Necessary and sufficient conditions for the stochastic comparison of Jackson networks

Necessary and sufficient conditions for the stochastic comparison of Jackson networks

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Article ID: iaor2005362
Country: United Kingdom
Volume: 17
Issue: 1
Start Page Number: 143
End Page Number: 151
Publication Date: Jan 2003
Journal: Probability in the Engineering and Informational Sciences
Authors:
Keywords: markov processes
Abstract:

External and internal monotonicity properties for Jackson networks have been established in the literature with the use of coupling constructions. Recently, Lopez et al. derived necessary and sufficient conditions for the (strong) stochastic comparison of two-station Jackson networks with increasing service rates, by constructing a certain Markovian coupling. In this article, we state necessary and sufficient conditions for the stochastic comparison of L-station Jackson networks in the general case. The proof is based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

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