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First passage times and lumpability of semi-Markov processes

Published online by Cambridge University Press:  14 July 2016

Ushio Sumita  and
Maria Rieders
Ushio Sumita
Affiliation:
University of Rochester
Maria Rieders
Affiliation:
University of Rochester
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Abstract

A necessary and sufficient condition of Serfozo (1971) for lumpability of semi-Markov processes is reinterpreted in terms of first-exit times. Furthermore, a new necessary and sufficient condition is developed by establishing relationships between first-passage times and lumpability of semi-Markov processes. The approach taken in this paper is entirely based on the Laplace-transform domain.

Keywords

PARTITION OF STATE SPACELUMPED PROCESSESFIRST-EXIT TIMESCHARACTERIZATION OF LUMPABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 675 - 687
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

This paper has been partially supported by the IBM Program of Support for Education in the Management of Information Systems and by NSF Grant ECS-8600992.

References

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