Aggregation/disaggregation method for safety models

Štěpán Klapka; Petr Mayer

Applications of Mathematics (2002)

  • Volume: 47, Issue: 2, page 127-137
  • ISSN: 0862-7940

Abstract

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The paper concerns the possibilities for mathematical modelling of safety related systems (equipment oriented on safety). Some mathematical models have been required by the present European Standards for the railway transport. We are interested in the possibility of using Markov’s models to meet these Standards. In the text an example of using that method in the interlocking equipment life cycle is given. An efficient aggregation/disaggregation method for computing some characteristics of Markov chains is presented.

How to cite

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Klapka, Štěpán, and Mayer, Petr. "Aggregation/disaggregation method for safety models." Applications of Mathematics 47.2 (2002): 127-137. <http://eudml.org/doc/33108>.

@article{Klapka2002,
abstract = {The paper concerns the possibilities for mathematical modelling of safety related systems (equipment oriented on safety). Some mathematical models have been required by the present European Standards for the railway transport. We are interested in the possibility of using Markov’s models to meet these Standards. In the text an example of using that method in the interlocking equipment life cycle is given. An efficient aggregation/disaggregation method for computing some characteristics of Markov chains is presented.},
author = {Klapka, Štěpán, Mayer, Petr},
journal = {Applications of Mathematics},
keywords = {Markov chain; stochastic matrix; stationary probability vector; aggregation/disaggregation algorithms; Markov chain; stochastic matrix; stationary probability vector; aggregation algorithm; disaggregation algorithm},
language = {eng},
number = {2},
pages = {127-137},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Aggregation/disaggregation method for safety models},
url = {http://eudml.org/doc/33108},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Klapka, Štěpán
AU - Mayer, Petr
TI - Aggregation/disaggregation method for safety models
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 2
SP - 127
EP - 137
AB - The paper concerns the possibilities for mathematical modelling of safety related systems (equipment oriented on safety). Some mathematical models have been required by the present European Standards for the railway transport. We are interested in the possibility of using Markov’s models to meet these Standards. In the text an example of using that method in the interlocking equipment life cycle is given. An efficient aggregation/disaggregation method for computing some characteristics of Markov chains is presented.
LA - eng
KW - Markov chain; stochastic matrix; stationary probability vector; aggregation/disaggregation algorithms; Markov chain; stochastic matrix; stationary probability vector; aggregation algorithm; disaggregation algorithm
UR - http://eudml.org/doc/33108
ER -

References

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  5. Reliability and safety of interlocking systems, NADAS, Praha, 1980. (Czech) (1980) 
  6. 10.1002/(SICI)1099-1506(199807/08)5:4<253::AID-NLA124>3.0.CO;2-B, Numer. Linear Algebra Appl. 5 (1998), 253–274. (1998) MR1640726DOI10.1002/(SICI)1099-1506(199807/08)5:4<253::AID-NLA124>3.0.CO;2-B
  7. Iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices can be finitely terminating, J. Differential Equations 3 (2001), 301–313. (2001) MR1848180
  8. Modelling with Generalized Stochastic Petri Nets, John Wiley & Sons, Chichester, 1995. (1995) 
  9. 10.1109/32.99196, IEEE transaction on software engineering 17 (1991), 1093–1108. (1991) MR1133053DOI10.1109/32.99196
  10. Models for analysis of safety computer interlocking systems, Habilitation thesis, University of Žilina, 1998. (Slovak) (1998) 
  11. Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Princenton, 1994. (1994) Zbl0821.65099MR1312831
  12. Stochastic Models in Economy, SNTL, Praha, 1970. (Czech) (1970) 

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