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The classification of matrix GI/M/1-type Markov chains with a tree structure and its applications to queueing
- Source :
- Journal of Applied Probability. 40:1087-1102
- Publication Year :
- 2003
- Publisher :
- Cambridge University Press (CUP), 2003.
-
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.
- Subjects :
- Statistics and Probability
Discrete mathematics
Queueing theory
Markov chain
General Mathematics
Variable-order Markov model
010102 general mathematics
01 natural sciences
Continuous-time Markov chain
010104 statistics & probability
symbols.namesake
Tree structure
Matrix analytic method
Jacobian matrix and determinant
symbols
Examples of Markov chains
0101 mathematics
Statistics, Probability and Uncertainty
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....9cc2333f6f88bad411762f76cd81a281