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The solution of certain two-dimensional Markov models

Published online by Cambridge University Press:  01 July 2016

G. Fayolle ,
P. J. B. King  and
I. Mitrani
G. Fayolle*
Affiliation:
INRIA
P. J. B. King*
Affiliation:
University of Newcastle upon Tyne
I. Mitrani*
Affiliation:
University of Newcastle upon Tyne
*
∗Postal address: INRIA, Domaine de Voluceau-Rocquencourt, B.P. 105–78150 Le Chesnay, France.
∗∗Postal address: Computing Laboratory, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 74U, U.K.
∗∗Postal address: Computing Laboratory, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 74U, U.K.
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Abstract

A class of two-dimensional birth-and-death processes, with applications in many modelling problems, is defined and analysed in the steady state. These are processes whose instantaneous transition rates are state-dependent in a restricted way. Generating functions for the steady-state distribution are obtained by solving a functional equation in two variables. That solution method lends itself readily to numerical implementation. Some aspects of the numerical solution are discussed, using a particular model as an example.

Keywords

ANALYTIC FUNCTIONBIRTH-AND-DEATH PROCESSGENERATING FUNCTIONRIEMANN-HILBERT PROBLEMSTATE DEPENDENCY
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 2 , June 1982 , pp. 295 - 308
Copyright
Copyright © Applied Probability Trust 1982 

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References

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