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Pathological behaviour in loss networks

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

P. J. Hunt
P. J. Hunt*
Affiliation:
University of Cambridge
*
∗Present address: NatWest Markets, 135 Bishopsgate, London EC2M 3UR, UK.
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Abstract

Hunt and Kurtz [9] consider a loss network as the number of circuits and the offered traffics become large. They prove a functional law of large numbers for such a network and illustrate their results with some simple examples. In this paper we apply their results to slightly more complicated examples to illustrate other, and sometimes surprising, behaviour of the loss networks in heavy traffic. The networks we consider operate under somewhat unusual routing rules but this is to enable us to produce the behaviour in networks with only a few links. In larger, real-world networks it is likely that much more ‘natural' and intuitively appealing routing rules could produce similar undesirable behaviour.

Keywords

FUNCTIONAL LAW OF LARGE NUMBERSROUTING RULES

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 519 - 533
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by Christ's College, Cambridge.

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