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The classification of matrix GI/M/1-type Markov chains with a tree structure and its applications to queueing

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Qi-Ming He
Qi-Ming He*
Affiliation:
Dalhousie University
*
∗Postal address: Department of Industrial Engineering, Dalhousie University, Halifax, Nova Scotia B3J 2X4, Canada. Email address: qi-ming.he@dal.ca
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Abstract

In this paper, we study the classification of matrix GI/M/1-type Markov chains with a tree structure. We show that the Perron–Frobenius eigenvalue of a Jacobian matrix provides information for classifying these Markov chains. A fixed-point approach is utilized. A queueing application is presented to show the usefulness of the classification method developed in this paper.

Keywords

Markov chaintree structurematrix-analytic methodsfixed-point theoryGI/M/1-type Markov chainqueueing theory

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1087 - 1102
Copyright
Copyright © Applied Probability Trust 2003 

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