Advances in Applied Probability

Decay rates for quasi-birth-and-death processes with countably many phases and tridiagonal block generators

Allan J. Motyer and Peter G. Taylor

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Abstract

We consider the class of level-independent quasi-birth-and-death (QBD) processes that have countably many phases and generator matrices with tridiagonal blocks that are themselves tridiagonal and phase independent. We derive simple conditions for possible decay rates of the stationary distribution of the `level' process. It may be possible to obtain decay rates satisfying these conditions by varying only the transition structure at level 0. Our results generalize those of Kroese, Scheinhardt, and Taylor, who studied in detail a particular example, the tandem Jackson network, from the class of QBD processes studied here. The conditions derived here are applied to three practical examples.

Article information

Source
Adv. in Appl. Probab. Volume 38, Number 2 (2006), 522-544.

Dates
First available: 26 June 2006

Permanent link to this document
http://projecteuclid.org/euclid.aap/1151337083

Digital Object Identifier
doi:10.1239/aap/1151337083

Mathematical Reviews number (MathSciNet)
MR2264956

Zentralblatt MATH identifier
1101.60073

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Keywords
Decay rate QBD process countable phase tridiagonal block generator stationary distribution two-node Jackson network

Citation

Motyer, Allan J.; Taylor, Peter G. Decay rates for quasi-birth-and-death processes with countably many phases and tridiagonal block generators. Advances in Applied Probability 38 (2006), no. 2, 522--544. doi:10.1239/aap/1151337083. http://projecteuclid.org/euclid.aap/1151337083.


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