Dependence Ordering For Queuing Networks With Breakdown And Repair

  • Authors:

  • Hans Daduna;Rafał Kulik;Cornelia Sauer;Ryszard Szekli

  • Affiliations:

  • Department of Mathematics, Hamburg University, 20146 Hamburg, Germany, E-mail: fm3a002@math.uni-hamburg.de;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,;, Department of Mathematics, Hamburg University, 20146 Hamburg, Germany, E-mail: fmcv007@math.uni-hamburg.de;Mathematical Institute, Wrocław University, 50-384 Wrocław, Poland, E-mail: szekli@math.uni.wroc.pl

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2006

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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.