Transcript Chapter 2 Probability, Statistics, and Traffic Theories

CS 6910 – Pervasive Computing
Spring 2007
Section 2 (Ch.2):
Probability, Statistics, and
Traffic Theories
Prof. Leszek Lilien
Department of Computer Science
Western Michigan University
Slides based on publisher’s slides for 1st and 2nd edition of:
Introduction to Wireless and Mobile Systems by Agrawal & Zeng
© 2003, 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved.
Some original slides were modified by L. Lilien, who strived to make such modifications clearly
visible. Some slides were added by L. Lilien, and are © 2006-2007 by Leszek T. Lilien.
Requests to use L. Lilien’s slides for non-profit purposes will be gladly granted upon a written
request.
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Chapter 2
Probability, Statistics, and Traffic Theories
Copyright © 2002, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
2
Outline of Chapter 2
We skip almost all sections in this Chapter
You have to use it on your own if needed (e.g., for your project)
Chapter 2 Contents:
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2.1. Introduction
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2.2. Basic Probability and Statistics Theories
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Random variables
Probability mass function (pmf)
Probability density function (pdf)
Cumulative distribution function (cdf)
Expected value, nth moment, nth central moment, and variance
Some important distributions
2.3. Traffic Theory
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Poisson arrival model, etc.
2.4. Basic Queuing Systems
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Little’s law
Basic queuing models
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
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2.1. Introduction

Many factors influence the performance of wireless systems:
 Density of mobile users
 Cell size
 Moving direction and speed of users
 Defined by mobility models
 Call rate, call duration
 Interference, etc.

Probability, statistics theory and traffic patterns, help make
these factors tractable
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
4
2.1. Introduction

Many factors influence the performance of wireless systems:
 Density of mobile users
 Cell size
 Moving direction and speed of users
 Defined by mobility models
 Call rate, call duration
 Interference, etc.

Probability, statistics theory and traffic patterns, help make
these factors tractable
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
5
Skipped 2 Subsections
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
6
2.4. Basic Queuing Systems
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What is queuing theory?
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Queuing theory is the study of queues
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Sometimes called waiting lines
Can be used to describe:
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Real world queues, or
Abstract queues
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Found in many branches of computer science, such as OSs
Basic queuing theory
Queuing theory is divided into 3 main sections:
 Traffic flow
 Scheduling
 Facility design and employee allocation
Much more in the textbook
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
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Skipped all Remaining Subsections
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
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The End of Section 2
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved
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