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Decay rates for some quasi-birth-and-death processes with phase-dependent transition rates

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Allan J. Motyer  and
Peter G. Taylor
Allan J. Motyer
Affiliation:
University of Melbourne, Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia. Email address: a.motyer@ms.unimelb.edu.au
Peter G. Taylor
Affiliation:
University of Melbourne, Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia. Email address: p.taylor@ms.unimelb.edu.au
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Abstract

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Recently, there has been considerable interest in the calculation of decay rates for models that can be viewed as quasi-birth-and-death (QBD) processes with infinitely many phases. In this paper we make a contribution to this endeavour by considering some classes of models in which the transition function is not homogeneous in the phase direction. We characterize the range of decay rates that are compatible with the dynamics of the process away from the boundary. In many cases, these rates can be attained by changing the transition structure of the QBD process at level 0. Our approach, which relies on the use of orthogonal polynomials, is an extension of that in Motyer and Taylor (2006) for the case where the generator has homogeneous blocks.

Keywords

Quasi-birth-and-death processcountable phasedecay ratestationary distribution

MSC classification

Primary: 60K25: Queueing theory
Type
Part 7. Queueing Theory and Markov Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 327 - 339
Copyright
Copyright © Applied Probability Trust 2011 

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