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© 1999

Introduction to Stochastic Networks

Book

Part of the Applications of Mathematics book series (SMAP, volume 44)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Richard Serfozo
    Pages 1-43
  3. Richard Serfozo
    Pages 44-73
  4. Richard Serfozo
    Pages 74-98
  5. Richard Serfozo
    Pages 99-134
  6. Richard Serfozo
    Pages 135-154
  7. Richard Serfozo
    Pages 155-180
  8. Richard Serfozo
    Pages 181-205
  9. Richard Serfozo
    Pages 230-263
  10. Richard Serfozo
    Pages 264-287
  11. Back Matter
    Pages 289-300

About this book

Introduction

In a stochastic network, such as those in computer/telecommunications and manufacturing, discrete units move among a network of stations where they are processed or served. Randomness may occur in the servicing and routing of units, and there may be queueing for services. This book describes several basic stochastic network processes, beginning with Jackson networks and ending with spatial queueing systems in which units, such as cellular phones, move in a space or region where they are served. The focus is on network processes that have tractable (closed-form) expressions for the equilibrium probability distribution of the numbers of units at the stations. These distributions yield network performance parameters such as expectations of throughputs, delays, costs, and travel times. The book is intended for graduate students and researchers in engineering, science and mathematics interested in the basics of stochastic networks that have been developed over the last twenty years. Assuming a graduate course in stochastic processes without measure theory, the emphasis is on multi-dimensional Markov processes. There is also some self-contained material on point processes involving real analysis. The book also contains rather complete introductions to reversible Markov processes, Palm probabilities for stationary systems, Little laws for queueing systems and space-time Poisson processes. This material is used in describing reversible networks, waiting times at stations, travel times and space-time flows in networks. Richard Serfozo received the Ph.D. degree in Industrial Engineering and Management Sciences at Northwestern University in 1969 and is currently Professor of Industrial and Systems Engineering at Georgia Institute of Technology. Prior to that he held positions in the Boeing Company, Syracuse University, and Bell Laboratories. He has held

Keywords

BCMP network Computer Jackson network Kelly network Markov process Poisson process Probability distribution Stochastic processes algorithms birth-death process ergodicity measure theory modeling point process stochastic network

Authors and affiliations

  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

Bibliographic information

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Reviews

From the reviews:

JOURNAL OF APPLIED MATHEMATICS AND STOCHASTIC ANALYSIS

"…integral to today’s development of analytical methods for queuing networks…[collects] an interesting summary of what one might view as the heart of network theory."

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"The book provides self-contained introductions to point processes and Palm probabilities, a point that I emphasize because these parts are extremely well-presented and might also be valuable for readers not particularly interested in stochastic networks…Serfozo has certainly written a book that is unique in its choice of topics and captures the most recent developments in research in stochastic networks. I recommend it to all mathematically interested readers in this area. I found the book extremely well written, with many insightful explanations that make it a pleasure to read. The notations used are very elegant and intuitive…thoroughly edited with very few typographical errors."