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Computational Probability

  • Winfried K. Grassmann

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 24)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Gianfranco Ciardo
    Pages 11-41
  3. Edmundo de Souza e Silva, H. Richard Gail
    Pages 43-79
  4. Brigitte Plateau, William J. Stewart
    Pages 113-151
  5. Winfried K. Grassmann, David A. Stanford
    Pages 153-203
  6. H. Richard Gail, Sidney L. Hantler, B. Alan Taylor
    Pages 205-255
  7. Joseph Abate, Gagan L. Choudhury, Ward Whitt
    Pages 257-323
  8. Shaler Stidham Jr.
    Pages 325-363
  9. Nico M. van Dijk, Winfried Grassmann
    Pages 409-443
  10. Jogesh K. Muppala, Ricardo M. Fricks, Kishor S. Trivedi
    Pages 445-479
  11. Back Matter
    Pages 481-490

About this book

Introduction

Great advances have been made in recent years in the field of computational probability. In particular, the state of the art - as it relates to queuing systems, stochastic Petri-nets and systems dealing with reliability - has benefited significantly from these advances. The objective of this book is to make these topics accessible to researchers, graduate students, and practitioners. Great care was taken to make the exposition as clear as possible. Every line in the book has been evaluated, and changes have been made whenever it was felt that the initial exposition was not clear enough for the intended readership.
The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail: Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.

Keywords

Markov Chains Markov chain Markov model modeling optimization

Editors and affiliations

  • Winfried K. Grassmann
    • 1
  1. 1.University of SaskatchewanCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4828-4
  • Copyright Information Springer-Verlag US 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-5100-7
  • Online ISBN 978-1-4757-4828-4
  • Series Print ISSN 0884-8289
  • Buy this book on publisher's site
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