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Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

José Niño-Mora  and
Kevin D. Glazebrook
José Niño-Mora*
Affiliation:
Universitat Pompeu Fabra
Kevin D. Glazebrook*
Affiliation:
Newcastle University
*
∗Postal address: Department of Economics and Business, Universitat Pompeu Fabra, E-08005 Barcelona, Spain. Email address: jose.nino-mora@econ.upf.es
∗∗Postal address: Department of Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK. Email address: kevin.glazebrook@ncl.ac.uk
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Abstract

We argue the importance both of developing simple sufficient conditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu–Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.

Keywords

Multiclass queueing networksstabilityfluid modelLu-Kumar network

MSC classification

Primary: 90B22: Queues and service
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 890 - 899
Copyright
Copyright © Applied Probability Trust 2000 

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