Poisson's equation for discrete-time quasi-birth-and-death processes

Authors:
Sarah Dendievel;Guy Latouche;Yuanyuan Liu
Affiliations:
-;-;-
Venue:
Performance Evaluation
Year:
2013

Citing 5
Cited 0

Drift conditions for matrix-analytic models

Mathematics of Operations Research
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Probability in the Engineering and Informational Sciences
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Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Markov Chains and Stochastic Stability

Markov Chains and Stochastic Stability
Level-phase independent stationary distributions for GI/M/1-type Markov chains with infinitely-many phases

Performance Evaluation

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Abstract

We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to lower levels, and the other is based on a recursive expression for the deviation matrix. We revisit the link between a solution of Poisson's equation and perturbation analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue as an illustrative example, and we measure the sensitivity of the expected queue size to the initial value.