Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-14T05:22:19.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Transient solutions for denumerable-state Markov processes

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Guang-Hui Hsu  and
Xue-Ming Yuan
Guang-Hui Hsu
Affiliation:
Institute of Applied Mathematics, Chinese Academy of Sciences
Xue-Ming Yuan*
Affiliation:
Institute of Applied Mathematics, Chinese Academy of Sciences
*
∗ Postal address for both authors: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China.
Get access Rights & Permissions [Opens in a new window]

Abstract

The algorithm for the transient solution for the denumerable state Markov process with an arbitrary initial distribution is given in this paper. The transient queue length distribution for a general Markovian queueing system can be obtained by this algorithm. As examples, some numerical results are presented.

Keywords

UNIFORMIZATION TECHNIQUEMARKOVIAN QUEUEING SYSTEMTRANSIENT QUEUE LENGTH

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 635 - 645
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Supported by the National Natural Science Foundation of China.

References

Anderson, W. J. (1991) Continuous-Time Markov Chain. Springer-Verlag, New York.CrossRefGoogle Scholar
Cinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Grassmann, W. K. (1977) Transient solutions in Markovian queueing systems. Comput. Operat. Res. 4, 47–53.Google Scholar
Grassmann, W. K. (1977) Transient solutions in Markovian queues. Eur. J. Operat. Res. 1, 396–402.Google Scholar
Grassmann, W. K. (1990) Computational methods in probability theory. In Handbooks in Operations Research and Management Science, Vol. 2, Stochastic Models, ed. Heyman, D. P. and Sobel, M. J., pp. 199–254. North-Holland, Amsterdam.Google Scholar
Gross, D. and Miller, D. R. (1984) The randomization technique as a modelling tool and solution procedure for transient Markov processes. Operat. Res. 32, 343–361.CrossRefGoogle Scholar
Kohlas, J. (1982) Stochastic Methods of Operations Research. Cambridge University Press.Google Scholar
Reibman, A. and Trivedi, K. (1988) Numerical transient analysis of Markov models. Comput. Operat. Res. 15, 19–36.Google Scholar
Zhang, J. and Coyle, E. J. (1989) Transient analysis of quasi-birth-death processes. Stoch. Models. 5, 459–496.CrossRefGoogle Scholar