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On the stochastic domination for batch-arrival, batch-service and assemble-transfer queueing networks

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Antonis Economou
Antonis Economou*
Affiliation:
University of Athens
*
∗Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, Athens 15784, Greece. Email address: aeconom@math.uoa.gr
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Abstract

Stochastic monotonicity properties for various classes of queueing networks have been established in the literature mainly with the use of coupling constructions. Miyazawa and Taylor (1997) introduced a class of batch-arrival, batch-service and assemble-transfer queueing networks which can be thought of as generalized Jackson networks with batch movements. We study conditions for stochastic domination within this class of networks. The proofs are based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

Keywords

Queueing networkstochastic orderbatch arrivalbatch serviceassemble transfer

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1103 - 1120
Copyright
Copyright © Applied Probability Trust 2003 

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