is your responsibility now to further research the details of how different parts of the system work. You (or your group) will be assigned one or more of the topics listed below. You are to research the topic, find at least 3 sources, and report your findings to the class so that they may better understand your selected topic. After everyone has presented his/her findings, the class should have a basic understanding of the whole cellular network.

The following is a list of topics with ideas for questions you should be able to answer after your research:

#Mathematics Tools

You will need to select and use mathematics tools that help to describe and solve the technology problem. These include skills that relate to problem solving, designing tables, graphing, and solving equations. In addition, the cellular tower problem involves basic statistics and geometry; the health and safety problem deals with topics from introductory statistics; the rate plan problem involves modeling and the use of piece-wise functions.

As you work on the technology problem, be sure to keep a record that is sufficiently detailed to allow a reader to repeat your work step by step. As you proceed through the course, it is imperative that you organize a record of all your work in a model portfolio. Cite all sources that you use. When you have completed the lab, you will present the model portfolio to an audience and deliver a defense of its embedded thesis.

Now that you have a basic understanding of what a cell phone is and how it works, you and your group will be assigned one or more of the following areas of concentration.

Developing a Solution

Section I
Cellular Tower Placement

For this activity, assume that your group (a consulting firm) has been approached by a group of investors that is interested in starting a cellular phone service in your area. They have asked your group to focus on the number and placement of cellular towers needed to service the area. Your assignment is to address the tasks listed below and to communicate your findings as if you were presenting them to the investors. The investors are particularly interested in where you found your information and in precisely how you reached the conclusions for your recommendations regarding placement of the cellular towers.

Section II
Health and Safety Issues

Your local Congressional Representative has hired your group (a consulting firm) to assess the health and safety issues concerning cellular phone usage. He is up for re-election and wants to cover all of the issues. Your assignment is to do the research described below and to prepare a report for your Representative. He does not want anyone catching him off guard with questions, so your report needs to cite all sources and to explain clearly how you developed recommendations concerning these issues.

 

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