Introduction to Matrix Analytic Methods in Stochastic Modeling

Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.

G. Latouche (Author), V. Ramaswami (Author)

9780898714258, Society for Industrial and Applied Mathematics

Paperback / softback, published 1 January 1987

348 pages
25 x 18 x 2 cm, 0.602 kg

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.

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.

Subject Areas: Probability & statistics [PBT]