A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains

Linear Algebra and Its Applications

Volumn 266, Issue 1-3, 1997, Pages 219-241

  Bai, Zhong Zhi ^a  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944447710     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)86522-6     Document Type: Article

References (19)

1. N. Akar and K. Sohraby, A new paradigm in teletraffic analysis of communication networks, in INFOCOM, 1996, pp. 1318-1326.
2. D. Bini and B. Meini, On the solution of a nonlinear matrix equation in queueing problems, SIAM J. Matrix Anal. Appl., submitted for publication.
3. D. Bini and B. Meini, On cyclic reduction applied to a class of Toeplitz-like matrices arising in queueing problems, in Proceedings of the 2nd International Workshop on Numerical Solutions of Markov Chains, Raleigh, N.C., 1995, pp. 21-38.
4. O. H. Hald, On a Newton-Moser type method, Numer. Math. 23:411-426 (1975).
5. G. Latouche, Newton's iteration for non-linear equations in Markov chains, IMA J. Numer. Anal. 14:583-598 (1994).
6. M. F. Neuts, Moment formulas for the Markov renewal branching process, Adv. Appl. Probab. 8:690-711 (1976).
7. M. F. Neuts, Markov chains with applications in queueing theory, which have a matrix-geometric invariant vector, Adv. Appl. Probab. 10:185-212 (1978).
8. M. F. Neuts, The M/M/1 queue with randomly varying rates, Opsearch 15:139-157 (1978).
9. M. F. Neuts, Further results on the M/M/1 queue with randomly varying rates, Opsearch 15:158-168 (1978).
10. M. F. Neuts, Queues solvable without Rouche's theorem, Oper. Res. 27:767-781 (1979).
11. M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models - An Algorithmic Approach, Johns Hopkins U.P., Baltimore, 1981.
12. M. F. Neuts, Matrix-analytic methods in queueing theory, European J. Oper. Res. 15:2-12 (1984).
13. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic, New York, 1970.
14. V. Ramaswami, Nonlinear matrix equations in applied probability - solution-techniques and open problems, SIAM Rev. 30:256-263 (1988).
15. V. Ramaswami, The N/G/1 queue and its detailed analysis, Adv. Appl. Probab. 12:226-261 (1980).
16. V. Ramaswami, The busy period of queues which have a matrix-geometric steady-state probability vector, Opsearch 19:238-261 (1982).
17. V. Ramaswami, Stable recursion for the steady state vector for Markov chains of M/G/1 type, Comm. Statist. Stochastic Models 4:183-188 (1988).
18. V. Ramaswami, A duality theorem for the matrix paradigms in queueing theory, Comm. Statist. Stochastic Models 6:151-161 (1991).
19. V. Ramaswami and G. Latouche, An experimental evaluation of the matrix-geometric method for the GI/PH/1 queue, Comm. Statist. Stochastic Models 5:629-667 (1989).