Probability, Stochastic Processes, and Queueing Theory

1. Front Matter

   Pages i-xxviii

   PDF

2. Introduction

   1. Introduction

      • Randolph Nelson

      Pages 1-14

3. Probability

   1. Front Matter

      Pages 15-15

      PDF

   2. Randomness and Probability

      • Randolph Nelson

      Pages 17-44

   3. Combinatorics

      • Randolph Nelson

      Pages 45-99

   4. Random Variables and Distributions

      • Randolph Nelson

      Pages 101-165

   5. Expectation and Fundamental Theorems

      • Randolph Nelson

      Pages 167-231

4. Stochastic Processes

   1. Front Matter

      Pages 233-233

      PDF

   2. The Poisson Process and Renewal Theory

      • Randolph Nelson

      Pages 235-282

   3. The M/G/1 Queue

      • Randolph Nelson

      Pages 283-327

   4. Markov Processes

      • Randolph Nelson

      Pages 329-389

   5. Matrix Geometric Solutions

      • Randolph Nelson

      Pages 391-428

   6. Queueing Networks

      • Randolph Nelson

      Pages 429-501

   7. Epilogue and Special Topics

      • Randolph Nelson

      Pages 503-512

5. Back Matter

   Pages 513-583

   PDF

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.

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

• OTA Limited Partnership, Purchase, USA

  Randolph Nelson

• Modeling Methodology, IBM T.J. Watson Research Center, Yorktown Heights, USA

  Randolph Nelson

Policies and ethics