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Exact and ordinary lumpability in finite Markov chains

Part of: Markov processes Computer system organization

Published online by Cambridge University Press:  14 July 2016

Peter Buchholz
Peter Buchholz*
Affiliation:
Universität Dortmund
*
∗ Postal address: Universität Dortmund, Informatik IV, D-44221 Dortmund, Germany.
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Abstract

Exact and ordinary lumpability in finite Markov chains is considered. Both concepts naturally define an aggregation of the Markov chain yielding an aggregated chain that allows the exact determination of several stationary and transient results for the original chain. We show which quantities can be determined without an error from the aggregated process and describe methods to calculate bounds on the remaining results. Furthermore, the concept of lumpability is extended to near lumpability yielding approximative aggregation.

Keywords

AGGREGATIONSTATIONARY AND TRANSIENT ANALYSISPERFORMANCE AND RELIABILITY MODELLING

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 59 - 75
Copyright
Copyright © Applied Probability Trust 1994 

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