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Stochastic Storage Processes

Queues, Insurance Risk, Dams, and Data Communication

  • Book
  • © 1998

Overview

Authors:
  1. N. U. Prabhu

    1. School of Operations Research and Industrial Engineering, Cornell University, Ithaca, USA

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Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 15)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction

    1. Introduction

      • N. U. Prabhu
      Pages 1-15

  3. The Single Server Queue

    1. Front Matter

      Pages 17-17
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    2. The Queue GI/G/1

      • N. U. Prabhu
      Pages 19-60

    3. Further Results for the Queue GI/G/1

      • N. U. Prabhu
      Pages 61-90

    4. The Queue M/M/1

      • N. U. Prabhu
      Pages 91-102

  4. Continuous Time Storage Models

    1. Front Matter

      Pages 103-103
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    2. The Basic Storage Model

      • N. U. Prabhu
      Pages 105-152

  5. Markov-Modulated Storage Models

    1. Front Matter

      Pages 153-153
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    2. The Markov-Modulated Single Server Queue

      • N. U. Prabhu
      Pages 155-165

    3. A Fluid Model for Data Communication

      • N. U. Prabhu
      Pages 166-179

    4. A Data Communication Model with Packets

      • N. U. Prabhu
      Pages 180-194

  6. Back Matter

    Pages 195-207
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Keywords

About this book

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.

Authors and Affiliations

  • School of Operations Research and Industrial Engineering, Cornell University, Ithaca, USA

    N. U. Prabhu

Bibliographic Information

  • Book Title: Stochastic Storage Processes

  • Book Subtitle: Queues, Insurance Risk, Dams, and Data Communication

  • Authors: N. U. Prabhu

  • Series Title: Stochastic Modelling and Applied Probability

  • DOI: https://doi.org/10.1007/978-1-4612-1742-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-387-98248-9Published: 05 December 1997

  • Softcover ISBN: 978-1-4612-7260-1Published: 27 September 2012

  • eBook ISBN: 978-1-4612-1742-8Published: 06 December 2012

  • Series ISSN: 0172-4568

  • Series E-ISSN: 2197-439X

  • Edition Number: 2

  • Number of Pages: XVI, 207

  • Topics: Statistics, general, Probability Theory and Stochastic Processes

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