The Annals of Applied Probability

The quasi-stationary behavior of quasi-birth-and-death processes

N. G. Bean, L. Bright, G. Latouche, C. E. M. Pearce, P. K. Pollett, and P. G. Taylor

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For evanescent Markov processes with a single transient communicating class, it is often of interest to examine the limiting probabilities that the process resides in the various transient states, conditional on absorption not having taken place. Such distributions are known as quasi-stationary (or limiting-conditional) distributions. In this paper we consider the determination of the quasi-stationary distribution of a general level-independent quasi-birth-and-death process (QBD). This distribution is shown to have a form analogous to the matrix-geometric form possessed by the stationary distribution of a positive recurrent QBD. We provide an algorithm for the explicit computation of the quasi-stationary distribution.

Article information

Ann. Appl. Probab., Volume 7, Number 1 (1997), 134-155.

First available in Project Euclid: 14 October 2002

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Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]

Quasi-birth-and-death process quasi-stationary distribution limiting-conditional distribution


Bean, N. G.; Bright, L.; Latouche, G.; Pearce, C. E. M.; Pollett, P. K.; Taylor, P. G. The quasi-stationary behavior of quasi-birth-and-death processes. Ann. Appl. Probab. 7 (1997), no. 1, 134--155. doi:10.1214/aoap/1034625256.

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