Markov chain representations of discrete distributions applied to queueing models

Computers and Operations Research

Volumn 31, Issue 14, 2004, Pages 2365-2385

  Alfa, Attahiru Sule ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Discrete distributions; Markov chain; Phase type distributions; Queueing models; Time reversibility

Indexed keywords

ALGORITHMS; DATA TRANSFER; MARKOV PROCESSES; MATHEMATICAL MODELS; MATRIX ALGEBRA; SERVERS;

DISCRETE DISTRIBUTIONS; PHASE TYPE DISTRIBUTIONS; QUEUEING MODELS; TIME REVERSIBILITY;

QUEUEING THEORY;

EID: 2342655445     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0305-0548(03)00192-8     Document Type: Article

References (14)

1. Yang T., Chaudhry M.L. On the steady-state queue size distribution of the discrete-time GI/G/1 queue. Advances in Applied Probability. 28:1996;1177-1200.
2. Latouche G, Ramaswami V. Introduction to matrix analytic methods in stochastic modeling. ASA-SIAM Series on Applied Probability, Philadelphia: SIAM, 1999.
3. Neuts M.F. Matrix-geometric solutions in stochastic models: an algorithmic approach. 1981;Johns Hopkins University Press, Baltimore, MD.
4. Neuts M.F. Structured stochastic matrices of the M/G/1 type and their applications. 1989;Marcel Dekker, New York.
5. Neuts MF. Probability distributions of phase type. Liber Amicorum Prof. Emeritus H. Florin. Department of Mathematics, University of Louvain, Belgium, 1975. p. 173-206.
6. Alfa A.S., Neuts M.F. Modelling vehicular traffic using the discrete time Markovian arrival process. Transportation Science. 29(2):1995;109-117.
7. Shi D.H., Guo J., Liu L. SPH-distributions and the rectangle-iterative algorithm. Chakravarthy S., Alfa A.S. Matrix-analytic methods in stochastic models. 1996;207-224 Marcel Dekker, New York.
8. Shi D., Liu D. Markovian models for non-negative random variables. Alfa A.S., Chakravarthy S. Advances in matrix analytic methods for stochastic models. 1998;403-427 Notable Publishers, New Jersey.
9. Ramaswami V. A duality theorem for the matrix paradigms in queueing theory. Stochastic Models. 6:1990;151-161.
10. Graham A. Kronecker products and matrix calculus: with applications. 1981;Ellis Horwood Ltd. Chichester.
11. Tweedie R.L. Operator-geometric stationary distributions for Markov chains, with applications to queueing models. Advances in Applied Probability. 12(2):1982;368-391.
12. Zhao Y.Q., Li W., Alfa A.S. Duality results for block-structured transition matrices. Journal of Applied Probability. 36:1999;1045-1057.
13. Alfa A.S., Li W. Matrix-geometric method for the discrete time GI/G/1 system. Stochastic Models. 17(4):2001;541-554.
14. X/G/1 systems. Queueing Systems - Theory and Application, 2003, accepted for publication.