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NECESSARY AND SUFFICIENT CONDITIONS FOR THE STOCHASTIC COMPARISON OF JACKSON NETWORKS

Published online by Cambridge University Press:  07 January 2003

Antonis Economou
Antonis Economou
Affiliation:
Department of Mathematics, University of Athens, Panepistemiopolis, Athens 15784, Greece, E-mail: [email protected]
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 17 , Issue 1 , January 2003 , pp. 143 - 151
Copyright
© 2003 Cambridge University Press

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