Necessary and sufficient conditions for strong comparability of multicomponent systems

• Published in: Discrete event dynamic systems Vol. 24; no. 1; pp. 1 - 14
• Main Authors: Delgado, Rosario, López, F. Javier, Sanz, Gerardo
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.03.2014
• Subjects: Control; Convex and Discrete Geometry; Dynamical systems; Dynamics; Electrical Engineering; Machines; Manufacturing; Mathematical analysis; Mathematics; Mathematics and Statistics; Networks; Operations Research/Decision Theory; Processes; Queues; Stations; Stochasticity; Systems Theory; Tasks; Stochastic comparison; Continuous-time Markov chains; Queueing networks
• ISSN: 0924-6703; 1573-7594
• DOI: 10.1007/s10626-012-0146-y

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 ).