Probability and Statistics with Reliability,
Queuing and Computer Science
Applications
Second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 4 :Expectationg
Copyright 2011 by K.S. Trivedi
Page 1 of 91
Expected (Mean, Average) Value
There are

Probability and Statistics with Reliability,
Queuing and Computer Science
Applications
Second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 5: Conditional Distribution and Expectation
Copyright 2011 by K.S. Trivedi
Page 1 of 26
Dependent Ran

Queueing Theory
Ivo Adan and Jacques Resing Department of Mathematics and Computing Science Eindhoven University of Technology P.O. Box 513, 5600 MB Eindhoven, The Netherlands February 14, 2001
Contents
1 Introduction 1.1 Examples . . . . . . . . . . . .

BASIC ELEMENTS OF QUEUEING
THEORY
Application to the Modelling of Computer
Systems
Lecture Notes
Philippe NAIN
INRIA
2004 route des Lucioles
06902 Sophia Antipolis, France
E-mail: nain@sophia.inria.fr
c
January
1998 by Philippe Nain
These lecture notes re

Probability and Statistics with Reliability,
Queuing and Computer Science Applications
Second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 8 (Part 5) :Continuous Time Markov Chains
Reliability Modeling
Dept. of Electrical & Computer enginee

Probability and Statistics with
Reliability, Queuing and Computer
Science Applications
second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 1 part 1: Introduction
Copyright 2011 by K.S. Trivedi
Page 1 of 72
Need to Model Random Phenomena
Ran

Probability and Statistics with
Reliability, Queuing and Computer
Science Applications
second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 1 part 2
Copyright 2011 by K.S. Trivedi
Page 1 of 27
Bayes Rule
Given: P( B), P( A | B), P( A | B )
W

Probability and Statistics with Reliability,
Queuing and Computer Science Applications
Second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 8 (Part 3): Continuous Time Markov Chains
Pure Performance Modeling
Dept. of Electrical & Computer en

Probability and Statistics with
Reliability, Queuing and Computer
Science Applications
Second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 7 : Discrete Time Markov Chains
Dept. of Electrical & Computer Engineering
Duke University
Email: kst

Exercises for Chapter 4
Markov Chain
1. A particle moves on a circle through points which
have been marked 0, 1, 2, 3, 4 (in a clockwise order). At each step, it has a probability p of moving
to the right and 1 p to the left. Let Xn denote its
location on

Probability and Statistics with Reliability,
Queuing and Computer Science
Applications
Second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 8 (Part 1) :Continuous Time Markov
Chains: Theory
Dept. of Electrical & Computer engineering
Duke Uni