Numerical methods for structured Markov chains / D.A. Bini, G. Latouche, B. Meini.

Format:

Book

Author/Creator:

Bini, Dario.

Contributor:

Latouche, G. (Guy)

Meini, B. (Beatrice)

Series:

Numerical mathematics and scientific computation.

Oxford science publications.

Numerical mathematics and scientific computation

Oxford science publications

Language:

English

Subjects (All):

Markov processes--Numerical solutions.

Markov processes.

Physical Description:

1 online resource (340 p.)

Place of Publication:

Oxford ; New York : Oxford University Press, 2005.

Language Note:

English

Summary:

Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible toengineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a sy

Contents:

Contents; PART I: TOOLS; 1 Introduction to Markov chains; 1.1 Discrete-time Markov chains; 1.2 Classification of states; 1.3 Irreducible classes; 1.4 First passages; 1.5 Stationary distribution; 1.6 Censoring of a Markov chain; 1.7 Continuous-time Markov processes; 1.8 Finite nonnegative matrices; 1.9 Bibliographic notes; 2 Structured matrix analysis; 2.1 Introduction; 2.2 Discrete Fourier transform; 2.3 Structured matrices; 2.4 Displacement operators; 2.5 Bibliographic notes; 3 Matrix equations and canonical factorizations; 3.1 Matrix power series and structured matrices

3.2 Wiener-Hopf factorization3.3 Nonlinear matrix equations; 3.4 Reduction of matrix equations; 3.5 Infinite systems and canonical factorization; 3.6 Shifting technique; 3.7 Bibliographic notes; PART II: STRUCTURED MARKOV CHAINS; 4 M/G/1-type Markov chains; 4.1 Introduction; 4.2 Markov chains skip-free to lower levels; 4.3 Ergodicity; 4.4 Properties of the generating function; 4.5 Canonical factorization; 4.6 Solutions of the matrix equation; 4.7 Irreducibility assumptions; 4.8 Bibliographic notes; 5 Phase-type queues; 5.1 Introduction; 5.2 G/M/1-type Markov chains; 5.3 A duality property

5.4 Toeplitz-like transitions5.5 Limited displacements; 5.6 Quasi-birth-death processes; 5.7 Reductions to QBDs; 5.8 Tree-like processes; 5.9 Bibliographic notes; PART III: ALGORITHMS; 6 Functional iterations; 6.1 Basic concepts; 6.2 Linearly convergent iterations; 6.3 Newton's iteration; 6.4 Bibliographic notes; 7 Logarithmic reduction and cyclic reduction; 7.1 Introduction; 7.2 Logarithmic reduction; 7.3 Cyclic reduction for quasi-birth-death processes; 7.4 Cyclic reduction for M/G/1-type Markov chains; 7.5 Computational issues of cyclic reduction; 7.6 Bibliographic notes

8 Alternative approaches8.1 Introduction; 8.2 Convergence acceleration; 8.3 Cyclic reduction and functional iterations; 8.4 Doubling methods; 8.5 Evaluation-interpolation techniques; 8.6 Invariant subspace method; 8.7 Bibliographic notes; 9 Specialized structures; 9.1 Introduction; 9.2 Markov chains with limited displacement; 9.3 Solving M/G/1-type Markov chains through a QBD; 9.4 Tree-like stochastic processes; 9.5 Bibliographic notes; Appendix; Notation; List of Algorithms; Bibliography; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 315-323) and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

9786612335129

1-4237-5819-6

0-19-152364-X

1-282-33512-X

OCLC:

64704861