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Loss networks and Markov random fields

Part of: Stochastic processes Computer system organization Special processes

Published online by Cambridge University Press:  14 July 2016

Stan Zachary  and
Ilze Ziedins
Stan Zachary*
Affiliation:
Heriot-Watt University
Ilze Ziedins*
Affiliation:
The University of Auckland
*
∗Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK. Email address: s.zachary@ma.hw.ac.uk.
∗∗Postal address: Department of Statistics, The University of Auckland, Private Bag 92019, Auckland, New Zealand.
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Abstract

This paper examines the connection between loss networks without controls and Markov random field theory. The approach taken yields insight into the structure and computation of network equilibrium distributions, and into the nature of spatial dependence in networks. In addition, it provides further insight into some commonly used approximations, enables the development of more refined approximations, and permits the derivation of some asymptotically exact results.

Keywords

Loss networksMarkov random fieldsreduced load approximationsErlang fixed point

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 60G60: Random fields 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 403 - 414
Copyright
Copyright © Applied Probability Trust 1999 

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