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

par Dendievel, Sarah ;Latouche, Guy ;Liu, Yuanyuan
Référence Performance evaluation, 70, 9, page (564-577)
Publication Publié, 2013

Article révisé par les pairs

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Résumé :

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. © 2013 Elsevier B.V. All rights reserved.