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State-dependent signalling in queueing networks

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

W. Henderson ,
B. S. Northcote  and
P. G. Taylor
W. Henderson
Affiliation:
University of Adelaide
B. S. Northcote
Affiliation:
University of Adelaide
P. G. Taylor*
Affiliation:
University of Adelaide
*
* Postal address: Teletraffic Research Centre, Department of Applied Mathematics, GPO Box 498, Adelaide, SA 5005, Australia.
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Abstract

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network.

This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

Keywords

PRODUCT FORMTRIGGERED MOTIONBATCH DEPARTURESSTATE DEPENDENCE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 436 - 455
Copyright
Copyright © Applied Probability Trust 1994 

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References

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Reference added in proof

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