1. 1 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 1 st and 2 nd 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.

2. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 2 Chapter 2 Probability, Statistics, and Traffic Theories Copyright © 2002, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved

3. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 3 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:  2.1. Introduction  2.2. Basic Probability and Statistics Theories  Random variables  Probability mass function (pmf)  Probability density function (pdf)  Cumulative distribution function (cdf)  Expected value, n th moment, n th central moment, and variance  Some important distributions  2.3. Traffic Theory  Poisson arrival model, etc.  2.4. Basic Queuing Systems  Little’s law  Basic queuing models

4. 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

5. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 5 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

6. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 6 Skipped 2 Subsections

7. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 7 2.4. Basic Queuing Systems What is queuing theory? Queuing theory is the study of queues Sometimes called waiting lines Can be used to describe: Real world queues, or Abstract queues 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

8. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 8 Skipped all Remaining Subsections

9. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 9 The End of Section 2