Journal of Applied Probability

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

Allan J. Motyer and Peter G. Taylor

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 48A (2011), 327-339.

Dates
First available in Project Euclid: 18 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1318940475

Digital Object Identifier
doi:10.1239/jap/1318940475

Mathematical Reviews number (MathSciNet)
MR2865636

Zentralblatt MATH identifier
1231.60099

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]

Keywords
Quasi-birth-and-death process countable phase decay rate stationary distribution

Citation

Motyer, Allan J.; Taylor, Peter G. Decay rates for some quasi-birth-and-death processes with phase-dependent transition rates. J. Appl. Probab. 48A (2011), 327--339. doi:10.1239/jap/1318940475. https://projecteuclid.org/euclid.jap/1318940475


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