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Replacement of train wheels: an application of dynamic reversal of a Markov process

Part of: Special processes Time-dependent statistical mechanics (dynamic and nonequilibrium) Markov processes

Published online by Cambridge University Press:  14 July 2016

David Gates  and
Mark Westcott
David Gates
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
Mark Westcott*
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
*
∗ Postal address for both authors: Division of Mathematics and Statistics, CSIRO, GPO Box 1965, Canberra, ACT 2601, Australia.
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Abstract

A problem of regrinding and recycling worn train wheels leads to a Markov population process with distinctive properties, including a product-form equilibrium distribution. A convenient framework for analyzing this process is via the notion of dynamic reversal, a natural extension of ordinary (time) reversal. The dynamically reversed process is of the same type as the original process, which allows a simple derivation of some important properties. The process seems not to belong to any class of Markov processes for which stationary distributions are known.

Keywords

INVENTORY PROCESSMIGRATION PROCESS

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 1 - 8
Copyright
Copyright © Applied Probability Trust 1994 

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References

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