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Stability for fluid queues: Characteristic inequalities

par Govorun, Maria ;Latouche, Guy ;Remiche, Marie-Ange
Référence Stochastic models, 29, 1, page (64-88)
Publication Publié, 2013-02

Article révisé par les pairs

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Résumé :

We explore the conditions under which a fluid queue is positive recurrent, null recurrent, or transient. We consider the simple system where fluid rates are independent of the level, and exploit the similarity found by Ramaswami between fluid queues and Quasi-Birth-and-Death (QBD) processes. Inspired by the Wiener-Hopf factorization obtained by Rogers for a key matrix, and by an earlier work by Latouche and Taylor on drift conditions for QBDs, we determine in this note two pairs of eigenvectors which combine to give four characteristic inequalities. This is illustrated on a simple example. © 2013 Taylor & Francis Group, LLC.