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February 2002 A Refinement of the Hunt-Kurtz Theory of Large Loss Networks, with an Application to Virtual Partitioning
Stan Zachary, Ilze Ziedins
Ann. Appl. Probab. 12(1): 1-22 (February 2002). DOI: 10.1214/aoap/1015961154

Abstract

This paper gives a refinement of the results of Hunt and Kurtz on the dynamical behavior of large loss networks. We introduce a Liapounov function technique which, under the limiting regime of Kelly, enables the unique identification of limiting dynamics in many applications. This technique considerably simplifies much previous work in this area. We further apply it to the study of the dynamical behavior of large single-resource loss systems under virtual partitioning, or dynamic trunk reservation, controls. We identify limiting dynamics under the above regime, describing the behavior of the number of calls of each type in the system. We show that all trajectories of these dynamics converge to a single fixed point, which we identify. We also identify limiting stationary behavior, including call acceptance probabilities.

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Stan Zachary. Ilze Ziedins. "A Refinement of the Hunt-Kurtz Theory of Large Loss Networks, with an Application to Virtual Partitioning." Ann. Appl. Probab. 12 (1) 1 - 22, February 2002. https://doi.org/10.1214/aoap/1015961154

Information

Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1012.60083
MathSciNet: MR1890055
Digital Object Identifier: 10.1214/aoap/1015961154

Subjects:
Primary: 60K20
Secondary: 60G17 , 68M20 , 90B12

Keywords: functional law of large numbers , Liapounov function , Loss network , partitioning , trunk reservation

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February 2002
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