# Probability, Stochastic Processes, and Queueing Theory

## The Mathematics of Computer Performance Modeling

• Randolph Nelson
Textbook

1. Front Matter
Pages i-xxviii
2. ### Introduction

1. Randolph Nelson
Pages 1-14
3. ### Probability

1. Front Matter
Pages 15-15
2. Randolph Nelson
Pages 17-44
3. Randolph Nelson
Pages 45-99
4. Randolph Nelson
Pages 101-165
5. Randolph Nelson
Pages 167-231
4. ### Stochastic Processes

1. Front Matter
Pages 233-233
2. Randolph Nelson
Pages 235-282
3. Randolph Nelson
Pages 283-327
4. Randolph Nelson
Pages 329-389
5. Randolph Nelson
Pages 391-428
6. Randolph Nelson
Pages 429-501
7. Randolph Nelson
Pages 503-512
5. Back Matter
Pages 513-583

### Introduction

We will occasionally footnote a portion of text with a "**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "their own" by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per­ sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative.

### Keywords

M/G/1 queue Markov process Poisson process Random variable combinatorics linear algebra modeling queueing theory renewal theory stochastic process

#### Authors and affiliations

• Randolph Nelson
• 1
• 2
1. 1.OTA Limited PartnershipPurchaseUSA
2. 2.Modeling MethodologyIBM T.J. Watson Research CenterYorktown HeightsUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-2426-4
• Copyright Information Springer-Verlag New York 1995
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4419-2846-7
• Online ISBN 978-1-4757-2426-4
• Buy this book on publisher's site