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Some new results on queueing networks with batch movement

Published online by Cambridge University Press:  14 July 2016

W. Henderson  and
P. G. Taylor
W. Henderson*
Affiliation:
University of Adelaide
P. G. Taylor*
Affiliation:
University of Western Australia
*
∗Postal address: Department of Applied Mathematics, University of Adelaide, GPO Box 498, Adelaide, SA 5001, Australia.
∗∗Postal address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

Product-form equilibrium distributions in networks of queues in which customers move singly have been known since 1957, when Jackson derived some surprising independence results. A product-form equilibrium distribution has also recently been shown to be valid for certain queueing networks with batch arrivals, batch services and even correlated routing.

This paper derives the joint equilibrium distribution of states immediately before and after a batch of customers is released into the network. The results are valid for either discrete- or continuous-time queueing networks: previously obtained results can be seen as marginal distributions within a more general framework. A generalisation of the classical ‘arrival theorem' for continuous-time networks is given, which compares the equilibrium distribution as seen by arrivals to the time-averaged equilibrium distribution.

Keywords

CORRELATED ROUTINGPRODUCT FORM
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 409 - 421
Copyright
Copyright © Applied Probability Trust 1991 

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