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A stochastic lower bound for assemble-transfer batch service queueing networks

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Antonis Economou
Antonis Economou*
Affiliation:
University of Athens
*
∗Postal address: 26 Papadiamandopoulou st., Athens 11528, Greece. Email address: aeconom@internet.gr
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Abstract

Miyazawa and Taylor (1997) introduced a class of assemble-transfer batch service queueing networks which do not have tractable stationary distribution. However by assuming a certain additional arrival process at each node when it is empty, they obtain a geometric product-form stationary distribution which is a stochastic upper bound for the stationary distribution of the original network. In this paper we develop a stochastic lower bound for the original network by introducing an additional departure process at each node which tends to remove all the customers present in it. This model in combination with the aforementioned upper bound model gives a better sense for the properties of the original network.

Keywords

Queueing networkbatch arrivalbatch serviceassemble-transferconcurrent movementproduct-formpartial balancegeometric distributionstochastic order

MSC classification

Primary: 60K25: Queueing theory 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 881 - 889
Copyright
Copyright © Applied Probability Trust 2000 

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