A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Pollett, PK and Thompson, MR (2003) A new method for analysing the equilibrium and time-dependent behaviour of Markovian models. Mathematical And Computer Modelling, 38 11-13: 1409-1418. doi:10.1016/S0895-7177(03)90144-0


Author Pollett, PK
Thompson, MR
Title A new method for analysing the equilibrium and time-dependent behaviour of Markovian models
Journal name Mathematical And Computer Modelling   Check publisher's open access policy
ISSN 0895-7177
Publication date 2003-01-01
Year available 2003
Sub-type Article (original research)
DOI 10.1016/S0895-7177(03)90144-0
Open Access Status DOI
Volume 38
Issue 11-13
Start page 1409
End page 1418
Total pages 10
Editor E.Y. Rodin
Place of publication Oxford, United Kingdom
Publisher Pergamon-Elsevier Science Ltd
Language eng
Subject C1
230202 Stochastic Analysis and Modelling
780101 Mathematical sciences
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 present two formulations of the idea of expected rates. The first provides a method for analysing time-dependent behaviour, while the second provides a highly accurate means of analysing equilibrium behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks. (C) 2003 Elsevier Ltd. All rights reserved.
Keyword Computer Science, Interdisciplinary Applications
Computer Science, Software Engineering
Mathematics, Applied
Markov Model
Transition Probability Approximation
Time-dependent Behaviour
Equilibrium Behaviour
Queuing
Loss Networks
Blocking
Q-Index Code C1
Institutional Status UQ

 
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Created: Wed, 15 Aug 2007, 05:20:17 EST