The analysis of continuous-time Markovian models using expected rates

Phil Pollett and Mark Thompson

[Full Text]

Abstract: Many large-scale stochastic systems, such as telecommunications networks, can be modelled using a continuous-time Markov chain. However, it is frequently the case that a satisfactory analysis of their time dependent, or even equilibrium behaviour, is impossible. In this paper we propose a new method of analyzing Markovian models, whereby the existing transition structure is replaced by a more amenable one. Using rates of transition given by the equilibrium expected rates of the corresponding transitions of the original chain, we are able to approximate its behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks.

Keywords: Markov chains, Approximation, Blocking probabilities, Erlang Fixed Point

Acknowledgement: This worked was funded by the Australian Research Council.

The authors:

• Phil Pollett, Discipline of Mathematics, The University of Queensland. pkp@maths.uq.edu.au
• Mark Thompson, Discipline of Mathematics, The University of Queensland. M.Thompson@qic.com.au

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Last modified: 10th June 1999