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Near Complete Decomposability: Bounding the Error by a Stochastic Comparison Method

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Laurent Truffet
Laurent Truffet*
Affiliation:
Université Paris VI
*
∗ Postal address: Université Paris VI, Institut Blaise Pascal, Laboratoire MASI-CNRS UA 818, 4, Place Jussieu, F-75252, Paris Cedex 05, France.
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Abstract

An aggregation technique of ‘near complete decomposable' Markovian systems has been proposed by Courtois [3]. It is an approximate method in many cases, except for some queuing networks, so the error between the exact and the approximate solution is an important problem. We know that the error is O(ε), where ε is defined as the maximum coupling between aggregates. Some authors developed techniques to obtain a O(ε k) error with k > 1 error with k > 1, while others developed a technique called ‘bounded aggregation’. All these techniques use linear algebra tools and do not utilize the fact that the steady-state probability vector represents the distribution of a random variable. In this work we propose a stochastic approach and we give a method to obtain stochastic bounds on all possible Markovian approximations of the two main dynamics: short-term and long-term dynamics.

Keywords

NEAR COMPLETE DECOMPOSABILITYSTOCHASTIC BOUNDSMATRIX COMPARISONSTRONG ORDERING

MSC classification

Primary: 60K99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 3 , September 1997 , pp. 830 - 855
Copyright
Copyright © Applied Probability Trust 1997 

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