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).
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Acknowledgements
The authors are grateful to the anonymous referees for their careful reading and useful suggestions which resulted in an improvement of the paper.
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R. Delgado is partially supported by: project ref. MTM2009-08869 of MICINN and FEDER.
F. J. López and G. Sanz are partially supported by: project ref. MTM2010-15972 of MICINN and FEDER.
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Delgado, R., López, F.J. & Sanz, G. Necessary and sufficient conditions for strong comparability of multicomponent systems. Discrete Event Dyn Syst 24, 1–14 (2014). https://doi.org/10.1007/s10626-012-0146-y
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DOI: https://doi.org/10.1007/s10626-012-0146-y