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Dynamics of large uncontrolled loss networks

Part of:Operations research and management scienceStochastic processesSpecial processesComputer system organization

Published online by Cambridge University Press:  14 July 2016

Stan Zachary
Stan Zachary*
Affiliation:
Heriot-Watt University
*
∗ Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK. Email address: s.zachary@ma.hw.ac.uk
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Abstract

This paper studies the connection between the dynamical and equilibrium behaviour of large uncontrolled loss networks. We consider the behaviour of the number of calls of each type in the network, and show that, under the limiting regime of Kelly (1986), all trajectories of the limiting dynamics converge to a single fixed point, which is necessarily that on which the limiting stationary distribution is concentrated. The approach uses Lyapunov techniques and involves the evolution of the transition rates of a stationary Markov process in such a way that it tends to reversibility.

Keywords

Loss networkLyapunov function

MSC classification

Primary:60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary:60G60: Random fields68M20: Performance evaluation; queueing; scheduling90B18: Communication networks

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000, pp. 685 - 695
Copyright
Copyright © Applied Probability Trust 2000 

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