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

  • Richard J. Boucherie

Abstract

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.

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References

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[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) 152187.
[2]Darroch, J. N. and Seneta, E., “On quasi-stationary distributions in absorbing discrete-time finite Markov chains”, J. Appl. Prob. 2 (1965) 88100.
[3]Darroch, J. N. and Seneta, E., “On quasi-stationary distributions in absorbing continuous-time finite Markov chains”, J. Appl. Prob. 4 (1967) 192196.
[4]Henderson, W. and Taylor, P. G., “Product-forms in networks of queues with batch arrival and batch services”, Queueing Systems 6 (1990) 7188.
[5]Kesten, H., “A ratio limit theorem for (sub) Markov chains on {1, 2,…} with bounded jumps”, Adv. Appl. Prob. 27 (1995) 652691.
[6]Seneta, E., Non-negative matrices and Markov chains (Springer-Verlag, New-York, 1981).
[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) 403434.
[8]Vere-Jones, D., “Geometric ergodicity in denumerable Markov chains”, Quart. J. Math. Oxford 13 (1962) 728.
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On the quasi-stationary distribution for queueing networks with defective routing

  • Richard J. Boucherie

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