A probabilistic interpretation of cyclic reduction and its relationships with logarithmic reduction

Calcolo

Volumn 45, Issue 3, 2008, Pages 207-216

  Bini, Dario A ^a   Meini, Beatrice ^a   Ramaswami, Vaidyanathan ^b  

^a UNIVERSITY OF PISA   (Italy)

^b AT AND T LABS RESEARCH   (United States)

Author keywords

Cyclic reduction; Logarithmic reduction; Markov chains; QBD processes

Indexed keywords

MARKOV PROCESSES;

CYCLIC REDUCTION; LOGARITHMIC REDUCTION; PROBABILISTIC INTERPRETATION; QBD PROCESS; REDUCTION ALGORITHMS; SIMPLE++;

CHAINS;

EID: 58449126549     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10092-008-0151-6     Document Type: Article

References (11)

1. Bini, D.A., Meini, B.: On cyclic reduction applied to a class of Toeplitz-like matrices arising in queueing problems. In: Stewart, W.J. (ed.): Computations with Markov chains. Boston: Kluwer 1995, pp. 21-38
2. D.A. Bini B. Meini 1996 On the solution of a nonlinear matrix equation arising in queueing problems SIAM J. Matrix Anal. Appl. 17 906 926
3. Bini, D.A., Latouche, G., Meini, B.: Numerical methods for structured Markov chains. Oxford Science Publications, London 2005
4. B.L. Buzbee G.H. Golub C.W. Nielson 1970 On direct methods for solving Poisson's equations SIAM J. Numer. Anal. 7 627 656
5. H.R. Gail S.L. Hantler B.A. Taylor 1996 Spectral analysis of M/G/1 and G/M/1 type Markov chains Adv. in Appl. Probab. 28 114 165
6. H.R. Gail S.L. Hantler B.A. Taylor 1998 Matrix-geometric invariant measures for G/M/1 type Markov chains Comm. Statist. Stochastic Models 14 537 569
7. E. Hunt 2003 A probabilistic algorithm for determining the fundamental matrix of a block M/G/1 Markov chain Math. Comput. Modelling 38 1203 1209
8. Hunt, E.: Determining the fundamental matrix of a block M/G/1 Markov chain. In: Wilson, R.J., Osaki, S., Faddy, M.J. (eds.): Stochastic models in engineering, technology and management. Brisbane: Centre for Statistics, University of Queensland 1999, pp. 446-455
9. G. Latouche V. Ramaswami 1993 A logarithmic reduction algorithm for quasi-birth-death processes J. Appl. Probab. 30 650 674
10. Latouche, G., Ramaswami, V.: Introduction to matrix analytic methods in stochasticmodeling. Philadelphia: SIAM 1999
11. Neuts, M.F.: Structured stochastic matrices of M/G/1 type and their applications. New York: Dekker 1989