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DEPENDENCE ORDERING FOR QUEUING NETWORKS WITH BREAKDOWN AND REPAIR

Published online by Cambridge University Press:  19 September 2006

Hans Daduna ,
Rafał Kulik ,
Cornelia Sauer  and
Ryszard Szekli
Hans Daduna
Affiliation:
Department of Mathematics, Hamburg University, 20146 Hamburg, Germany, E-mail: fm3a002@math.uni-hamburg.de
Rafał Kulik
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW.2006, Australia, E-mail: rkuli@maths.usyd.edu.au, and, Mathematical Institute, Wrocław University, 50-384 Wrocław, Poland
Cornelia Sauer
Affiliation:
Department of Mathematics, Hamburg University, 20146 Hamburg, Germany, E-mail: fmcv007@math.uni-hamburg.de
Ryszard Szekli
Affiliation:
Mathematical Institute, Wrocław University, 50-384 Wrocław, Poland, E-mail: szekli@math.uni.wroc.pl
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Abstract

In this article we introduce isotone differences stochastic ordering of Markov processes on lattice ordered state spaces as a device to compare the internal dependencies of two such processes. We derive a characterization in terms of intensity matrices. This enables us to compare the internal dependency structure of different degradable Jackson networks in which the nodes are subject to random breakdowns and repairs. We show that the performance behavior and the availability of such networks can be compared.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 4 , October 2006 , pp. 575 - 594
Copyright
© 2006 Cambridge University Press

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References

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