Introduction to Matrix Analytic Methods in Stochastic Modeling
Part of ASA-SIAM Series on Statistics and Applied Probability
- Authors:
- G. Latouche
- V. Ramaswami
- Date Published: January 1999
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
- format: Paperback
- isbn: 9780898714258
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Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included.
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×Product details
- Date Published: January 1999
- format: Paperback
- isbn: 9780898714258
- length: 348 pages
- dimensions: 250 x 180 x 20 mm
- weight: 0.602kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
Table of Contents
Preface
Part I. Quasi-Birth-and-Death Processes. 1. Examples
Part II. The Method of Phases. 2. PH Distributions
3. Markovian Point Processes
Part III. The Matrix-Geometric Distribution. 4. Birth-and-Death Processes
5. Processes Under a Taboo
6. Homogeneous QBDs
7. Stability Condition
Part IV. Algorithms. 8. Algorithms for the Rate Matrix
9. Spectral Analysis
10. Finite QBDs
11. First Passage Times
Part V. Beyond Simple QBDs. 12. Nonhomogeneous QBDs
13. Processes, Skip-Free in One Direction
14. Tree Processes
15. Product Form Networks
16. Nondenumerable States
Bibliography
Index.
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