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Type: Journal article
Title: Dynamic and equilibrium behaviour of controlled loss networks
Author: Bean, N.
Gibbens, R.
Zachary, S.
Citation: Annals of Applied Probability, 1997; 7(4):873-885
Publisher: Institute of Mathematical Statistics
Issue Date: 1997
ISSN: 1050-5164
Statement of
N. G. Bean, R. J. Gibbens and S. Zachary
Abstract: We study the behavior of large loss networks in which the offered traffic is subject to acceptance controls. Hunt and Kurtz proved a functional law of large numbers for the dynamics of such networks, as capacity and offered traffic are allowed to increase in proportion. However, limiting dynamics were not in general uniquely identified. We establish further results identifying these dynamics under given conditions. We also investigate the existence of fixed points for these dynamics and relate them to limiting equilibrium behavior, permitting the investigation of common modelling assumptions. We study in detail single- and two-resource networks and we give an example of bistability for the former.
Rights: 1997 © Institute of Mathematical Statistics
RMID: 0030006798
DOI: 10.1214/aoap/1043862415
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Appears in Collections:Applied Mathematics publications
Environment Institute publications

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