β-invariant measures for transition matrices of GI/M/1 type

Stochastic Models

Volumn 19, Issue 2, 2003, Pages 201-233

  Li, Quan Lin ^a,b   Zhao, Yiqiang Q ^a  

^a CARLETON UNIVERSITY   (Canada)

^b INSTITUTE OF AUTOMATION   (China)

Author keywords

invariant measures; Markov chains of GI M 1 type; Quasi stationary distributions; Radius of convergence; Spectral analysis; The RG factorizations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; SPECTRUM ANALYSIS; THEOREM PROVING;

CONVERGENCE RADIUS; QUASI STATIONARY DISTRIBUTIONS; TRANSITION MATRIX;

MATRIX ALGEBRA;

EID: 0037592879     PISSN: 15326349     EISSN: None     Source Type: Journal    
DOI: 10.1081/STM-120020387     Document Type: Article

References (21)

1. Bean, N.G.; Bright, L.; Latouche, G.; Pearce, C.E.M.; Pollett, P.K.; Taylor, P.G. The quasi-stationary behavior of quasi-birth-and-death processes. Ann. Appl. Prob. 1997, 7(1), 134-155.
2. Bean, N.G.; Pollett, P.K.; Taylor, P.G. The quasistationary distributions of level-independent quasi-birth-and-death processes. Stoc. Models 1998, 14 (1&2), 389-406.
3. Bean, N.G.; Pollett, P.K.; Taylor, P.G. Quasistationary distributions for level-dependent quasi-birth-and-death processes. Stoc. Models 2000, 16 (5), 511-541.
4. Gail, H.R.; Hantler, S.L.; Taylor, B.A. Solutions of the basic matrix equation for M/G/1 type and G/M/1 type Markov chains. Stoc. Models 1994, 10 (1), 1-43.
5. Gail, H.R.; Hantler, S.L.; Taylor, B.A. Matrix-geometric invariant measures for G/M/1 type Markov chains. Stoc. Models 1998, 14 (3), 537-569.
6. Kemeny, J.G.; Snell, J.L.; Knapp, A.W. Denumerable Markov Chains, 2nd Ed.; Springer-Verlag: New York, 1976.
7. Kijima, M. Quasi-stationary distributions of single-server phase-type queues. Math. Oper. Res. 1993, 18 (2), 423-437.
8. Kijima, M. Markov Processes for Stochastic Modeling; Chapman & Hall: London, 1997.
9. Kijima, M.; Makimoto, N. Quasi-stationary distributions of Markov chains arising from queueing processes. In Applied Probability and Stochastic Processes; Shanthikummar, J.G., Sumita, U., Kluwer Academic Publishers: Boston, 1999; 277-311.
10. Latouche, G.; Pearce, C.E.M.; Taylor, P.G. Invariant measures for quasi-birth-and-death processes. Stoc. Models 1998, 14 (1&2), 443-460.
11. Latouche, G.; Ramaswami, V. Introduction to Matrix Analytic Methods in Stochastic Modeling; SIAM: Philadelphia, 1999.
12. Li, Q.L. Stochastic Integral Functionals and Quasi-Stationary Distributions in Stochastic Models. Ph.D. Thesis, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China, 1997.
13. Li, Q.L.; Zhao, Y.Q. A constructive method for finding β-invariant measures for transition matrices of M/G/1 type. In Matrix-Analytic Methods Theory and Applications; Latouche, G., Taylor, P.G., World Scientific: New Jersey, 2002; 237-263.
14. Li, Q.L.; Zhao, Y.Q. Light-tailed Asymptotics of Stationary Probability Vectors of Markov Chains of GI/G/1 Type; Technical Report No 365, Laboratory for Research in Statistics and Probability, Carleton University and University of Ottawa, 2002.
15. Makimoto, N. Quasi-stationary distributions in a PH/PH/c queue. Stoc. Models 1993, 9 (2), 195-212.
16. Neuts, M.F. Matrix-Geometric Solutions in Stochastic Models-An Algorithmic Approach; The Johns Hopkins University Press: Baltimore, 1981.
17. Neuts, M.F. Structured Stochastic Matrices of M/G/1 Type and Their Applications; Marcel Decker Inc.: New York, 1989.
18. Ramaswami, V. A stable recursive solution for the steady-state vector in Markov chains of M/G/1 type. Stoc. Models 1988, 4 (1), 183-188.
19. Seneta, E. Non-Negative Matrices and Markov Chains; Springer-Verlag: New York, 1980.
20. Zhao, Y.Q. Censoring technique in studying block-structured Markov chains. In Advances in Algorithmic Methods for Stochastic Models; Latouche, G., Taylor, P.G., Notable Publications Inc.: New Jersey, 2000; 417-433.
21. Zhao, Y.Q.; Li, W.; Braun, W.J. Censoring, Factorization, and Spectral Analysis for Transition Matrices with Block-Repeating Entries; Technical Report No. 355, Laboratory for Research in Statistics and Probability, Carleton University and University of Ottawa, 2001.