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Drift Conditions for Matrix-Analytic Models

Université Libre de Bruxelles, Département d'Informatique, CP 212, Boulevard du Triomphe, 1050 Bruxelles, Belgium
Department of Mathematics and Statistics, University of Melbourne, Melbourne, VIC 3010, Australia
guy.latouche{at}ulb.ac.be
p.taylor{at}ms.unimelb.edu.au

In his seminal work, Neuts gave drift criteria by which one can determine whether processes of GI/M/1 or M/G/1 type are positive recurrent. Recently, a different drift condition to determine the ergodic character of a quasi-birth-and-death process (QBD) appeared in the literature, although its justification does not seem to have been formally established.

In this paper, we provide a proof for this new drift condition in a general context. We also give a simple proof for Neuts@ original condition and establish a number of new drift conditions for the ergodic character of matrix-analytic models.

Key Words: Matrix-analytic models; quasi-birth-and-death processes; ergodicity condition; paradoxical games
History: Received: June 23, 2000; revision received: August 13, 2002;revision received: August 27, 2002;