Stochastic Storage Processes

Queues, Insurance Risk, Dams, and Data Communication
2. Auflage 1998
ISBN: 978-0-387-98248-9
Verlag: Springer

Buch, Englisch, Band 15, 207 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 512 g

Reihe: Stochastic Modelling and Applied Probability

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.

Zielgruppe

Research

Autoren/Hrsg.

Prabhu, N. U.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

1. A Class of Stochastic Models.- 2. Problems Arising from the Models.- 3. The Scope of This Book.- 4. Further Remarks.- Problems.- Selected Bibliography.- I. The Single Server Queue.- 1. The Queue GI/G/1.- 2. Further Results for the Queue GI/G/1.- 3. The Queue M/M/1.- II. Continuous Time Storage Models.- 4. The Basic Storage Model.- III. Markov-Modulated Storage Models.- 5. The Markov-Modulated Single Server Queue.- 6. A Fluid Model for Data Communication.- 7. A Data Communication Model with Packets.- Appendix A.- Appendix B.- Appendix C.