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

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

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Article ID: iaor2004787
Country: United States
Volume: 37
Issue: 3
Start Page Number: 881
End Page Number: 889
Publication Date: Sep 2000
Journal: Journal of Applied Probability
Authors:
Keywords: networks: path
Abstract:

Miyazawa and Taylor 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.

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