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v1 (2009-02-17)

v2 (2010-08-20)

Comparing Markov chains: Aggregation and precedence relations applied to sets of states, with applications to assemble-to-order systems

Ana Busic (  Corresponding author ) 1, Ingrid Vliegen 2, Alan Scheller-Wolf 3

(2009-02-15)

Solving Markov chains is in general difficult if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward theory: Our method constructs bounds by redirecting selected sets of transitions, facilitating an intuitive interpretation of the modifications of the original system. We show that our method is compatible with strong aggregation of Markov chains; thus we can obtain bounds for an initial chain by analyzing a much smaller chain. We illustrate our method by using it to prove monotonicity results and bounds for assemble-to-order systems.

1:	TREC (INRIA Rocquencourt)
	INRIA – Ecole Normale Supérieure de Paris - ENS Paris
2:	School of Management and Governance
	University of Twente
3:	Tepper School of Business
	Carnegie Mellon University

Subject

:

Computer Science/Discrete Mathematics Computer Science/Performance and Reliability Mathematics/Probability

Keyword(s): Markov chains – precedence relations – bounding models – aggregation – supermodularity – assemble-to-order (ATO) systems

hal-00361430, version 2

http://hal.archives-ouvertes.fr/hal-00361430

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From: Ana Busic <>

Submitted on: Friday, 20 August 2010 16:39:30

Updated on: Friday, 20 August 2010 17:48:43