The Maclaurin series for performance functions of Markov chains

Advances in Applied Probability

Volumn 30, Issue 3, 1998, Pages 676-692

  Cao, Xi Ren ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Fundamental matrix; Perturbation analysis; Sample path estimation

Indexed keywords

EID: 0009843739     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800008545     Document Type: Article

References (17)

1. BENES, V. E. (1965). Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, New York.
2. BERMAN, A. AND PLEMMONS, R. J. (1994). Nonnegative Matrices in the Mathematical Sciences. SIAM, Philadelphia.
3. BLANC, J. P. C. (1990). A numerical approach to cyclic-server queueing models. Queueing Systems 6, 173-188.
4. BREIMAN, L. (1968). Probability. Addison-Wesley, Reading, MA.
5. CAO, X. R. AND CHEN, H. F. (1997). Potentials, perturbation realization, and sensitivity analysis of Markov processes. IEEE Trans. Automatic Control 42, 1382-1393.
6. ÇINLAR, E. (1975). Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ.
7. GIRISH, M. K. AND HU, J. Q. (1996). The departure process of the MAP/G/1 queue. Submitted.
8. GONG, W. B. AND HU, J. Q. (1992). The Maclaurin series for the GI/G/1 queue. J. Appl. Prob. 29, 176-184.
9. HO, Y. C. AND CAO, X. R. (1991). Perturbation Analysis of Discrete-Event Dynamic Systems. Kluwer, Boston.
10. HOOGHIEMSTRA, G., KEANE, M. AND VAN DE REE, S. (1988). Power series for stationary distribution of coupled processor systems. SIAM J. Appl. Math. 48, 1159-1166.
11. HU, J. Q., NANANUKUL, S. AND GONG, W. B. (1993). A new approach to (s, S) inventory systems. J. Appl. Prob. 30, 898-912.
12. KEMENY, J. G. AND SNELL, J. L. (1960). Finite Markov Chains. Van Nostrand, New York.
13. LASSERRE, L. B. (1991). Exact formula for sensitivity analysis of Markov chains. J. Optimization Theory Appl. 71, 407-413.
14. LASSERRE, L. B. (1994). A formula for singular pertubations of Markov chains. J. Appl. Prob 31, 829-833.
15. MEYER, C. D., JR. (1975). The role of the group generalized inverse in the theory of finite Markov chains. SIAM Rev. 17, 443-464.
16. PUTERMAN, M. L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York.
17. ZHU, Y. AND LI, H. (1993). The MacLaurin expansion for a G/G/1 queue with Markov-modulated arrivals and services. Questa 11, 125-134.