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March 2013 Computing stationary expectations in level-dependent QBD processes
Hendrik Baumann, Werner Sandmann
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J. Appl. Probab. 50(1): 151-165 (March 2013). DOI: 10.1239/jap/1363784430

Abstract

Stationary expectations corresponding to long-run averages of additive functionals on level-dependent quasi-birth-and-death processes are considered. Special cases include long-run average costs or rewards, moments and cumulants of steady-state queueing network performance measures, and many others. We provide a matrix-analytic scheme for numerically computing such stationary expectations without explicitly computing the stationary distribution of the process, which yields an algorithm that is as quick as its counterparts for stationary distributions but requires far less computer storage. Specific problems arising in the case of infinite state spaces are discussed and the application of the algorithm is demonstrated by a queueing network example.

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Hendrik Baumann. Werner Sandmann. "Computing stationary expectations in level-dependent QBD processes." J. Appl. Probab. 50 (1) 151 - 165, March 2013. https://doi.org/10.1239/jap/1363784430

Information

Published: March 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1273.60089
MathSciNet: MR3076778
Digital Object Identifier: 10.1239/jap/1363784430

Subjects:
Primary: 60J22
Secondary: 60J27, 60J28

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 1 • March 2013
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