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Geometric product form queueing networks with concurrent batch movements

Part of: Operations research and management science Markov processes Special processes

Published online by Cambridge University Press:  01 July 2016

Hideaki Yamashita  and
Masakiyo Miyazawa
Hideaki Yamashita*
Affiliation:
Tohoku University
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: Faculty of Economics, Tohoku University, Kawauchi, Sendai 980-8576, Japan. Email address: hideaki@econ.tohoku.ac.jp
∗∗ Postal address: Department of Information Sciences, Science University of Tokyo, Noda, Chiba 278-8510, Japan.
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Abstract

Queueing networks have been rather restricted in order to have product form distributions for network states. Recently, several new models have appeared and enlarged this class of product form networks. In this paper, we consider another new type of queueing network with concurrent batch movements in terms of such product form results. A joint distribution of the requested batch sizes for departures and the batch sizes of the corresponding arrivals may be arbitrary. Under a certain modification of the network and mild regularity conditions, we give necessary and sufficient conditions for the network state to have the product form distribution, which is shown to provide an upper bound for the one in the original network. It is shown that two special settings satisfy these conditions. Algorithms to calculate their stationary distributions are considered, with numerical examples.

Keywords

Markovian queueing networkconcurrent batch movementgeometric distributionproduct form stationary distributioncharacterizationstochastic order

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998 , pp. 1111 - 1129
Copyright
Copyright © Applied Probability Trust 1998 

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