The Annals of Applied Probability

Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains

L. C. G. Rogers

Full-text: Open access

Abstract

This paper applies the earlier work of Barlow, Rogers and Williams on the Wiener-Hopf factorization of finite Markov chains to a number of questions in the theory of fluid models of queues. Specifically, the invariant distribution for an infinite-buffer model and for a finite-buffer model are derived. The laws of other functionals of the fluid models can be easily derived and compactly expressed in terms of the fundamental Wiener-Hopf factorization.

Article information

Source
Ann. Appl. Probab., Volume 4, Number 2 (1994), 390-413.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005065

Digital Object Identifier
doi:10.1214/aoap/1177005065

Mathematical Reviews number (MathSciNet)
MR1272732

Zentralblatt MATH identifier
0806.60052

JSTOR
links.jstor.org

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 60K15: Markov renewal processes, semi-Markov processes

Keywords
Markov chain fluid model Wiener-Hopf factorization invariant distribution noisy Wiener-Hopf

Citation

Rogers, L. C. G. Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains. Ann. Appl. Probab. 4 (1994), no. 2, 390--413. doi:10.1214/aoap/1177005065. https://projecteuclid.org/euclid.aoap/1177005065


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