Classification of Markov processes of M/G/1 type with a tree structure and its applications to queueing models

Operations Research Letters

Volumn 26, Issue 2, 2000, Pages 67-80

  He, Qi Ming ^a  

^a DALHOUSIE UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILITY; QUEUEING THEORY; THEOREM PROVING; TREES (MATHEMATICS);

LYAPUNOV FUNCTION; MEAN DRIFT METHOD; NULL RECURRENCE; POSITIVE RECURRENCE; TRANSIENCE; TREE STRUCTURE;

MARKOV PROCESSES;

EID: 0033891805     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(99)00057-7     Document Type: Article

References (17)

1. G. Fayolle, V.A. Malyshev, M.V. Menshikov, Topics in the Constructive Theory of Countable Markov Chains, Cambridge University Press, Cambridge, 1995.
2. Gajrat A.S., Malyshev V.A., Menshikov M.V., Pelih K.D. Classification of Markov chains describing the evolution of a string of characters. Uspehi Matematicheskih Nauk. 50(2):1995;5-24.
3. F.R. Gantmacher, The Theory of Matrices, Chelsea, New York, 1959.
4. He Q.-M. Queues with marked customers. Adv. Appl. Proab. 28:1996;567-587.
5. Q.-M. He, Classification of Markov processes of matrix M/G/1 type with a tree structure and its applications to queueing models, submitted for publication.
6. Q.-M. He, A.S. Alfa, The MMAP[K]/PH[K]/1 queues with a last-come-first-served preemptive service discipline, Queueing Systems 29 (1998) 269-291.
7. He Q.-M., Neuts M.F. Markov arrival processes with marked transitions. Stochastic Process Appl. 74/1:1998;37-52.
8. J.G. Kemeny, J.L. Snell, A.W. Knapp, Denumerable Markov Chains, D. Van Nostrand Company, Inc., Princeton, NJ, 1966.
9. Kumar P.R., Meyn S.P. Duality and linear programs for stability and performance analysis of queueing networks and scheduling policies. IEEE Trans. Automat. Control. 41(1):1996;4-17.
10. Malyshev V.A. Interacting strings of symbols. Russian Math. Surveys. 52(2):1997;59-86.
11. V.A. Malyshev, Stochastic evolution via graph grammars, INRIA Research Report # 3380, 1998.
12. S.P. Meyn, R. Tweedie, Markov Chains and Stochastic Stability, Springer, Berlin, 1993.
13. Neuts M.F. A versatile Markovian point process. J. Appl. Probab. 16:1979;764-779.
14. M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An algorithmic Approach, The Johns Hopkins University Press, Baltimore, 1981.
15. M.F. Neuts, Structured Stochastic Matrices of M/G/1 type and Their Applications, Marcel Dekker, New York, 1989.
16. Takine T., Sengupta B., Yeung R.W. A generalization of the matrix M/G/1 paradigm for Markov chains with a tree structure. Stochastic Models. 11:1995;411-421.
17. Yeung R.W., Sengupta B. Matrix product-form solutions for Markov chains with a tree structure. Adv. Appl. Probab. 26(4):1994;965-987.