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On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

Part of: Markov processes Special processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Yutaka Sakuma  and
Masakiyo Miyazawa
Yutaka Sakuma*
Affiliation:
Tokyo University of Science
Masakiyo Miyazawa*
Affiliation:
Tokyo University of Science
*
∗Postal address: Department of Information Sciences, Tokyo University of Science, Noda City, Chiba 278-8510, Japan.
∗Postal address: Department of Information Sciences, Tokyo University of Science, Noda City, Chiba 278-8510, Japan.
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Abstract

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We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

Keywords

Decay rateJackson networkfinite truncationstationary distribution

MSC classification

Secondary: 60K25: Queueing theory 60F10: Large deviations 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 199 - 222
Copyright
© Applied Probability Trust 2005 

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