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Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Xiuli Chao  and
Masakiyo Miyazawa
Xiuli Chao*
Affiliation:
New Jersey Institute of Thechnology
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: New Jersey Institute of Technology, Newark, NJ 07102, USA.
∗∗ Postal address: Science University of Tokyo Noda, Chiba 278, Japan.
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Abstract

In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.

Keywords

Networks of queuespositive and negative signalsquasi-reversibilitycouplingdelayed and non-delayed signalsproduct form solutionstochastic bound

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 1 , March 2000 , pp. 284 - 313
Copyright
Copyright © Applied Probability Trust 2000 

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