Page 193 - A First Course In Stochastic Models
P. 193
186 CONTINUOUS-TIME MARKOV CHAINS
Adan, I.J.B.F., Wessels, J. and Zijm, W.H.M. (1993) A compensation approach for two-
dimensional Markov processes. Adv. Appl. Prob., 25, 783–817.
Adan, I.J.B.F., De Kok, A.G. and Resing, J.A.C. (1999) A multi-server queueing model
with locking. Euro. J. Operat. Res., 116, 249–258.
Anderson, W.J. (1991) Continuous-Time Markov Chains: An Applications-Oriented
Approach. Springer-Verlag, Berlin.
Blanc, J.P.C. (1992) The power-series algorithm application to the shortest queue model.
Operat. Res., 40, 157–167.
Chung, K.L. (1967) Markov Chains with Stationary Transition Probabilities, 2nd edn.
Springer-Verlag, Berlin.
Daigle, J.N. (1991) Queueing Theory for Telecommunications. Addison-Wesley, Reading
MA.
De Soua e Silva, E. and Gail, H.R. (1986) Calculating cumulative operational time distri-
butions of repairable computer systems. IEEE Trans. Comput., 35, 322–332.
Goyal, A. and Tantawi, A.N. (1988) A measure of guaranteed availability and its numerical
evaluation. IEEE Trans. Comput., 37, 25–32.
Hermanns, H. (2001) Construction and verification of performance and reliability models.
Bull. EACTS, 74, 135–154.
Hooghiemstra, G., Keane, M. and Van de Ree, S. (1988) Power series for stationary distri-
bution of coupled processor models. SIAM J. Math. Appl., 48, 1159–1166.
Jensen, A. (1953) Markov chains as an aid in the study of Markoff process. Skand. Aktuar-
ietidskr., 36, 87–91.
Kamoun, F. and Kleinrock, L. (1980) Analysis of a shared finite storage in a computer
network node environment under general traffic conditions. IEEE Trans. Commun., 28,
992–1003.
Kosten, L. (1973) Stochastic Theory of Service Systems. Pergamon Press, London.
Latouche, G. and Ramaswami, V. (1993) A logarithmic reduction algorithm for quasi-birth-
death processes. J. Appl. Prob., 30, 650–674.
Lin, W. and Kumar, P. (1984) Optimal control of a queueing system with two heterogeneous
servers. IEEE Trans. Automat. Contr., 29, 696–703.
Mitrani, I. and Avi-Itzhak, B. (1968) A many-server queue with service interruptions. Operat.
Res., 16, 628–638.
Mitrani, I. and Mitra, D. (1992) A spectral expansion method for random walks on semi-
infinite strips. In Iterative Methods in Linear Algebra, edited by R. Beauwens and P.
Groen. North-Holland, Amsterdam.
Morse, P.M. (1955) Stochastic properties of waiting lines. Operat. Res., 3, 255–261.
Neuts, M. (1981) Matrix-Geometric Solutions in Stochastic Models. Johns Hopkins Univer-
sity Press, Baltimore MD.
Odoni, A.R. and Roth, E. (1983) An empirical investigation of the transient behaviour of
stationary queueing systems. Operat. Res., 31, 432–455.
Sericola, B. (2000) Occupation times in Markov processes. Stochastic Models, 16, 339–351.
Tak´ acs, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.
Tijms, H.C. and Veldman, R. (2000) A fast algorithm for the transient reward distribution
in continuous-time Markov chains. Operat. Res. Lett., 26, 155–158.