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

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 14 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034625256

Digital Object Identifier
doi:10.1214/aoap/1034625256

Mathematical Reviews number (MathSciNet)
MR1428753

Zentralblatt MATH identifier
0883.60085

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1034625256


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