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Computing the invariant law of a fluid model

Part of:Markov processesSpecial processes

Published online by Cambridge University Press:  14 July 2016

L. C. G. Rogers and
Z. Shi
L. C. G. Rogers*
Affiliation:
Queen Mary and Westfield College, University of London
Z. Shi*
Affiliation:
Queen Mary and Westfield College, University of London
*
∗ Present address: School of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK.
∗∗ Present address: L.S.T.A. Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France. Research supported by SERC grant number GR/H 00444.
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Abstract

In this paper, we discuss a variety of methods for computing the Wiener-Hopf factorization of a finite Markov chain associated to a fluctuating additive functional. The importance of this is that the equilibrium law of a fluid model can be expressed in terms of these Wiener–Hopf factors. The diagonalization methods considered are actually quite efficient, and provide an effective solution to the problem.

Keywords

MARKOV CHAINWIENER–HOPF FACTORIZATIONNOISY WIENER–HOPF PROBLEM

MSC classification

Primary:60J27: Continuous-time Markov processes on discrete state spaces
Secondary:60K15: Markov renewal processes, semi-Markov processes60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)60K25: Queueing theory

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994, pp. 885 - 896
Copyright
Copyright © Applied Probability Trust 1994 

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