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Introduction to matrix analytic methods in stochastic modeling / G. Latouche, V. Ramaswami.
- Format:
- Book
- Author/Creator:
- Latouche, G. (Guy)
- Series:
- ASA-SIAM series on statistics and applied probability ; 5.
- ASA-SIAM series on statistics and applied probability ; 5
- Language:
- English
- Subjects (All):
- Markov processes.
- Queuing theory.
- Matrix analytic methods.
- Physical Description:
- 1 electronic text (xiv, 334 p.) : ill., digital file.
- Place of Publication:
- Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1999.
- Language Note:
- English
- System Details:
- Mode of access: World Wide Web.
- System requirements: Adobe Acrobat Reader.
- Summary:
- 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.
- 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.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references (p. 313-324) and index.
- Title from title screen, viewed 12/30/2010.
- ISBN:
- 0-89871-973-9
- Publisher Number:
- SA05 SIAM
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