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Fixed-delay Events in Generalized Semi-Markov Processes Revisited

Basic information
Original title:Fixed-delay Events in Generalized Semi-Markov Processes Revisited
Authors:Tomáš Brázdil, Jan Krčál, Jan Křetínský, Vojtěch Řehák
Further information
Citation:BRÁZDIL, Tomáš, Jan KRČÁL, Jan KŘETÍNSKÝ and Vojtěch ŘEHÁK. Fixed-delay Events in Generalized Semi-Markov Processes Revisited. In CONCUR 2011 - Concurrency Theory: 22nd International Conference. Berlin Heidelberg New York: Springer, 2011. p. 140-155, 16 pp. ISBN 978-3-642-23216-9.Export BibTeX
@inproceedings{948678,
author = {Brázdil, Tomáš and Krčál, Jan and Křetínský, Jan and Řehák, Vojtěch},
address = {Berlin Heidelberg New York},
booktitle = {CONCUR 2011 - Concurrency Theory: 22nd International Conference},
keywords = {generalized semi-Markov processes; long-run average; stability; discrete events},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Berlin Heidelberg New York},
isbn = {978-3-642-23216-9},
pages = {140-155},
publisher = {Springer},
title = {Fixed-delay Events in Generalized Semi-Markov Processes Revisited},
year = {2011}
}
Original language:English
Field:Informatics
Type:Article in Proceedings
Keywords:generalized semi-Markov processes; long-run average; stability; discrete events

We study long run average behavior of generalized semi-Markov processes with both fixed-delay events as well as variable-delay events. We show that allowing two fixed-delay events and one variable-delay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not exist). We use this observation to disprove several results from literature. Next we study GSMP with at most one fixed-delay event combined with an arbitrary number of variable-delay events. We prove that such a GSMP always possesses an invariant measure which means that the frequencies of states are always well defined and we provide algorithms for approximation of these frequencies. Additionally, we show that the positive results remain valid even if we allow an arbitrary number of reasonably restricted fixed-delay events.

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