Necessary and sufficient conditions for strong comparability of multicomponent systems

Rosario Delgado, F. Javier López, Gerardo Sanz

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this article we analyze the stochastic comparison of continuous time Markov chains with state space E = {0,1,2,.} N used as models for N -component systems. Although the conditions for comparability of such processes are known in the theory, they involve a huge family of sets which makes their checking a difficult task. We show how, under some assumptions on the transitions allowed in the chains, the conditions can be greatly simplified, writing them in terms of conditions for each component. As an application we give the necessary and sufficient conditions for the stochastic comparability of two batch-arrival assemble-transfer queueing networks in terms of conditions for their single stations, improving previous results on the subject (Economou, J Appl Probab 40:1103-1120, 2003b). We also analyze a finite site version of interacting particle systems studied in Borrello (Electron J Probab 16:106-151, 2011). © 2012 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)1-14
JournalDiscrete Event Dynamic Systems: Theory and Applications
Volume24
DOIs
Publication statusPublished - 1 Mar 2014

Keywords

  • Continuous-time Markov chains
  • Queueing networks
  • Stochastic comparison

Fingerprint Dive into the research topics of 'Necessary and sufficient conditions for strong comparability of multicomponent systems'. Together they form a unique fingerprint.

  • Cite this