Stochastic Storage Processes

Queues, Insurance Risk, Dams, and Data Communication

  • N. U. Prabhu

Part of the Applications of Mathematics book series (SMAP, volume 15)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Introduction

    1. N. U. Prabhu
      Pages 1-15
  3. The Single Server Queue

    1. Front Matter
      Pages 17-17
    2. N. U. Prabhu
      Pages 19-60
    3. N. U. Prabhu
      Pages 61-90
    4. N. U. Prabhu
      Pages 91-102
  4. Continuous Time Storage Models

    1. Front Matter
      Pages 103-103
    2. N. U. Prabhu
      Pages 105-152
  5. Markov-Modulated Storage Models

    1. Front Matter
      Pages 153-153
    2. N. U. Prabhu
      Pages 155-165
    3. N. U. Prabhu
      Pages 166-179
    4. N. U. Prabhu
      Pages 180-194
  6. Back Matter
    Pages 195-207

About this book

Introduction

This is a revised and expanded version of the earlier edition. The new material is on Markov-modulated storage processes arising from queueing and data commu­ nication models. The analysis of these models is based on the fluctuation theory of Markov-additive processes and their discrete time analogues, Markov random walks. The workload and queue length processes, omitted from the earlier edition, are also presented. In addition, many sections have been rewritten, with new re­ sults and proofs, as well as further examples. The mathematical level and style of presentation, however, remain the same. Chapter I contains a comprefensive treatment of the waiting time and related quantities in a single server queue, combining Chapters 1 and 2 of the earlier edition. In Chapter 2 we treat the (continuous time) workload and queue length processes using their semiregenerative properties. Also included are bulk queues omitted from the earlier edition, but included in its Russian translation. The queue MIMIl is presented in Chapter 3. This is the so-called simple queue, but its treat­ ment in most of the literature is far from simple. Our analysis of the queue length process is elementary and yields explicit results for various distributions of interest. are treated in Chapter 4, combining Chapters 3 Continuous time storage models and 4 of the earlier edition. We present extensive new material, omitting much of the old Chapter 4. This has resulted in a streamlined account of this important class of models.

Keywords

Stochastic processes Stochastischer Prozess Warteschlange random walk stochastic process

Authors and affiliations

  • N. U. Prabhu
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1742-8
  • Copyright Information Springer-Verlag New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7260-1
  • Online ISBN 978-1-4612-1742-8
  • Series Print ISSN 0172-4568
  • About this book