General theory on spectral properties of state-homogeneous finite-state quasi-birth-death processes

European Journal of Operational Research

Volumn 128, Issue 2, 2001, Pages 402-417

  Fadiloglu, Mehmet Murat ^a   Yeralan, Sencer ^b  

^a BILKENT UNIVERSITY   (Turkey)

^b Rigel Corporation   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; POLYNOMIALS; PROBABILITY DISTRIBUTIONS; QUEUEING THEORY; THEOREM PROVING;

JORDAN CANONICAL FORMS; QUASI-BIRTH-DEATH PROCESSES;

OPERATIONS RESEARCH;

EID: 0035157296     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(99)00367-7     Document Type: Article

References (13)

1. Dallery Y., Gershwin S.B. Manufacturing flow line systems: A review of models and analytical results. Queuing Systems. 12(3):1992;3-94.
2. Evans R.V. Geometric distribution in some two-dimensional queuing systems. Operations Research. 15:1967;830-846.
3. M.M. Fadiloglu, S. Yeralan, Models of production lines as quasi-birth-death processes, Mathematical and Computer Modelling, to appear.
4. Gohberg I., Lancester P., Rodman L. Matrix Polynomials. 1982;Academic Press, New York.
5. Hajek B. Birth-and-death processes on integers with phases and general boundaries. Journal of Applied Probability. 19:1982;488-499.
6. Latouche G., Ramaswami V. A logarithmic reduction algorithm for quasi-birth-death processes. Journal of Applied Probability. 30:1993;650-674.
7. Mitrani I., Chakka R. Spectral expansion for a class of Markov models: Application and comparison with the matrix-geometric method. Performance Evaluation. 23:1995;241-260.
8. Neuts M.F. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. 1981;Johns Hopkins University Press, Baltimore, MD.
9. B. Tan, A decomposition method for multistation production systems, Ph.D. Dissertation, Industrial and Systems Engineering, University of Florida, Gainesville, 1994.
10. V. Wallace, The solution of quasi birth and death processes arising from multiple, Ph.D. Thesis, Systems Engineering Laboratory, University of Michigan, Ann Arbor, 1969.
11. Ye J., Li S. Folding algorithm: A computational reduction algorithm for QBD processes with level-dependent transitions. IEEE Transactions on Communications. 42:1994;625-639.
12. Yeralan S., Muth E.J. A general model of a production line with intermediate buffer and station breakdown. IIE Transactions. 19(2):1987;130-139.
13. Yeralan S., Tan B. Analysis of multistation production systems with limited buffer capacity part 1: The subsystem model. Mathematical and Computer Modelling. 25(7):1997;109-122.