Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T10:56:39.282Z Has data issue: false hasContentIssue false
  • English
  • Français

On the quasi-stationary distribution for queueing networks with defective routing

Published online by Cambridge University Press:  17 February 2009

Richard J. Boucherie
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note introduces quasi-local-balance for discrete-time Markov chains with absorbing states. From quasi-local-balance product-form quasi-stationary distributions are derived by analogy with product-form stationary distributions for Markov chains that satisfy local balance.

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 4 , April 1997 , pp. 454 - 463
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Boucherie, R. J. and van Dijk, N. M., “Product-forms for queueing networks with state dependent multiple job transitions”, Adv. Appl. Prob. 23 (1991) 152–187.CrossRefGoogle Scholar
[2]Darroch, J. N. and Seneta, E., “On quasi-stationary distributions in absorbing discrete-time finite Markov chains”, J. Appl. Prob. 2 (1965) 88–100.CrossRefGoogle Scholar
[3]Darroch, J. N. and Seneta, E., “On quasi-stationary distributions in absorbing continuous-time finite Markov chains”, J. Appl. Prob. 4 (1967) 192–196.CrossRefGoogle Scholar
[4]Henderson, W. and Taylor, P. G., “Product-forms in networks of queues with batch arrival and batch services”, Queueing Systems 6 (1990) 71–88.CrossRefGoogle Scholar
[5]Kesten, H., “A ratio limit theorem for (sub) Markov chains on {1, 2,…} with bounded jumps”, Adv. Appl. Prob. 27 (1995) 652–691.CrossRefGoogle Scholar
[6]Seneta, E., Non-negative matrices and Markov chains (Springer-Verlag, New-York, 1981).CrossRefGoogle Scholar
[7]Seneta, E. and Vere-Jones, D., “On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states”, J. Appl. Prob. 3 (1966) 403–434.CrossRefGoogle Scholar
[8]Vere-Jones, D., “Geometric ergodicity in denumerable Markov chains”, Quart. J. Math. Oxford 13 (1962) 7–28.CrossRefGoogle Scholar